descriptive formula in research

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, generate accurate citations for free.

• Knowledge Base

Methodology

• Descriptive Research | Definition, Types, Methods & Examples

Descriptive Research | Definition, Types, Methods & Examples

Published on May 15, 2019 by Shona McCombes . Revised on June 22, 2023.

Descriptive research aims to accurately and systematically describe a population, situation or phenomenon. It can answer what , where , when and how   questions , but not why questions.

A descriptive research design can use a wide variety of research methods  to investigate one or more variables . Unlike in experimental research , the researcher does not control or manipulate any of the variables, but only observes and measures them.

Table of contents

When to use a descriptive research design, descriptive research methods, other interesting articles.

Descriptive research is an appropriate choice when the research aim is to identify characteristics, frequencies, trends, and categories.

It is useful when not much is known yet about the topic or problem. Before you can research why something happens, you need to understand how, when and where it happens.

Descriptive research question examples

• How has the Amsterdam housing market changed over the past 20 years?
• Do customers of company X prefer product X or product Y?
• What are the main genetic, behavioural and morphological differences between European wildcats and domestic cats?
• What are the most popular online news sources among under-18s?
• How prevalent is disease A in population B?

Prevent plagiarism. Run a free check.

Descriptive research is usually defined as a type of quantitative research , though qualitative research can also be used for descriptive purposes. The research design should be carefully developed to ensure that the results are valid and reliable .

Survey research allows you to gather large volumes of data that can be analyzed for frequencies, averages and patterns. Common uses of surveys include:

• Describing the demographics of a country or region
• Gauging public opinion on political and social topics
• Evaluating satisfaction with a company’s products or an organization’s services

Observations

Observations allow you to gather data on behaviours and phenomena without having to rely on the honesty and accuracy of respondents. This method is often used by psychological, social and market researchers to understand how people act in real-life situations.

Observation of physical entities and phenomena is also an important part of research in the natural sciences. Before you can develop testable hypotheses , models or theories, it’s necessary to observe and systematically describe the subject under investigation.

Case studies

A case study can be used to describe the characteristics of a specific subject (such as a person, group, event or organization). Instead of gathering a large volume of data to identify patterns across time or location, case studies gather detailed data to identify the characteristics of a narrowly defined subject.

Rather than aiming to describe generalizable facts, case studies often focus on unusual or interesting cases that challenge assumptions, add complexity, or reveal something new about a research problem .

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

• Normal distribution
• Degrees of freedom
• Null hypothesis
• Discourse analysis
• Control groups
• Mixed methods research
• Non-probability sampling
• Quantitative research
• Ecological validity

Research bias

• Rosenthal effect
• Implicit bias
• Cognitive bias
• Selection bias
• Negativity bias
• Status quo bias

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

McCombes, S. (2023, June 22). Descriptive Research | Definition, Types, Methods & Examples. Scribbr. Retrieved September 15, 2024, from https://www.scribbr.com/methodology/descriptive-research/

Is this article helpful?

Shona McCombes

Other students also liked, what is quantitative research | definition, uses & methods, correlational research | when & how to use, descriptive statistics | definitions, types, examples, get unlimited documents corrected.

✔ Free APA citation check included ✔ Unlimited document corrections ✔ Specialized in correcting academic texts

Root out friction in every digital experience, super-charge conversion rates, and optimize digital self-service

Uncover insights from any interaction, deliver AI-powered agent coaching, and reduce cost to serve

Increase revenue and loyalty with real-time insights and recommendations delivered to teams on the ground

Know how your people feel and empower managers to improve employee engagement, productivity, and retention

Take action in the moments that matter most along the employee journey and drive bottom line growth

Whatever they’re saying, wherever they’re saying it, know exactly what’s going on with your people

Get faster, richer insights with qual and quant tools that make powerful market research available to everyone

Run concept tests, pricing studies, prototyping + more with fast, powerful studies designed by UX research experts

Track your brand performance 24/7 and act quickly to respond to opportunities and challenges in your market

Explore the platform powering Experience Management

• Free Account
• Product Demos
• For Digital
• For Customer Care
• For Human Resources
• For Researchers
• Financial Services
• All Industries

Popular Use Cases

• Customer Experience
• Employee Experience
• Net Promoter Score
• Voice of Customer
• Customer Success Hub
• Product Documentation
• Training & Certification
• XM Institute
• Popular Resources
• Customer Stories
• Artificial Intelligence

Market Research

• Partnerships
• Marketplace

The annual gathering of the experience leaders at the world’s iconic brands building breakthrough business results, live in Salt Lake City.

• English/AU & NZ
• Español/Europa
• Español/América Latina
• Português Brasileiro
• REQUEST DEMO
• Experience Management
• Descriptive Statistics

Try Qualtrics for free

Descriptive statistics in research: a critical component of data analysis.

15 min read With any data, the object is to describe the population at large, but what does that mean and what processes, methods and measures are used to uncover insights from that data? In this short guide, we explore descriptive statistics and how it’s applied to research.

What do we mean by descriptive statistics?

With any kind of data, the main objective is to describe a population at large — and using descriptive statistics, researchers can quantify and describe the basic characteristics of a given data set.

For example, researchers can condense large data sets, which may contain thousands of individual data points or observations, into a series of statistics that provide useful information on the population of interest. We call this process “describing data”.

In the process of producing summaries of the sample, we use measures like mean, median, variance, graphs, charts, frequencies, histograms, box and whisker plots, and percentages. For datasets with just one variable, we use univariate descriptive statistics. For datasets with multiple variables, we use bivariate correlation and multivariate descriptive statistics.

Want to find out the definitions?

Univariate descriptive statistics: this is when you want to describe data with only one characteristic or attribute

Bivariate correlation: this is when you simultaneously analyze (compare) two variables to see if there is a relationship between them

Multivariate descriptive statistics: this is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable

Then, after describing and summarizing the data, as well as using simple graphical analyses, we can start to draw meaningful insights from it to help guide specific strategies. It’s also important to note that descriptive statistics can employ and use both quantitative and qualitative research .

Describing data is undoubtedly the most critical first step in research as it enables the subsequent organization, simplification and summarization of information — and every survey question and population has summary statistics. Let’s take a look at a few examples.

Examples of descriptive statistics

Consider for a moment a number used to summarize how well a striker is performing in football — goals scored per game. This number is simply the number of shots taken against how many of those shots hit the back of the net (reported to three significant digits). If a striker is scoring 0.333, that’s one goal for every three shots. If they’re scoring one in four, that’s 0.250.

A classic example is a student’s grade point average (GPA). This single number describes the general performance of a student across a range of course experiences and classes. It doesn’t tell us anything about the difficulty of the courses the student is taking, or what those courses are, but it does provide a summary that enables a degree of comparison with people or other units of data.

Ultimately, descriptive statistics make it incredibly easy for people to understand complex (or data intensive) quantitative or qualitative insights across large data sets.

Take your research to the next level with XM for Strategy & Research

Types of descriptive statistics

To quantitatively summarize the characteristics of raw, ungrouped data, we use the following types of descriptive statistics:

• Measures of Central Tendency ,
• Measures of Dispersion and
• Measures of Frequency Distribution.

Following the application of any of these approaches, the raw data then becomes ‘grouped’ data that’s logically organized and easy to understand. To visually represent the data, we then use graphs, charts, tables etc.

Let’s look at the different types of measurement and the statistical methods that belong to each:

Measures of Central Tendency are used to describe data by determining a single representative of central value. For example, the mean, median or mode.

Measures of Dispersion are used to determine how spread out a data distribution is with respect to the central value, e.g. the mean, median or mode. For example, while central tendency gives the person the average or central value, it doesn’t describe how the data is distributed within the set.

Measures of Frequency Distribution are used to describe the occurrence of data within the data set (count).

The methods of each measure are summarized in the table below:

Mean: The most popular and well-known measure of central tendency. The mean is equal to the sum of all the values in the data set divided by the number of values in the data set.

Median: The median is the middle score for a set of data that has been arranged in order of magnitude. If you have an even number of data, e.g. 10 data points, take the two middle scores and average the result.

Mode: The mode is the most frequently occurring observation in the data set.  

Range: The difference between the highest and lowest value.

Standard deviation: Standard deviation measures the dispersion of a data set relative to its mean and is calculated as the square root of the variance.

Quartile deviation : Quartile deviation measures the deviation in the middle of the data.

Variance: Variance measures the variability from the average of mean.

Absolute deviation: The absolute deviation of a dataset is the average distance between each data point and the mean.

Count: How often each value occurs.

Scope of descriptive statistics in research

Descriptive statistics (or analysis) is considered more vast than other quantitative and qualitative methods as it provides a much broader picture of an event, phenomenon or population.

But that’s not all: it can use any number of variables, and as it collects data and describes it as it is, it’s also far more representative of the world as it exists.

However, it’s also important to consider that descriptive analyses lay the foundation for further methods of study. By summarizing and condensing the data into easily understandable segments, researchers can further analyze the data to uncover new variables or hypotheses.

Mostly, this practice is all about the ease of data visualization. With data presented in a meaningful way, researchers have a simplified interpretation of the data set in question. That said, while descriptive statistics helps to summarize information, it only provides a general view of the variables in question.

It is, therefore, up to the researchers to probe further and use other methods of analysis to discover deeper insights.

Things you can do with descriptive statistics

Define subject characteristics

If a marketing team wanted to build out accurate buyer personas for specific products and industry verticals, they could use descriptive analyses on customer datasets (procured via a survey) to identify consistent traits and behaviors.

They could then ‘describe’ the data to build a clear picture and understanding of who their buyers are, including things like preferences, business challenges, income and so on.

Measure data trends

Let’s say you wanted to assess propensity to buy over several months or years for a specific target market and product. With descriptive statistics, you could quickly summarize the data and extract the precise data points you need to understand the trends in product purchase behavior.

Compare events, populations or phenomena

How do different demographics respond to certain variables? For example, you might want to run a customer study to see how buyers in different job functions respond to new product features or price changes. Are all groups as enthusiastic about the new features and likely to buy? Or do they have reservations? This kind of data will help inform your overall product strategy and potentially how you tier solutions.

Validate existing conditions

When you have a belief or hypothesis but need to prove it, you can use descriptive techniques to ascertain underlying patterns or assumptions.

Form new hypotheses

With the data presented and surmised in a way that everyone can understand (and infer connections from), you can delve deeper into specific data points to uncover deeper and more meaningful insights — or run more comprehensive research.

Guiding your survey design to improve the data collected

To use your surveys as an effective tool for customer engagement and understanding, every survey goal and item should answer one simple, yet highly important question:

What am I really asking?

It might seem trivial, but by having this question frame survey research, it becomes significantly easier for researchers to develop the right questions that uncover useful, meaningful and actionable insights.

Planning becomes easier, questions clearer and perspective far wider and yet nuanced.

Hypothesize – what’s the problem that you’re trying to solve? Far too often, organizations collect data without understanding what they’re asking, and why they’re asking it.

Finally, focus on the end result. What kind of data do you need to answer your question? Also, are you asking a quantitative or qualitative question? Here are a few things to consider:

• Clear questions are clear for everyone. It takes time to make a concept clear
• Ask about measurable, evident and noticeable activities or behaviors.
• Make rating scales easy. Avoid long lists, confusing scales or “don’t know” or “not applicable” options.
• Ensure your survey makes sense and flows well. Reduce the cognitive load on respondents by making it easy for them to complete the survey.
• Read your questions aloud to see how they sound.
• Pretest by asking a few uninvolved individuals to answer.

Furthermore…

As well as understanding what you’re really asking, there are several other considerations for your data:

Keep it random

How you select your sample is what makes your research replicable and meaningful. Having a truly random sample helps prevent bias, increasingly the quality of evidence you find.

Plan for and avoid sample error

Before starting your research project, have a clear plan for avoiding sample error. Use larger sample sizes, and apply random sampling to minimize the potential for bias.

Don’t over sample

Remember, you can sample 500 respondents selected randomly from a population and they will closely reflect the actual population 95% of the time.

Think about the mode

Match your survey methods to the sample you select. For example, how do your current customers prefer communicating? Do they have any shared characteristics or preferences? A mixed-method approach is critical if you want to drive action across different customer segments.

Use a survey tool that supports you with the whole process

Surveys created using a survey research software can support researchers in a number of ways:

• Employee satisfaction survey template
• Employee exit survey template
• Customer satisfaction (CSAT) survey template
• Ad testing survey template
• Brand awareness survey template
• Product pricing survey template
• Product research survey template
• Employee engagement survey template
• Customer service survey template
• NPS survey template
• Product package testing survey template
• Product features prioritization survey template

These considerations have been included in Qualtrics’ survey software , which summarizes and creates visualizations of data, making it easy to access insights, measure trends, and examine results without complexity or jumping between systems.

Uncover your next breakthrough idea with Stats iQ™

What makes Qualtrics so different from other survey providers is that it is built in consultation with trained research professionals and includes high-tech statistical software like Qualtrics Stats iQ .

With just a click, the software can run specific analyses or automate statistical testing and data visualization. Testing parameters are automatically chosen based on how your data is structured (e.g. categorical data will run a statistical test like Chi-squared), and the results are translated into plain language that anyone can understand and put into action.

Get more meaningful insights from your data

Stats iQ includes a variety of statistical analyses, including: describe, relate, regression, cluster, factor, TURF, and pivot tables — all in one place!

Confidently analyze complex data

Built-in artificial intelligence and advanced algorithms automatically choose and apply the right statistical analyses and return the insights in plain english so everyone can take action.

Integrate existing statistical workflows

For more experienced stats users, built-in R code templates allow you to run even more sophisticated analyses by adding R code snippets directly in your survey analysis.

Advanced statistical analysis methods available in Stats iQ

Regression analysis – Measures the degree of influence of independent variables on a dependent variable (the relationship between two or multiple variables).

Analysis of Variance (ANOVA) test – Commonly used with a regression study to find out what effect independent variables have on the dependent variable. It can compare multiple groups simultaneously to see if there is a relationship between them.

Conjoint analysis – Asks people to make trade-offs when making decisions, then analyses the results to give the most popular outcome. Helps you understand why people make the complex choices they do.

T-Test – Helps you compare whether two data groups have different mean values and allows the user to interpret whether differences are meaningful or merely coincidental.

Crosstab analysis – Used in quantitative market research to analyze categorical data – that is, variables that are different and mutually exclusive, and allows you to compare the relationship between two variables in contingency tables.

Go from insights to action

Now that you have a better understanding of descriptive statistics in research and how you can leverage statistical analysis methods correctly, now’s the time to utilize a tool that can take your research and subsequent analysis to the next level.

Try out a Qualtrics survey software demo so you can see how it can take you through descriptive research and further research projects from start to finish.

Related resources

Mixed methods research 17 min read, market intelligence 10 min read, marketing insights 11 min read, ethnographic research 11 min read, qualitative vs quantitative research 13 min read, qualitative research questions 11 min read, qualitative research design 12 min read, request demo.

Ready to learn more about Qualtrics?

• Chester Fritz Library
• Library of the Health Sciences
• Thormodsgard Law Library
• University of North Dakota
• Research Guides
• SMHS Library Resources

Statistics - explanations and formulas

Descriptive statistics.

• Absolute Risk Reduction
• Bell-shaped Curve
• Confidence Interval
• Control Event Rate
• Correlation
• Discrete Stats
• Experimental Event Rate
• Forest Plots
• Hazard Ratio
• Heterogeneity / Statistical Heterogeneity
• Inferential Statistics
• Intention to Treat
• Internal Validity / External Validity
• Kaplan-Meier Curves
• Kruskal-Wallis Test
• Likelihood Ratios
• Logistics Regression
• Mann-Whitney U Test
• Mean Difference
• Misclassification Bias
• Multiple Regression Coefficients
• Nominal Data
• Noninferiority Studies
• Noninferiority Trials
• Nonparametric Analysis
• Normal Distribution
• Number Needed to Treat - including how to calculate
• Power Analysis
• Predictive Power
• Probability
• Propensity Score
• Random Sample
• Regression Analysis
• Relative Risk
• Sampling Error
• Spearman Rank Correlation
• Specificity and Sensitivity
• Statistical Significance versus Clinical Significance
• Survivor Analysis
• Wilcoxon Rank Sum Test
• Excel formulas
• Picking the appropriate method

Descriptive statistics are techniques used for describing, graphing, organizing and summarizing quantitative data . They describe something, either visually or statistically, about individual variables or the association among two or more variables. For instance, a social researcher may want to know how many people in his/her study are male or female, what the average age of the respondents is, or what the median income is. Researchers often need to know how closely their data represent the population from which it is drawn so that they can assess the data’s representativeness.

Descriptive statistics include mean, standard deviation, mode,and median.

Descriptive information gives researchers a general picture of their data, as opposed to an explanation for why certain variables may be associated with each other. Descriptive statistics are often contrasted with inferential statistics, which are used to make inferences, or to explain factors, about the population. Data can be summarized at the univariate level with visual pictures, such as graphs, histograms, and pie charts. Statistical techniques used to describe individual variables include frequencies, the mean , median, mode, cumulative percent, percentile, standard deviation, variance, and interquartile range. Data can also be summarized at the bivariate level. Measures of association between two variables include calculations of eta, gamma, lambda, Pearson’s r, Kendall’s tau, Spearman’s rho, and chi2, among others. Bivariate relationships can also be illustrated in visual graphs that describe the association between two variables.

(from Oxford Reference Online )

• << Previous: Correlation
• Next: Discrete Stats >>

• Last Updated: Jul 3, 2024 12:02 PM
• URL: https://libguides.und.edu/statistics

Educational resources and simple solutions for your research journey

What is Descriptive Research? Definition, Methods, Types and Examples

Descriptive research is a methodological approach that seeks to depict the characteristics of a phenomenon or subject under investigation. In scientific inquiry, it serves as a foundational tool for researchers aiming to observe, record, and analyze the intricate details of a particular topic. This method provides a rich and detailed account that aids in understanding, categorizing, and interpreting the subject matter.

Descriptive research design is widely employed across diverse fields, and its primary objective is to systematically observe and document all variables and conditions influencing the phenomenon.

After this descriptive research definition, let’s look at this example. Consider a researcher working on climate change adaptation, who wants to understand water management trends in an arid village in a specific study area. She must conduct a demographic survey of the region, gather population data, and then conduct descriptive research on this demographic segment. The study will then uncover details on “what are the water management practices and trends in village X.” Note, however, that it will not cover any investigative information about “why” the patterns exist.

Table of Contents

What is descriptive research?

If you’ve been wondering “What is descriptive research,” we’ve got you covered in this post! In a nutshell, descriptive research is an exploratory research method that helps a researcher describe a population, circumstance, or phenomenon. It can help answer what , where , when and how questions, but not why questions. In other words, it does not involve changing the study variables and does not seek to establish cause-and-effect relationships.

Importance of descriptive research

Now, let’s delve into the importance of descriptive research. This research method acts as the cornerstone for various academic and applied disciplines. Its primary significance lies in its ability to provide a comprehensive overview of a phenomenon, enabling researchers to gain a nuanced understanding of the variables at play. This method aids in forming hypotheses, generating insights, and laying the groundwork for further in-depth investigations. The following points further illustrate its importance:

Provides insights into a population or phenomenon: Descriptive research furnishes a comprehensive overview of the characteristics and behaviors of a specific population or phenomenon, thereby guiding and shaping the research project.

Offers baseline data: The data acquired through this type of research acts as a reference for subsequent investigations, laying the groundwork for further studies.

Allows validation of sampling methods: Descriptive research validates sampling methods, aiding in the selection of the most effective approach for the study.

Helps reduce time and costs: It is cost-effective and time-efficient, making this an economical means of gathering information about a specific population or phenomenon.

Ensures replicability: Descriptive research is easily replicable, ensuring a reliable way to collect and compare information from various sources.

When to use descriptive research design?

Determining when to use descriptive research depends on the nature of the research question. Before diving into the reasons behind an occurrence, understanding the how, when, and where aspects is essential. Descriptive research design is a suitable option when the research objective is to discern characteristics, frequencies, trends, and categories without manipulating variables. It is therefore often employed in the initial stages of a study before progressing to more complex research designs. To put it in another way, descriptive research precedes the hypotheses of explanatory research. It is particularly valuable when there is limited existing knowledge about the subject.

Some examples are as follows, highlighting that these questions would arise before a clear outline of the research plan is established:

• In the last two decades, what changes have occurred in patterns of urban gardening in Mumbai?
• What are the differences in climate change perceptions of farmers in coastal versus inland villages in the Philippines?

Characteristics of descriptive research

Coming to the characteristics of descriptive research, this approach is characterized by its focus on observing and documenting the features of a subject. Specific characteristics are as below.

• Quantitative nature: Some descriptive research types involve quantitative research methods to gather quantifiable information for statistical analysis of the population sample.
• Qualitative nature: Some descriptive research examples include those using the qualitative research method to describe or explain the research problem.
• Observational nature: This approach is non-invasive and observational because the study variables remain untouched. Researchers merely observe and report, without introducing interventions that could impact the subject(s).
• Cross-sectional nature: In descriptive research, different sections belonging to the same group are studied, providing a “snapshot” of sorts.
• Springboard for further research: The data collected are further studied and analyzed using different research techniques. This approach helps guide the suitable research methods to be employed.

Types of descriptive research

There are various descriptive research types, each suited to different research objectives. Take a look at the different types below.

• Surveys: This involves collecting data through questionnaires or interviews to gather qualitative and quantitative data.
• Observational studies: This involves observing and collecting data on a particular population or phenomenon without influencing the study variables or manipulating the conditions. These may be further divided into cohort studies, case studies, and cross-sectional studies:
• Cohort studies: Also known as longitudinal studies, these studies involve the collection of data over an extended period, allowing researchers to track changes and trends.
• Case studies: These deal with a single individual, group, or event, which might be rare or unusual.
• Cross-sectional studies : A researcher collects data at a single point in time, in order to obtain a snapshot of a specific moment.
• Focus groups: In this approach, a small group of people are brought together to discuss a topic. The researcher moderates and records the group discussion. This can also be considered a “participatory” observational method.
• Descriptive classification: Relevant to the biological sciences, this type of approach may be used to classify living organisms.

Descriptive research methods

Several descriptive research methods can be employed, and these are more or less similar to the types of approaches mentioned above.

• Surveys: This method involves the collection of data through questionnaires or interviews. Surveys may be done online or offline, and the target subjects might be hyper-local, regional, or global.
• Observational studies: These entail the direct observation of subjects in their natural environment. These include case studies, dealing with a single case or individual, as well as cross-sectional and longitudinal studies, for a glimpse into a population or changes in trends over time, respectively. Participatory observational studies such as focus group discussions may also fall under this method.

Researchers must carefully consider descriptive research methods, types, and examples to harness their full potential in contributing to scientific knowledge.

Examples of descriptive research

Now, let’s consider some descriptive research examples.

• In social sciences, an example could be a study analyzing the demographics of a specific community to understand its socio-economic characteristics.
• In business, a market research survey aiming to describe consumer preferences would be a descriptive study.
• In ecology, a researcher might undertake a survey of all the types of monocots naturally occurring in a region and classify them up to species level.

These examples showcase the versatility of descriptive research across diverse fields.

Advantages of descriptive research

There are several advantages to this approach, which every researcher must be aware of. These are as follows:

• Owing to the numerous descriptive research methods and types, primary data can be obtained in diverse ways and be used for developing a research hypothesis .
• It is a versatile research method and allows flexibility.
• Detailed and comprehensive information can be obtained because the data collected can be qualitative or quantitative.
• It is carried out in the natural environment, which greatly minimizes certain types of bias and ethical concerns.
• It is an inexpensive and efficient approach, even with large sample sizes

Disadvantages of descriptive research

On the other hand, this design has some drawbacks as well:

• It is limited in its scope as it does not determine cause-and-effect relationships.
• The approach does not generate new information and simply depends on existing data.
• Study variables are not manipulated or controlled, and this limits the conclusions to be drawn.
• Descriptive research findings may not be generalizable to other populations.
• Finally, it offers a preliminary understanding rather than an in-depth understanding.

To reiterate, the advantages of descriptive research lie in its ability to provide a comprehensive overview, aid hypothesis generation, and serve as a preliminary step in the research process. However, its limitations include a potential lack of depth, inability to establish cause-and-effect relationships, and susceptibility to bias.

Frequently asked questions

When should researchers conduct descriptive research.

Descriptive research is most appropriate when researchers aim to portray and understand the characteristics of a phenomenon without manipulating variables. It is particularly valuable in the early stages of a study.

What is the difference between descriptive and exploratory research?

Descriptive research focuses on providing a detailed depiction of a phenomenon, while exploratory research aims to explore and generate insights into an issue where little is known.

What is the difference between descriptive and experimental research?

Descriptive research observes and documents without manipulating variables, whereas experimental research involves intentional interventions to establish cause-and-effect relationships.

Is descriptive research only for social sciences?

No, various descriptive research types may be applicable to all fields of study, including social science, humanities, physical science, and biological science.

How important is descriptive research?

The importance of descriptive research lies in its ability to provide a glimpse of the current state of a phenomenon, offering valuable insights and establishing a basic understanding. Further, the advantages of descriptive research include its capacity to offer a straightforward depiction of a situation or phenomenon, facilitate the identification of patterns or trends, and serve as a useful starting point for more in-depth investigations. Additionally, descriptive research can contribute to the development of hypotheses and guide the formulation of research questions for subsequent studies.

Editage All Access is a subscription-based platform that unifies the best AI tools and services designed to speed up, simplify, and streamline every step of a researcher’s journey. The Editage All Access Pack is a one-of-a-kind subscription that unlocks full access to an AI writing assistant, literature recommender, journal finder, scientific illustration tool, and exclusive discounts on professional publication services from Editage.  

Based on 22+ years of experience in academia, Editage All Access empowers researchers to put their best research forward and move closer to success. Explore our top AI Tools pack, AI Tools + Publication Services pack, or Build Your Own Plan. Find everything a researcher needs to succeed, all in one place –  Get All Access now starting at just $14 a month !    

Related Posts

Join Us for Peer Review Week 2024

How Editage All Access is Boosting Productivity for Academics in India

A Guide on Data Analysis

3 descriptive statistics.

When you have an area of interest that you want to research, a problem that you want to solve, a relationship that you want to investigate, theoretical and empirical processes will help you.

Estimand is defined as “a quantity of scientific interest that can be calculated in the population and does not change its value depending on the data collection design used to measure it (i.e., it does not vary with sample size and survey design, or the number of non-respondents, or follow-up efforts).” ( Rubin 1996 )

Estimands include:

• population means
• Population variances
• correlations
• factor loading
• regression coefficients

3.1 Numerical Measures

There are differences between a population and a sample

Order Statistics: \(y_{(1)},y_{(2)},...,y_{(n)}\) where \(y_{(1)}<y_{(2)}<...<y_{(n)}\)

Coefficient of variation: standard deviation over mean. This metric is stable, dimensionless statistic for comparison.

Symmetric: mean = median, skewness = 0

Skewed right: mean > median, skewness > 0

Skewed left: mean < median, skewness < 0

Central moments: \(\mu=E(Y)\) , \(\mu_2 = \sigma^2=E(Y-\mu)^2\) , \(\mu_3 = E(Y-\mu)^3\) , \(\mu_4 = E(Y-\mu)^4\)

For normal distributions, \(\mu_3=0\) , so \(g_1=0\)

\(\hat{g_1}\) is distributed approximately as \(N(0,6/n)\) if sample is from a normal population. (valid when \(n > 150\) )

• For large samples, inference on skewness can be based on normal tables with 95% confidence interval for \(g_1\) as \(\hat{g_1}\pm1.96\sqrt{6/n}\)
• For small samples, special tables from Snedecor and Cochran 1989, Table A 19(i) or Monte Carlo test

For a normal distribution, \(g_2^*=3\) . Kurtosis is often redefined as: \(g_2=\frac{E(Y-\mu)^4}{\sigma^4}-3\) where the 4th central moment is estimated by \(m_4=\sum_{i=1}^{n}(y_i-\overline{y})^4/n\)

• the asymptotic sampling distribution for \(\hat{g_2}\) is approximately \(N(0,24/n)\) (with \(n > 1000\) )
• large sample on kurtosis uses standard normal tables
• small sample uses tables by Snedecor and Cochran, 1989, Table A 19(ii) or Geary 1936

3.2 Graphical Measures

3.2.1 shape.

It’s a good habit to label your graph, so others can easily follow.

Others more advanced plots

3.2.2 Scatterplot

3.3 normality assessment.

Since Normal (Gaussian) distribution has many applications, we typically want/ wish our data or our variable is normal. Hence, we have to assess the normality based on not only Numerical Measures but also Graphical Measures

3.3.1 Graphical Assessment

The straight line represents the theoretical line for normally distributed data. The dots represent real empirical data that we are checking. If all the dots fall on the straight line, we can be confident that our data follow a normal distribution. If our data wiggle and deviate from the line, we should be concerned with the normality assumption.

3.3.2 Summary Statistics

Sometimes it’s hard to tell whether your data follow the normal distribution by just looking at the graph. Hence, we often have to conduct statistical test to aid our decision. Common tests are

Methods based on normal probability plot

• Correlation Coefficient with Normal Probability Plots
• Shapiro-Wilk Test

Methods based on empirical cumulative distribution function

• Anderson-Darling Test
• Kolmogorov-Smirnov Test
• Cramer-von Mises Test
• Jarque–Bera Test

3.3.2.1 Methods based on normal probability plot

3.3.2.1.1 correlation coefficient with normal probability plots.

( Looney and Gulledge Jr 1985 ) ( Samuel S. Shapiro and Francia 1972 ) The correlation coefficient between \(y_{(i)}\) and \(m_i^*\) as given on the normal probability plot:

\[W^*=\frac{\sum_{i=1}^{n}(y_{(i)}-\bar{y})(m_i^*-0)}{(\sum_{i=1}^{n}(y_{(i)}-\bar{y})^2\sum_{i=1}^{n}(m_i^*-0)^2)^.5}\]

where \(\bar{m^*}=0\)

Pearson product moment formula for correlation:

\[\hat{p}=\frac{\sum_{i-1}^{n}(y_i-\bar{y})(x_i-\bar{x})}{(\sum_{i=1}^{n}(y_{i}-\bar{y})^2\sum_{i=1}^{n}(x_i-\bar{x})^2)^.5}\]

• When the correlation is 1, the plot is exactly linear and normality is assumed.
• The closer the correlation is to zero, the more confident we are to reject normality
• Inference on W* needs to be based on special tables ( Looney and Gulledge Jr 1985 )

3.3.2.1.2 Shapiro-Wilk Test

( Samuel Sanford Shapiro and Wilk 1965 )

\[W=(\frac{\sum_{i=1}^{n}a_i(y_{(i)}-\bar{y})(m_i^*-0)}{(\sum_{i=1}^{n}a_i^2(y_{(i)}-\bar{y})^2\sum_{i=1}^{n}(m_i^*-0)^2)^.5})^2\]

where \(a_1,..,a_n\) are weights computed from the covariance matrix for the order statistics.

• Researchers typically use this test to assess normality. (n < 2000) Under normality, W is close to 1, just like \(W^*\) . Notice that the only difference between W and W* is the “weights”.

3.3.2.2 Methods based on empirical cumulative distribution function

The formula for the empirical cumulative distribution function (CDF) is:

\(F_n(t)\) = estimate of probability that an observation \(\le\) t = (number of observation \(\le\) t)/n

This method requires large sample sizes. However, it can apply to distributions other than the normal (Gaussian) one.

3.3.2.2.1 Anderson-Darling Test

The Anderson-Darling statistic ( T. W. Anderson and Darling 1952 ) :

\[A^2=\int_{-\infty}^{\infty}(F_n(t)=F(t))^2\frac{dF(t)}{F(t)(1-F(t))}\]

• a weight average of squared deviations (it weights small and large values of t more)

For the normal distribution,

\(A^2 = - (\sum_{i=1}^{n}(2i-1)(ln(p_i) +ln(1-p_{n+1-i}))/n-n\)

where \(p_i=\Phi(\frac{y_{(i)}-\bar{y}}{s})\) , the probability that a standard normal variable is less than \(\frac{y_{(i)}-\bar{y}}{s}\)

Reject normal assumption when \(A^2\) is too large

Evaluate the null hypothesis that the observations are randomly selected from a normal population based on the critical value provided by ( Marsaglia and Marsaglia 2004 ) and ( Stephens 1974 )

This test can be applied to other distributions:

• Exponential
• Extreme-value
• Weibull: log(Weibull) = Gumbel
• Log-normal (two-parameter)

Consult ( Stephens 1974 ) for more detailed transformation and critical values.

3.3.2.2.2 Kolmogorov-Smirnov Test

• Based on the largest absolute difference between empirical and expected cumulative distribution
• Another deviation of K-S test is Kuiper’s test

3.3.2.2.3 Cramer-von Mises Test

• Based on the average squared discrepancy between the empirical distribution and a given theoretical distribution. Each discrepancy is weighted equally (unlike Anderson-Darling test weights end points more heavily)

3.3.2.2.4 Jarque–Bera Test

( Bera and Jarque 1981 )

Based on the skewness and kurtosis to test normality.

\(JB = \frac{n}{6}(S^2+(K-3)^2/4)\) where \(S\) is the sample skewness and \(K\) is the sample kurtosis

\(S=\frac{\hat{\mu_3}}{\hat{\sigma}^3}=\frac{\sum_{i=1}^{n}(x_i-\bar{x})^3/n}{(\sum_{i=1}^{n}(x_i-\bar{x})^2/n)^\frac{3}{2}}\)

\(K=\frac{\hat{\mu_4}}{\hat{\sigma}^4}=\frac{\sum_{i=1}^{n}(x_i-\bar{x})^4/n}{(\sum_{i=1}^{n}(x_i-\bar{x})^2/n)^2}\)

recall \(\hat{\sigma^2}\) is the estimate of the second central moment (variance) \(\hat{\mu_3}\) and \(\hat{\mu_4}\) are the estimates of third and fourth central moments.

If the data comes from a normal distribution, the JB statistic asymptotically has a chi-squared distribution with two degrees of freedom.

The null hypothesis is a joint hypothesis of the skewness being zero and the excess kurtosis being zero.

3.4 Bivariate Statistics

Correlation between

• Two Continuous variables
• Two Discrete variables
• Categorical and Continuous

Questions to keep in mind:

• Is the relationship linear or non-linear?
• If the variable is continuous, is it normal and homoskadastic?
• How big is your dataset?

3.4.1 Two Continuous

3.4.1.1 pearson correlation.

• Good with linear relationship

3.4.1.2 Spearman Correlation

3.4.2 categorical and continuous, 3.4.2.1 point-biserial correlation.

Similar to the Pearson correlation coefficient, the point-biserial correlation coefficient is between -1 and 1 where:

-1 means a perfectly negative correlation between two variables

0 means no correlation between two variables

1 means a perfectly positive correlation between two variables

Alternatively

3.4.2.2 Logistic Regression

See 3.4.2.2

3.4.3 Two Discrete

3.4.3.1 distance metrics.

Some consider distance is not a correlation metric because it isn’t unit independent (i.e., if you scale the distance, the metrics will change), but it’s still a useful proxy. Distance metrics are more likely to be used for similarity measure.

Euclidean Distance

Manhattan Distance

Chessboard Distance

Minkowski Distance

Canberra Distance

Hamming Distance

Cosine Distance

Sum of Absolute Distance

Sum of Squared Distance

Mean-Absolute Error

3.4.3.2 Statistical Metrics

3.4.3.2.1 chi-squared test, 3.4.3.2.1.1 phi coefficient, 3.4.3.2.1.2 cramer’s v.

• between nominal categorical variables (no natural order)

\[ \text{Cramer's V} = \sqrt{\frac{\chi^2/n}{\min(c-1,r-1)}} \]

\(\chi^2\) = Chi-square statistic

\(n\) = sample size

\(r\) = # of rows

\(c\) = # of columns

Alternatively,

ncchisq noncentral Chi-square

nchisqadj Adjusted noncentral Chi-square

fisher Fisher Z transformation

fisheradj bias correction Fisher z transformation

3.4.3.2.1.3 Tschuprow’s T

• 2 nominal variables

3.4.3.3 Ordinal Association (Rank correlation)

• Good with non-linear relationship

3.4.3.3.1 Ordinal and Nominal

3.4.3.3.1.1 freeman’s theta.

• Ordinal and nominal

3.4.3.3.1.2 Epsilon-squared

3.4.3.3.2 two ordinal, 3.4.3.3.2.1 goodman kruskal’s gamma.

• 2 ordinal variables

3.4.3.3.2.2 Somers’ D

or Somers’ Delta

3.4.3.3.2.3 Kendall’s Tau-b

3.4.3.3.2.4 yule’s q and y.

Special version \((2 \times 2)\) of the Goodman Kruskal’s Gamma coefficient.

\[ \text{Yule's Q} = \frac{ad - bc}{ad + bc} \]

We typically use Yule’s \(Q\) in practice while Yule’s Y has the following relationship with \(Q\) .

\[ \text{Yule's Y} = \frac{\sqrt{ad} - \sqrt{bc}}{\sqrt{ad} + \sqrt{bc}} \]

\[ Q = \frac{2Y}{1 + Y^2} \]

\[ Y = \frac{1 = \sqrt{1-Q^2}}{Q} \]

3.4.3.3.2.5 Tetrachoric Correlation

• is a special case of Polychoric Correlation when both variables are binary

3.4.3.3.2.6 Polychoric Correlation

• between ordinal categorical variables (natural order).
• Assumption: Ordinal variable is a discrete representation of a latent normally distributed continuous variable. (Income = low, normal, high).

3.5 Summary

Get the correlation table for continuous variables only

Alternatively, you can also have the

Different comparison between different correlation between different types of variables (i.e., continuous vs. categorical) can be problematic. Moreover, the problem of detecting non-linear vs. linear relationship/correlation is another one. Hence, a solution is that using mutual information from information theory (i.e., knowing one variable can reduce uncertainty about the other).

To implement mutual information, we have the following approximations

\[ \downarrow \text{prediction error} \approx \downarrow \text{uncertainty} \approx \downarrow \text{association strength} \]

More specifically, following the X2Y metric , we have the following steps:

Predict \(y\) without \(x\) (i.e., baseline model)

Average of \(y\) when \(y\) is continuous

Most frequent value when \(y\) is categorical

Predict \(y\) with \(x\) (e.g., linear, random forest, etc.)

Calculate the prediction error difference between 1 and 2

To have a comprehensive table that could handle

continuous vs. continuous

categorical vs. continuous

continuous vs. categorical

categorical vs. categorical

the suggested model would be Classification and Regression Trees (CART). But we can certainly use other models as well.

The downfall of this method is that you might suffer

• Symmetry: \((x,y) \neq (y,x)\)
• Comparability : Different pair of comparison might use different metrics (e.g., misclassification error vs. MAE)

3.5.1 Visualization

More general form,

Both heat map and correlation at the same time

More elaboration with ggplot2

Popular searches

• How to Get Participants For Your Study
• How to Do Segmentation?
• Conjoint Preference Share Simulator
• MaxDiff Analysis
• Likert Scales
• Reliability & Validity

Request consultation

Do you need support in running a pricing or product study? We can help you with agile consumer research and conjoint analysis.

Looking for an online survey platform?

Conjointly offers a great survey tool with multiple question types, randomisation blocks, and multilingual support. The Basic tier is always free.

Research Methods Knowledge Base

• Navigating the Knowledge Base
• Foundations
• Measurement
• Research Design
• Conclusion Validity
• Data Preparation
• Correlation
• Inferential Statistics
• Table of Contents

Fully-functional online survey tool with various question types, logic, randomisation, and reporting for unlimited number of surveys.

Completely free for academics and students .

Descriptive Statistics

Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample and the measures. Together with simple graphics analysis, they form the basis of virtually every quantitative analysis of data.

Descriptive statistics are typically distinguished from inferential statistics . With descriptive statistics you are simply describing what is or what the data shows. With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone. For instance, we use inferential statistics to try to infer from the sample data what the population might think. Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance in this study. Thus, we use inferential statistics to make inferences from our data to more general conditions; we use descriptive statistics simply to describe what’s going on in our data.

Descriptive Statistics are used to present quantitative descriptions in a manageable form. In a research study we may have lots of measures. Or we may measure a large number of people on any measure. Descriptive statistics help us to simplify large amounts of data in a sensible way. Each descriptive statistic reduces lots of data into a simpler summary. For instance, consider a simple number used to summarize how well a batter is performing in baseball, the batting average. This single number is simply the number of hits divided by the number of times at bat (reported to three significant digits). A batter who is hitting .333 is getting a hit one time in every three at bats. One batting .250 is hitting one time in four. The single number describes a large number of discrete events. Or, consider the scourge of many students, the Grade Point Average (GPA). This single number describes the general performance of a student across a potentially wide range of course experiences.

Every time you try to describe a large set of observations with a single indicator you run the risk of distorting the original data or losing important detail. The batting average doesn’t tell you whether the batter is hitting home runs or singles. It doesn’t tell whether she’s been in a slump or on a streak. The GPA doesn’t tell you whether the student was in difficult courses or easy ones, or whether they were courses in their major field or in other disciplines. Even given these limitations, descriptive statistics provide a powerful summary that may enable comparisons across people or other units.

Univariate Analysis

Univariate analysis involves the examination across cases of one variable at a time. There are three major characteristics of a single variable that we tend to look at:

• the distribution
• the central tendency
• the dispersion

In most situations, we would describe all three of these characteristics for each of the variables in our study.

The Distribution

The distribution is a summary of the frequency of individual values or ranges of values for a variable. The simplest distribution would list every value of a variable and the number of persons who had each value. For instance, a typical way to describe the distribution of college students is by year in college, listing the number or percent of students at each of the four years. Or, we describe gender by listing the number or percent of males and females. In these cases, the variable has few enough values that we can list each one and summarize how many sample cases had the value. But what do we do for a variable like income or GPA? With these variables there can be a large number of possible values, with relatively few people having each one. In this case, we group the raw scores into categories according to ranges of values. For instance, we might look at GPA according to the letter grade ranges. Or, we might group income into four or five ranges of income values.

One of the most common ways to describe a single variable is with a frequency distribution . Depending on the particular variable, all of the data values may be represented, or you may group the values into categories first (e.g. with age, price, or temperature variables, it would usually not be sensible to determine the frequencies for each value. Rather, the value are grouped into ranges and the frequencies determined.). Frequency distributions can be depicted in two ways, as a table or as a graph. The table above shows an age frequency distribution with five categories of age ranges defined. The same frequency distribution can be depicted in a graph as shown in Figure 1. This type of graph is often referred to as a histogram or bar chart.

Distributions may also be displayed using percentages. For example, you could use percentages to describe the:

• percentage of people in different income levels
• percentage of people in different age ranges
• percentage of people in different ranges of standardized test scores

Central Tendency

The central tendency of a distribution is an estimate of the “center” of a distribution of values. There are three major types of estimates of central tendency:

The Mean or average is probably the most commonly used method of describing central tendency. To compute the mean all you do is add up all the values and divide by the number of values. For example, the mean or average quiz score is determined by summing all the scores and dividing by the number of students taking the exam. For example, consider the test score values:

The sum of these 8 values is 167 , so the mean is 167/8 = 20.875 .

The Median is the score found at the exact middle of the set of values. One way to compute the median is to list all scores in numerical order, and then locate the score in the center of the sample. For example, if there are 500 scores in the list, score #250 would be the median. If we order the 8 scores shown above, we would get:

There are 8 scores and score #4 and #5 represent the halfway point. Since both of these scores are 20 , the median is 20 . If the two middle scores had different values, you would have to interpolate to determine the median.

The Mode is the most frequently occurring value in the set of scores. To determine the mode, you might again order the scores as shown above, and then count each one. The most frequently occurring value is the mode. In our example, the value 15 occurs three times and is the model. In some distributions there is more than one modal value. For instance, in a bimodal distribution there are two values that occur most frequently.

Notice that for the same set of 8 scores we got three different values ( 20.875 , 20 , and 15 ) for the mean, median and mode respectively. If the distribution is truly normal (i.e. bell-shaped), the mean, median and mode are all equal to each other.

Dispersion refers to the spread of the values around the central tendency. There are two common measures of dispersion, the range and the standard deviation. The range is simply the highest value minus the lowest value. In our example distribution, the high value is 36 and the low is 15 , so the range is 36 - 15 = 21 .

The Standard Deviation is a more accurate and detailed estimate of dispersion because an outlier can greatly exaggerate the range (as was true in this example where the single outlier value of 36 stands apart from the rest of the values. The Standard Deviation shows the relation that set of scores has to the mean of the sample. Again lets take the set of scores:

to compute the standard deviation, we first find the distance between each value and the mean. We know from above that the mean is 20.875 . So, the differences from the mean are:

Notice that values that are below the mean have negative discrepancies and values above it have positive ones. Next, we square each discrepancy:

Now, we take these “squares” and sum them to get the Sum of Squares (SS) value. Here, the sum is 350.875 . Next, we divide this sum by the number of scores minus 1 . Here, the result is 350.875 / 7 = 50.125 . This value is known as the variance . To get the standard deviation, we take the square root of the variance (remember that we squared the deviations earlier). This would be SQRT(50.125) = 7.079901129253 .

Although this computation may seem convoluted, it’s actually quite simple. To see this, consider the formula for the standard deviation:

• X is each score,
• X̄ is the mean (or average),
• n is the number of values,
• Σ means we sum across the values.

In the top part of the ratio, the numerator, we see that each score has the mean subtracted from it, the difference is squared, and the squares are summed. In the bottom part, we take the number of scores minus 1 . The ratio is the variance and the square root is the standard deviation. In English, we can describe the standard deviation as:

the square root of the sum of the squared deviations from the mean divided by the number of scores minus one.

Although we can calculate these univariate statistics by hand, it gets quite tedious when you have more than a few values and variables. Every statistics program is capable of calculating them easily for you. For instance, I put the eight scores into SPSS and got the following table as a result:

which confirms the calculations I did by hand above.

The standard deviation allows us to reach some conclusions about specific scores in our distribution. Assuming that the distribution of scores is normal or bell-shaped (or close to it!), the following conclusions can be reached:

• approximately 68% of the scores in the sample fall within one standard deviation of the mean
• approximately 95% of the scores in the sample fall within two standard deviations of the mean
• approximately 99% of the scores in the sample fall within three standard deviations of the mean

For instance, since the mean in our example is 20.875 and the standard deviation is 7.0799 , we can from the above statement estimate that approximately 95% of the scores will fall in the range of 20.875-(2*7.0799) to 20.875+(2*7.0799) or between 6.7152 and 35.0348 . This kind of information is a critical stepping stone to enabling us to compare the performance of an individual on one variable with their performance on another, even when the variables are measured on entirely different scales.

Cookie Consent

Conjointly uses essential cookies to make our site work. We also use additional cookies in order to understand the usage of the site, gather audience analytics, and for remarketing purposes.

For more information on Conjointly's use of cookies, please read our Cookie Policy .

Which one are you?

I am new to conjointly, i am already using conjointly.

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

14 Quantitative analysis: Descriptive statistics

Numeric data collected in a research project can be analysed quantitatively using statistical tools in two different ways. Descriptive analysis refers to statistically describing, aggregating, and presenting the constructs of interest or associations between these constructs. Inferential analysis refers to the statistical testing of hypotheses (theory testing). In this chapter, we will examine statistical techniques used for descriptive analysis, and the next chapter will examine statistical techniques for inferential analysis. Much of today’s quantitative data analysis is conducted using software programs such as SPSS or SAS. Readers are advised to familiarise themselves with one of these programs for understanding the concepts described in this chapter.

Data preparation

In research projects, data may be collected from a variety of sources: postal surveys, interviews, pretest or posttest experimental data, observational data, and so forth. This data must be converted into a machine-readable, numeric format, such as in a spreadsheet or a text file, so that they can be analysed by computer programs like SPSS or SAS. Data preparation usually follows the following steps:

Data coding. Coding is the process of converting data into numeric format. A codebook should be created to guide the coding process. A codebook is a comprehensive document containing a detailed description of each variable in a research study, items or measures for that variable, the format of each item (numeric, text, etc.), the response scale for each item (i.e., whether it is measured on a nominal, ordinal, interval, or ratio scale, and whether this scale is a five-point, seven-point scale, etc.), and how to code each value into a numeric format. For instance, if we have a measurement item on a seven-point Likert scale with anchors ranging from ‘strongly disagree’ to ‘strongly agree’, we may code that item as 1 for strongly disagree, 4 for neutral, and 7 for strongly agree, with the intermediate anchors in between. Nominal data such as industry type can be coded in numeric form using a coding scheme such as: 1 for manufacturing, 2 for retailing, 3 for financial, 4 for healthcare, and so forth (of course, nominal data cannot be analysed statistically). Ratio scale data such as age, income, or test scores can be coded as entered by the respondent. Sometimes, data may need to be aggregated into a different form than the format used for data collection. For instance, if a survey measuring a construct such as ‘benefits of computers’ provided respondents with a checklist of benefits that they could select from, and respondents were encouraged to choose as many of those benefits as they wanted, then the total number of checked items could be used as an aggregate measure of benefits. Note that many other forms of data—such as interview transcripts—cannot be converted into a numeric format for statistical analysis. Codebooks are especially important for large complex studies involving many variables and measurement items, where the coding process is conducted by different people, to help the coding team code data in a consistent manner, and also to help others understand and interpret the coded data.

Data entry. Coded data can be entered into a spreadsheet, database, text file, or directly into a statistical program like SPSS. Most statistical programs provide a data editor for entering data. However, these programs store data in their own native format—e.g., SPSS stores data as .sav files—which makes it difficult to share that data with other statistical programs. Hence, it is often better to enter data into a spreadsheet or database where it can be reorganised as needed, shared across programs, and subsets of data can be extracted for analysis. Smaller data sets with less than 65,000 observations and 256 items can be stored in a spreadsheet created using a program such as Microsoft Excel, while larger datasets with millions of observations will require a database. Each observation can be entered as one row in the spreadsheet, and each measurement item can be represented as one column. Data should be checked for accuracy during and after entry via occasional spot checks on a set of items or observations. Furthermore, while entering data, the coder should watch out for obvious evidence of bad data, such as the respondent selecting the ‘strongly agree’ response to all items irrespective of content, including reverse-coded items. If so, such data can be entered but should be excluded from subsequent analysis.

Data transformation. Sometimes, it is necessary to transform data values before they can be meaningfully interpreted. For instance, reverse coded items—where items convey the opposite meaning of that of their underlying construct—should be reversed (e.g., in a 1-7 interval scale, 8 minus the observed value will reverse the value) before they can be compared or combined with items that are not reverse coded. Other kinds of transformations may include creating scale measures by adding individual scale items, creating a weighted index from a set of observed measures, and collapsing multiple values into fewer categories (e.g., collapsing incomes into income ranges).

Univariate analysis

Univariate analysis—or analysis of a single variable—refers to a set of statistical techniques that can describe the general properties of one variable. Univariate statistics include: frequency distribution, central tendency, and dispersion. The frequency distribution of a variable is a summary of the frequency—or percentages—of individual values or ranges of values for that variable. For instance, we can measure how many times a sample of respondents attend religious services—as a gauge of their ‘religiosity’—using a categorical scale: never, once per year, several times per year, about once a month, several times per month, several times per week, and an optional category for ‘did not answer’. If we count the number or percentage of observations within each category—except ‘did not answer’ which is really a missing value rather than a category—and display it in the form of a table, as shown in Figure 14.1, what we have is a frequency distribution. This distribution can also be depicted in the form of a bar chart, as shown on the right panel of Figure 14.1, with the horizontal axis representing each category of that variable and the vertical axis representing the frequency or percentage of observations within each category.

With very large samples, where observations are independent and random, the frequency distribution tends to follow a plot that looks like a bell-shaped curve—a smoothed bar chart of the frequency distribution—similar to that shown in Figure 14.2. Here most observations are clustered toward the centre of the range of values, with fewer and fewer observations clustered toward the extreme ends of the range. Such a curve is called a normal distribution .

Lastly, the mode is the most frequently occurring value in a distribution of values. In the previous example, the most frequently occurring value is 15, which is the mode of the above set of test scores. Note that any value that is estimated from a sample, such as mean, median, mode, or any of the later estimates are called a statistic .

Bivariate analysis

Bivariate analysis examines how two variables are related to one another. The most common bivariate statistic is the bivariate correlation —often, simply called ‘correlation’—which is a number between -1 and +1 denoting the strength of the relationship between two variables. Say that we wish to study how age is related to self-esteem in a sample of 20 respondents—i.e., as age increases, does self-esteem increase, decrease, or remain unchanged?. If self-esteem increases, then we have a positive correlation between the two variables, if self-esteem decreases, then we have a negative correlation, and if it remains the same, we have a zero correlation. To calculate the value of this correlation, consider the hypothetical dataset shown in Table 14.1.

After computing bivariate correlation, researchers are often interested in knowing whether the correlation is significant (i.e., a real one) or caused by mere chance. Answering such a question would require testing the following hypothesis:

Social Science Research: Principles, Methods and Practices (Revised edition) Copyright © 2019 by Anol Bhattacherjee is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.

Share This Book

• Privacy Policy

Home » Descriptive Analytics – Methods, Tools and Examples

Descriptive Analytics – Methods, Tools and Examples

Table of Contents

Descriptive Analytics

Definition:

Descriptive analytics focused on describing or summarizing raw data and making it interpretable. This type of analytics provides insight into what has happened in the past. It involves the analysis of historical data to identify patterns, trends, and insights. Descriptive analytics often uses visualization tools to represent the data in a way that is easy to interpret.

Descriptive Analytics in Research

Descriptive analytics plays a crucial role in research, helping investigators understand and describe the data collected in their studies. Here’s how descriptive analytics is typically used in a research setting:

• Descriptive Statistics: In research, descriptive analytics often takes the form of descriptive statistics . This includes calculating measures of central tendency (like mean, median, and mode), measures of dispersion (like range, variance, and standard deviation), and measures of frequency (like count, percent, and frequency). These calculations help researchers summarize and understand their data.
• Visualizing Data: Descriptive analytics also involves creating visual representations of data to better understand and communicate research findings . This might involve creating bar graphs, line graphs, pie charts, scatter plots, box plots, and other visualizations.
• Exploratory Data Analysis: Before conducting any formal statistical tests, researchers often conduct an exploratory data analysis, which is a form of descriptive analytics. This might involve looking at distributions of variables, checking for outliers, and exploring relationships between variables.
• Initial Findings: Descriptive analytics are often reported in the results section of a research study to provide readers with an overview of the data. For example, a researcher might report average scores, demographic breakdowns, or the percentage of participants who endorsed each response on a survey.
• Establishing Patterns and Relationships: Descriptive analytics helps in identifying patterns, trends, or relationships in the data, which can guide subsequent analysis or future research. For instance, researchers might look at the correlation between variables as a part of descriptive analytics.

Descriptive Analytics Techniques

Descriptive analytics involves a variety of techniques to summarize, interpret, and visualize historical data. Some commonly used techniques include:

Statistical Analysis

This includes basic statistical methods like mean, median, mode (central tendency), standard deviation, variance (dispersion), correlation, and regression (relationships between variables).

Data Aggregation

It is the process of compiling and summarizing data to obtain a general perspective. It can involve methods like sum, count, average, min, max, etc., often applied to a group of data.

Data Mining

This involves analyzing large volumes of data to discover patterns, trends, and insights. Techniques used in data mining can include clustering (grouping similar data), classification (assigning data into categories), association rules (finding relationships between variables), and anomaly detection (identifying outliers).

Data Visualization

This involves presenting data in a graphical or pictorial format to provide clear and easy understanding of the data patterns, trends, and insights. Common data visualization methods include bar charts, line graphs, pie charts, scatter plots, histograms, and more complex forms like heat maps and interactive dashboards.

This involves organizing data into informational summaries to monitor how different areas of a business are performing. Reports can be generated manually or automatically and can be presented in tables, graphs, or dashboards.

Cross-tabulation (or Pivot Tables)

It involves displaying the relationship between two or more variables in a tabular form. It can provide a deeper understanding of the data by allowing comparisons and revealing patterns and correlations that may not be readily apparent in raw data.

Descriptive Modeling

Some techniques use complex algorithms to interpret data. Examples include decision tree analysis, which provides a graphical representation of decision-making situations, and neural networks, which are used to identify correlations and patterns in large data sets.

Descriptive Analytics Tools

Some common Descriptive Analytics Tools are as follows:

Excel: Microsoft Excel is a widely used tool that can be used for simple descriptive analytics. It has powerful statistical and data visualization capabilities. Pivot tables are a particularly useful feature for summarizing and analyzing large data sets.

Tableau: Tableau is a data visualization tool that is used to represent data in a graphical or pictorial format. It can handle large data sets and allows for real-time data analysis.

Power BI: Power BI, another product from Microsoft, is a business analytics tool that provides interactive visualizations with self-service business intelligence capabilities.

QlikView: QlikView is a data visualization and discovery tool. It allows users to analyze data and use this data to support decision-making.

SAS: SAS is a software suite that can mine, alter, manage and retrieve data from a variety of sources and perform statistical analysis on it.

SPSS: SPSS (Statistical Package for the Social Sciences) is a software package used for statistical analysis. It’s widely used in social sciences research but also in other industries.

Google Analytics: For web data, Google Analytics is a popular tool. It allows businesses to analyze in-depth detail about the visitors on their website, providing valuable insights that can help shape the success strategy of a business.

R and Python: Both are programming languages that have robust capabilities for statistical analysis and data visualization. With packages like pandas, matplotlib, seaborn in Python and ggplot2, dplyr in R, these languages are powerful tools for descriptive analytics.

Looker: Looker is a modern data platform that can take data from any database and let you start exploring and visualizing.

When to use Descriptive Analytics

Descriptive analytics forms the base of the data analysis workflow and is typically the first step in understanding your business or organization’s data. Here are some situations when you might use descriptive analytics:

Understanding Past Behavior: Descriptive analytics is essential for understanding what has happened in the past. If you need to understand past sales trends, customer behavior, or operational performance, descriptive analytics is the tool you’d use.

Reporting Key Metrics: Descriptive analytics is used to establish and report key performance indicators (KPIs). It can help in tracking and presenting these KPIs in dashboards or regular reports.

Identifying Patterns and Trends: If you need to identify patterns or trends in your data, descriptive analytics can provide these insights. This might include identifying seasonality in sales data, understanding peak operational times, or spotting trends in customer behavior.

Informing Business Decisions: The insights provided by descriptive analytics can inform business strategy and decision-making. By understanding what has happened in the past, you can make more informed decisions about what steps to take in the future.

Benchmarking Performance: Descriptive analytics can be used to compare current performance against historical data. This can be used for benchmarking and setting performance goals.

Auditing and Regulatory Compliance: In sectors where compliance and auditing are essential, descriptive analytics can provide the necessary data and trends over specific periods.

Initial Data Exploration: When you first acquire a dataset, descriptive analytics is useful to understand the structure of the data, the relationships between variables, and any apparent anomalies or outliers.

Examples of Descriptive Analytics

Examples of Descriptive Analytics are as follows:

Retail Industry: A retail company might use descriptive analytics to analyze sales data from the past year. They could break down sales by month to identify any seasonality trends. For example, they might find that sales increase in November and December due to holiday shopping. They could also break down sales by product to identify which items are the most popular. This analysis could inform their purchasing and stocking decisions for the next year. Additionally, data on customer demographics could be analyzed to understand who their primary customers are, guiding their marketing strategies.

Healthcare Industry: In healthcare, descriptive analytics could be used to analyze patient data over time. For instance, a hospital might analyze data on patient admissions to identify trends in admission rates. They might find that admissions for certain conditions are higher at certain times of the year. This could help them allocate resources more effectively. Also, analyzing patient outcomes data can help identify the most effective treatments or highlight areas where improvement is needed.

Finance Industry: A financial firm might use descriptive analytics to analyze historical market data. They could look at trends in stock prices, trading volume, or economic indicators to inform their investment decisions. For example, analyzing the price-earnings ratios of stocks in a certain sector over time could reveal patterns that suggest whether the sector is currently overvalued or undervalued. Similarly, credit card companies can analyze transaction data to detect any unusual patterns, which could be signs of fraud.

Advantages of Descriptive Analytics

Descriptive analytics plays a vital role in the world of data analysis, providing numerous advantages:

• Understanding the Past: Descriptive analytics provides an understanding of what has happened in the past, offering valuable context for future decision-making.
• Data Summarization: Descriptive analytics is used to simplify and summarize complex datasets, which can make the information more understandable and accessible.
• Identifying Patterns and Trends: With descriptive analytics, organizations can identify patterns, trends, and correlations in their data, which can provide valuable insights.
• Inform Decision-Making: The insights generated through descriptive analytics can inform strategic decisions and help organizations to react more quickly to events or changes in behavior.
• Basis for Further Analysis: Descriptive analytics lays the groundwork for further analytical activities. It’s the first necessary step before moving on to more advanced forms of analytics like predictive analytics (forecasting future events) or prescriptive analytics (advising on possible outcomes).
• Performance Evaluation: It allows organizations to evaluate their performance by comparing current results with past results, enabling them to see where improvements have been made and where further improvements can be targeted.
• Enhanced Reporting and Dashboards: Through the use of visualization techniques, descriptive analytics can improve the quality of reports and dashboards, making the data more understandable and easier to interpret for stakeholders at all levels of the organization.
• Immediate Value: Unlike some other types of analytics, descriptive analytics can provide immediate insights, as it doesn’t require complex models or deep analytical capabilities to provide value.

Disadvantages of Descriptive Analytics

While descriptive analytics offers numerous benefits, it also has certain limitations or disadvantages. Here are a few to consider:

• Limited to Past Data: Descriptive analytics primarily deals with historical data and provides insights about past events. It does not predict future events or trends and can’t help you understand possible future outcomes on its own.
• Lack of Deep Insights: While descriptive analytics helps in identifying what happened, it does not answer why it happened. For deeper insights, you would need to use diagnostic analytics, which analyzes data to understand the root cause of a particular outcome.
• Can Be Misleading: If not properly executed, descriptive analytics can sometimes lead to incorrect conclusions. For example, correlation does not imply causation, but descriptive analytics might tempt one to make such an inference.
• Data Quality Issues: The accuracy and usefulness of descriptive analytics are heavily reliant on the quality of the underlying data. If the data is incomplete, incorrect, or biased, the results of the descriptive analytics will be too.
• Over-reliance on Descriptive Analytics: Businesses may rely too much on descriptive analytics and not enough on predictive and prescriptive analytics. While understanding past and present data is important, it’s equally vital to forecast future trends and make data-driven decisions based on those predictions.
• Doesn’t Provide Actionable Insights: Descriptive analytics is used to interpret historical data and identify patterns and trends, but it doesn’t provide recommendations or courses of action. For that, prescriptive analytics is needed.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

You may also like

Sentiment Analysis – Tools, Techniques and...

What is Data Science? Components, Process and Tools

Emerging Research Methods – Types and Examples

Digital Ethnography – Types, Methods and Examples

What is Big Data? Types, Tools and Examples

Blockchain Research – Methods, Types and Examples

Descriptive Research in Psychology: Methods, Applications, and Importance

Picture a psychologist’s toolkit, brimming with an array of methods designed to unravel the mysteries of the human mind—among them, the unsung hero of descriptive research, a powerful lens through which we can observe, understand, and illuminate the vast landscape of human behavior and cognition. This versatile approach to psychological inquiry serves as a cornerstone in our quest to comprehend the intricacies of the human experience, offering insights that shape our understanding of everything from child development to social interactions.

Descriptive research in psychology is like a skilled artist’s sketch, capturing the essence of human behavior and mental processes with precision and depth. It’s the foundation upon which many psychological theories are built, providing a rich tapestry of observations that inform more complex studies. Unlike experimental methods that manipulate variables to establish cause-and-effect relationships, descriptive research aims to paint a vivid picture of what is, rather than what could be.

Defining Descriptive Research in Psychology: More Than Meets the Eye

At its core, descriptive research in psychology is a systematic approach to observing and cataloging human behavior, thoughts, and emotions in their natural context. It’s the scientific equivalent of people-watching, but with a structured methodology and a keen eye for detail. This type of research doesn’t just scratch the surface; it dives deep into the nuances of human experience, capturing the subtleties that might otherwise go unnoticed.

The beauty of descriptive research lies in its versatility. It can take many forms, each offering a unique perspective on the human psyche. From participant observation in psychology , where researchers immerse themselves in the world they’re studying, to meticulous case studies that explore individual experiences in depth, descriptive research adapts to the questions at hand.

One of the primary goals of descriptive research is to provide a comprehensive account of a phenomenon. It’s not about proving or disproving hypotheses; instead, it’s about gathering rich, detailed information that can later inform more targeted inquiries. This approach is particularly valuable when exploring new or understudied areas of psychology, serving as a springboard for future research.

Methods and Techniques: The Descriptive Researcher’s Toolkit

The methods employed in descriptive research are as diverse as the questions they seek to answer. Let’s take a closer look at some of the key tools in the descriptive researcher’s arsenal:

1. Observational methods: Picture a researcher sitting quietly in a playground, noting how children interact. This direct observation can yield invaluable insights into social development and behavior patterns.

2. Case studies: These in-depth explorations of individual experiences can shed light on rare psychological phenomena or provide detailed accounts of therapeutic interventions.

3. Surveys and questionnaires: By tapping into the thoughts and opinions of large groups, researchers can identify trends and patterns in attitudes and behaviors.

4. Archival research in psychology : Delving into historical records and existing datasets can uncover long-term trends and provide context for current psychological phenomena.

5. Naturalistic observation: This method involves studying behavior in its natural environment, without interference from the researcher. It’s like being a fly on the wall, capturing authentic human interactions.

Each of these methods has its strengths and limitations, and skilled researchers often combine multiple approaches to gain a more comprehensive understanding of their subject matter.

Applications: Descriptive Research in Action

The applications of descriptive research in psychology are as varied as human behavior itself. Let’s explore how this approach illuminates different areas of psychological study:

In developmental psychology, descriptive research plays a crucial role in understanding how children grow and change over time. Longitudinal studies in psychology , which follow the same group of individuals over an extended period, provide invaluable insights into the trajectory of human development.

Social psychology relies heavily on descriptive methods to explore how people interact and influence one another. For instance, observational studies in public spaces can reveal patterns of nonverbal communication or group dynamics that might be difficult to capture in a laboratory setting.

Clinical psychology often employs case studies to delve into the complexities of mental health disorders. These detailed accounts can provide rich, contextual information about the lived experiences of individuals dealing with psychological challenges.

In educational psychology, descriptive research helps identify effective teaching strategies and learning patterns. Classroom observations and student surveys can inform educational policies and practices, ultimately improving learning outcomes.

Real-world examples of descriptive studies abound. Consider the famous “Bobo doll” experiments by Albert Bandura, which used observational methods to explore how children learn aggressive behaviors. While not strictly descriptive in nature, these studies incorporated descriptive elements that provided crucial insights into social learning theory.

Strengths and Limitations: A Balanced View

Like any research method, descriptive research has its strengths and limitations. On the plus side, it offers a level of ecological validity that’s hard to match in controlled experiments. By studying behavior in natural settings, researchers can capture the complexity and nuance of real-world phenomena.

Descriptive research is also particularly adept at identifying patterns and generating hypotheses. It’s often the first step in a longer research process, providing the foundation for more targeted experimental studies. This approach can be especially valuable when dealing with sensitive topics or populations that might be difficult to study in more controlled settings.

However, it’s important to acknowledge the limitations of descriptive research. One of the primary challenges is the directionality problem in psychology . While descriptive studies can identify relationships between variables, they can’t establish causation. This limitation can sometimes lead to misinterpretation of results or overreaching conclusions.

Another potential pitfall is researcher bias. The subjective nature of some descriptive methods, particularly observational studies, can introduce unintended biases into the data collection and interpretation process. Researchers must be vigilant in maintaining objectivity and employing strategies to minimize bias.

When compared to experimental research, descriptive studies may seem less rigorous or definitive. However, this perception overlooks the unique value that descriptive research brings to the table. While experiments are excellent for testing specific hypotheses and establishing causal relationships, they often lack the richness and contextual detail that descriptive methods provide.

Conducting a Descriptive Study: From Planning to Publication

Embarking on a descriptive research project requires careful planning and execution. Here’s a roadmap for aspiring researchers:

1. Define your research question: Start with a clear, focused question that guides your inquiry. What specific aspect of human behavior or cognition do you want to explore?

2. Choose your method: Select the descriptive technique(s) best suited to answer your research question. Will you be conducting surveys, observing behavior, or delving into case studies?

3. Develop your data collection tools: Create robust instruments for gathering information, whether it’s a well-designed questionnaire or a structured observation protocol.

4. Recruit participants: If your study involves human subjects, ensure you have a representative sample and obtain proper informed consent.

5. Collect data: Implement your chosen method(s) with consistency and attention to detail. Remember, the quality of your data will directly impact the value of your findings.

6. Analyze and interpret: Once you’ve gathered your data, it’s time to make sense of it. Look for patterns, themes, and relationships within your observations.

7. Draw conclusions: Based on your analysis, what can you say about the phenomenon you’ve studied? Be careful not to overstate your findings or imply causation where none has been established.

Throughout this process, it’s crucial to keep ethical considerations at the forefront. Respect for participants’ privacy, confidentiality, and well-being should guide every step of your research.

The Future of Descriptive Research: Evolving Methods and New Frontiers

As we look to the future, descriptive research in psychology continues to evolve and adapt to new challenges and opportunities. Emerging technologies are opening up exciting possibilities for data collection and analysis. For instance, wearable devices and smartphone apps are enabling researchers to gather real-time data on behavior and physiological responses in natural settings.

The rise of big data and advanced analytics is also transforming descriptive research. By analyzing vast datasets of human behavior online, researchers can identify patterns and trends on a scale previously unimaginable. However, this new frontier also brings ethical challenges, particularly around privacy and consent.

Another promising direction is the integration of descriptive methods with other research approaches. Quasi-experiments in psychology , which combine elements of descriptive and experimental research, offer a middle ground that can leverage the strengths of both approaches.

As we continue to unravel the complexities of the human mind, descriptive research will undoubtedly play a crucial role. Its ability to capture the richness and diversity of human experience makes it an indispensable tool in the psychologist’s toolkit.

In conclusion, descriptive research in psychology is far more than just a preliminary step in the scientific process. It’s a powerful approach that provides the foundation for our understanding of human behavior and mental processes. By offering detailed, contextual insights into the human experience, descriptive research helps us identify patterns, generate hypotheses, and ultimately advance our knowledge of psychology.

From exploring the intricacies of child development to unraveling the dynamics of social interactions, descriptive research continues to illuminate the vast landscape of human psychology. As we move forward, the challenge for researchers will be to harness new technologies and methodologies while maintaining the core strengths of descriptive approaches – their ability to capture the nuance, complexity, and diversity of human experience.

In the end, it’s this deep, rich understanding of human behavior that drives psychological science forward, informing theories, shaping interventions, and ultimately helping us to better understand ourselves and others. As we continue to explore the fascinating world of the human mind, descriptive research will remain an essential tool, helping us to see the world through the eyes of those we study and to tell their stories with clarity, empathy, and scientific rigor.

References:

1. Coolican, H. (2014). Research methods and statistics in psychology. Psychology Press.

2. Creswell, J. W., & Creswell, J. D. (2017). Research design: Qualitative, quantitative, and mixed methods approaches. Sage publications.

3. Goodwin, C. J., & Goodwin, K. A. (2016). Research in psychology: Methods and design. John Wiley & Sons.

4. Kazdin, A. E. (2011). Single-case research designs: Methods for clinical and applied settings. Oxford University Press.

5. Leedy, P. D., & Ormrod, J. E. (2015). Practical research: Planning and design. Pearson.

6. Marczyk, G., DeMatteo, D., & Festinger, D. (2005). Essentials of research design and methodology. John Wiley & Sons.

7. Mertens, D. M. (2014). Research and evaluation in education and psychology: Integrating diversity with quantitative, qualitative, and mixed methods. Sage publications.

8. Rosenthal, R., & Rosnow, R. L. (2008). Essentials of behavioral research: Methods and data analysis. McGraw-Hill.

9. Shaughnessy, J. J., Zechmeister, E. B., & Zechmeister, J. S. (2015). Research methods in psychology. McGraw-Hill Education.

10. Willig, C., & Rogers, W. S. (Eds.). (2017). The SAGE handbook of qualitative research in psychology. Sage.

Similar Posts

Psychology Qualifications: Essential Steps to Becoming a Licensed Professional

Unlocking the human mind’s complexities requires more than just a passion for understanding behavior; it demands a rigorous journey through education and training to become a licensed psychology professional. This path, while challenging, offers a rewarding career that allows individuals to make a profound impact on people’s lives. But what exactly does it take to…

Dark Humor Psychology: Unraveling the Appeal of Morbid Jokes

A morbid chuckle, a guilty grin—dark humor has long been a fascinating enigma, captivating minds and sparking debates about the fine line between wit and impropriety. It’s that uncomfortable laughter that bubbles up when we least expect it, often leaving us wondering, “Should I really be laughing at this?” But what is it about dark…

Psychology’s Power: Transforming Your Life Through Mental Health Insights

Diving into the mind’s vast potential, psychology emerges as a transformative force, empowering individuals to reshape their lives and unlock new realms of personal growth and well-being. It’s a field that has captivated the human imagination for centuries, offering insights into the intricate workings of our minds and behaviors. As we navigate the complexities of…

Metronome Uses in Psychology: Exploring Rhythmic Applications in Mental Health

From the steady ticking of a musician’s tool to the rhythmic heartbeat of psychological innovation, metronomes have found a new tempo in the realm of mental health. Who would have thought that this simple device, originally designed to keep musicians in time, could become a powerful instrument in the symphony of psychological well-being? It’s a…

Chaining Psychology: Unlocking Behavior Modification Techniques

Chaining psychology, a powerful yet often overlooked behavior modification tool, holds the key to unlocking the potential for lasting change and skill acquisition in various domains of life. This fascinating approach to learning and behavior modification has been quietly revolutionizing the way we understand and implement personal growth strategies. But what exactly is chaining psychology,…

Psychology of Repeating Yourself: Causes, Consequences, and Coping Strategies

From the annoying friend who won’t stop telling the same story to the politician rehashing talking points, repetitive speech patterns are a pervasive phenomenon that can strain even the most patient listener. We’ve all been there, caught in the verbal quicksand of someone who seems to be stuck on repeat. But what drives this behavior?…

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

Methods and formulas for Descriptive Statistics (Tables)

In this topic, standard deviation, n nonmissing, row percent, column percent, total percents.

The mean is the sum of all observations divided by the number of (non-missing) observations. Use the following formula to calculate the mean for each cell or margin using the data corresponding to that cell or margin.

The median is the middle value in an ordered data set. Thus, at least half the observations are less than or equal to the median, and at least half the observations are greater than or equal to the median.

If the number of observations in a data set is odd, the median is the value in the middle. If the number of observations in a data set is even, the median is the average of the two middle values.

The smallest data value that is in a table cell or margin.

The largest data value that is in a table cell or margin.

The sum is the total of all the data values that are in a table cell or margin.

The standard deviation is the most common measure of dispersion, or how spread out the data are about the mean. The more widely the values are spread out, the larger the standard deviation. The standard deviation is calculated by taking the square root of the variance.

Use this formula to calculate the standard deviation for each cell or margin using the data from that cell or margin.

The number of non-missing observations that are in a table cell or margin.

The number of missing observations that are in a table cell or margin.

The count is the number of times each combination of categories occurs.

The row percent is obtained by multiplying the ratio of a cell count to the corresponding row total by 100 and is given by:

The column percent is obtained by multiplying the ratio of a cell count to the corresponding column total by 100 and is given by:

The total percent is obtained by multiplying the ratio of a cell count to the total number of observations by 100 and is given by:

• Minitab.com
• License Portal
• Cookie Settings

You are now leaving support.minitab.com.

Click Continue to proceed to:

• School Guide
• Mathematics
• Number System and Arithmetic
• Trigonometry
• Probability
• Mensuration
• Maths Formulas
• Class 8 Maths Notes
• Class 9 Maths Notes
• Class 10 Maths Notes
• Class 11 Maths Notes
• Class 12 Maths Notes

Descriptive Statistics

Descriptive statistics is a subfield of statistics that deals with characterizing the features of known data. Descriptive statistics give summaries of either population or sample data. Aside from descriptive statistics, inferential statistics is another important discipline of statistics used to draw conclusions about population data.

Descriptive statistics is divided into two categories:

Measures of Central Tendency

Measures of dispersion.

In this article, we will learn about descriptive statistics, including their many categories, formulae, and examples in detail.

What is Descriptive Statistics?

Descriptive statistics is a branch of statistics focused on summarizing, organizing, and presenting data in a clear and understandable way. Its primary aim is to define and analyze the fundamental characteristics of a dataset without making sweeping generalizations or assumptions about the entire data set.

The main purpose of descriptive statistics is to provide a straightforward and concise overview of the data, enabling researchers or analysts to gain insights and understand patterns, trends, and distributions within the dataset.

Descriptive statistics typically involve measures of central tendency (such as mean, median, mode), dispersion (such as range, variance, standard deviation), and distribution shape (including skewness and kurtosis). Additionally, graphical representations like charts, graphs, and tables are commonly used to visualize and interpret the data.

Histograms, bar charts, pie charts, scatter plots, and box plots are some examples of widely used graphical techniques in descriptive statistics.

Descriptive Statistics Definition

Descriptive statistics is a type of statistical analysis that uses quantitative methods to summarize the features of a population sample. It is useful to present easy and exact summaries of the sample and observations using metrics such as mean, median, variance, graphs, and charts.

Types of Descriptive Statistics

There are three types of descriptive statistics:

Measures of Frequency Distribution

The central tendency is defined as a statistical measure that may be used to describe a complete distribution or dataset with a single value, known as a measure of central tendency. Any of the central tendency measures accurately describes the whole data distribution. In the following sections, we will look at the central tendency measures, their formulae, applications, and kinds in depth.

Mean is the sum of all the components in a group or collection divided by the number of items in that group or collection. Mean of a data collection is typically represented as x̄ (pronounced “x bar”). The formula for calculating the mean for ungrouped data to express it as the measure is given as follows:

For a series of observations:

x̄ = Σx / n

• x̄ = Mean Value of Provided Dataset
• Σx = Sum of All Terms
• n = Number of Terms

Example: Weights of 7 girls in kg are 54, 32, 45, 61, 20, 66 and 50. Determine the mean weight for the provided collection of data.

Mean = Σx/n = (54 + 32 + 45 + 61 + 20 + 66 + 50)/7 = 328 / 7 = 46.85 Thus, the group’s mean weight is 46.85 kg.

Median of a data set is the value of the middle-most observation obtained after organizing the data in ascending order, which is one of the measures of central tendency. Median formula may be used to compute the median for many types of data, such as grouped and ungrouped data.

Ungrouped Data Median (n is odd): [(n + 1)/2] th  term Ungrouped Data Median (n is even): [(n / 2) th  term + ((n / 2) + 1) th  term]/2

Example: Weights of 7 girls in kg are 54, 32, 45, 61, 20, 66 and 50. Determine the median weight for the provided collection of data.

Arrange the provided data collection in ascending order: 20, 32, 45, 50, 54, 61, 66 Median = [(n + 1) / 2] th  term = [(7 + 1) / 2] th  term = 4 th  term = 50 Thus, group’s median weight is 50 kg.

Mode is one of the measures of central tendency, defined as the value that appears the most frequently in the provided data, i.e. the observation with the highest frequency is known as the mode of data. The mode formulae provided below can be used to compute the mode for ungrouped data.

Mode of Ungrouped Data: Most Repeated Observation in Dataset

Example: Weights of 7 girls in kg are 54, 32, 45, 61, 20, 45 and 50. Determine the mode weight for the provided collection of data.

Mode = Most repeated observation in Dataset = 45 Thus, group’s mode weight is 45 kg.

If the variability of data within an experiment must be established, absolute measures of variability should be employed. These metrics often reflect differences in a data collection in terms of the average deviations of the observations. The most prevalent absolute measurements of deviation are mentioned below. In the following sections, we will look at the variability measures, their formulae in depth.

Standard Deviation

The range represents the spread of your data from the lowest to the highest value in the distribution. It is the most straightforward measure of variability to compute. To get the range, subtract the data set’s lowest and highest values.

Range = Highest Value – Lowest Value

Example: Calculate the range of the following data series:  5, 13, 32, 42, 15, 84

Arrange the provided data series in ascending order: 5, 13, 15, 32, 42, 84 Range = H – L = 84 – 5 = 79 So, the range is 79.

Standard deviation (s or SD) represents the average level of variability in your dataset. It represents the average deviation of each score from the mean. The higher the standard deviation, the more varied the dataset is.

To calculate standard deviation, follow these six steps:

Step 1: Make a list of each score and calculate the mean.

Step 2: Calculate deviation from the mean, by subtracting the mean from each score.

Step 3: Square each of these differences.

Step 4: Sum up all squared variances.

Step 5: Divide the total of squared variances by N-1.

Step 6: Find the square root of the number that you discovered.

Example: Calculate standard deviation of the following data series:  5, 13, 32, 42, 15, 84.

Step 1: First we have to calculate the mean of following series using formula: Σx / n

Step 2: Now calculate the deviation from mean, subtract the mean from each series.

Step 3: Squared the deviation from mean and then add all the deviation.

Step 4: Divide the squared deviation with N-1 => 4182.84 / 5 = 836.57

Step 5: √836.57 = 28.92

So, the standard deviation is 28.92

Variance is calculated as average of squared departures from the mean. Variance measures the degree of dispersion in a data collection. The more scattered the data, the larger the variance in relation to the mean. To calculate the variance, square the standard deviation.

Symbol for variance is s 2

Example: Calculate the variance of the following data series:  5, 13, 32, 42, 15, 84.

First we have to calculate the standard deviation, that we calculate above i.e. SD = 28.92 s 2 = (SD) 2 = (28.92) 2 = 836.37 So, the variance is 836.37

Mean Deviation

Mean Deviation  is used to find the average of the absolute value of the data about the mean, median, or mode. Mean Deviation is some times also known as absolute deviation. The formula mean deviation is given as follows:

Mean Deviation = ∑ n 1 |X – μ|/n

•   μ is Central Value

Quartile Deviation

Quartile Deviation is the Half of difference between the third and first quartile. The formula for quartile deviation is given as follows:

Quartile Deviation = (Q 3 − Q 1 )/2

•   Q 3 is Third Quartile
• Q 1 is First Quartile

Other measures of dispersion include the relative measures also known as the coefficients of dispersion.

Datasets consist of various scores or values. Statisticians employ graphs and tables to summarize the occurrence of each possible value of a variable, often presented in percentages or numerical figures.

For instance, suppose you were conducting a poll to determine people’s favorite Beatles. You would create one column listing all potential options (John, Paul, George, and Ringo) and another column indicating the number of votes each received. Statisticians represent these frequency distributions through graphs or tables

Univariate Descriptive Statistics

Univariate descriptive statistics focus on one thing at a time. We look at each thing individually and use different ways to understand it better. Programs like SPSS and Excel can help us with this.

If we only look at the average (mean) of something, like how much people earn, it might not give us the true picture, especially if some people earn a lot more or less than others. Instead, we can also look at other things like the middle value (median) or the one that appears most often (mode). And to understand how spread out the values are, we use things like standard deviation and variance along with the range.

Bivariate Descriptive Statistics

When we have information about more than one thing, we can use bivariate or multivariate descriptive statistics to see if they are related. Bivariate analysis compares two things to see if they change together. Before doing any more complicated tests, it’s important to look at how the two things compare in the middle.

Multivariate analysis is similar to bivariate analysis, but it looks at more than two things at once, which helps us understand relationships even better.

Representations of Data in Descriptive Statistics

Descriptive statistics use a variety of ways to summarize and present data in an understandable manner. This helps us grasp the data set’s patterns, trends, and properties.

Frequency Distribution Tables: Frequency distribution tables divide data into categories or intervals and display the number of observations (frequency) that fall into each one. For example, suppose we have a class of 20 students and are tracking their test scores. We may make a frequency distribution table that contains score ranges (e.g., 0-10, 11-20) and displays how many students scored in each range.

Graphs and Charts: Graphs and charts graphically display data, making it simpler to understand and analyze. For example, using the same test score data, we may generate a bar graph with the x-axis representing score ranges and the y-axis representing the number of students. Each bar on the graph represents a score range, and its height shows the number of students scoring within that range.

These approaches help us summarize and visualize data, making it easier to discover trends, patterns, and outliers, which is critical for making informed decisions and reaching meaningful conclusions in a variety of sectors.

Descriptive Statistics Applications

Descriptive statistics are used in a variety of sectors to summarize, organize, and display data in a meaningful and intelligible way. Here are a few popular applications:

• Business and Economics: Descriptive statistics are useful for analyzing sales data, market trends, and customer behaviour. They are used to generate averages, medians, and standard deviations in order to better evaluate product performance, pricing strategies, and financial metrics.
• Healthcare: Descriptive statistics are used to analyze patient data such as demographics, medical histories, and treatment outcomes. They assist healthcare workers in determining illness prevalence, assessing treatment efficacy, and identifying risk factors.
• Education: Descriptive statistics are useful in education since they summarize student performance on tests and examinations. They assist instructors in assessing instructional techniques, identifying areas for improvement, and monitoring student growth over time.
• Market Research: Descriptive statistics are used to analyze customer preferences, product demand, and market trends. They enable businesses to make educated decisions about product development, advertising campaigns, and market segmentation.
• Finance and investment: Descriptive statistics are used to analyze stock market data, portfolio performance, and risk management. They assist investors in determining investment possibilities, tracking asset values, and evaluating financial instruments.

Difference Between Descriptive Statistics and Inferential Statistics

Difference between Descriptive Statistics and Inferential Statistics is studied using the table added below as,

Example of Descriptive Statistics Examples

Example 1: Calculate the Mean, Median and Mode for the following series: {4, 8, 9, 10, 6, 12, 14, 4, 5, 3, 4}

First, we are going to calculate the mean. Mean = Σx / n = (4 + 8 + 9 + 10 + 6 + 12 + 14 + 4 + 5 + 3 + 4)/11 = 79 / 11 = 7.1818 Thus, the Mean is 7.1818. Now, we are going to calculate the median. Arrange the provided data collection in ascending order: 3, 4, 4, 4, 5, 6, 8, 9, 10, 12, 14 Median = [(n + 1) / 2] th  term = [(11 + 1) / 2] th  term = 6 th  term = 6 Thus, the median is 6. Now, we are going to calculate the mode. Mode = The most repeated observation in the dataset = 4 Thus, the mode is 4.

Example 2: Calculate the Range for the following series: {4, 8, 9, 10, 6, 12, 14, 4, 5, 3, 4}

Arrange the provided data series in ascending order: 3, 4, 4, 4, 5, 6, 8, 9, 10, 12, 14 Range = H – L = 14 – 3 = 11 So, the range is 11.

Example 3: Calculate the standard deviation and variance of following data: {12, 24, 36, 48, 10, 18}

First we are going to compute standard deviation. For standard deviation calculate the mean, deviation from mean and squared deviation.

Dividing squared deviation with N-1 => 1093.351 / 5 = 218.67

√(218.67) = 14.79

So, the standard deviation is 14.79.

Now we are going to calculate the variance.

s 2 = 218.744

So, the variance is 218.744

Practice Problems on Descriptive Statistics

P1) Determine the sample variance of the following series: {17, 21, 52, 28, 26, 23}

P2) Determine the mean and mode of the following series: {21, 14, 56, 41, 18, 15, 18, 21, 15, 18}

P3) Find the median of the following series: {7, 24, 12, 8, 6, 23, 11}

P4) Find the standard deviation and variance of the following series: {17, 28, 42, 48, 36, 42, 20}

FAQs of Descriptive Statistics

What is meant by descriptive statistics.

Descriptive statistics seek to summarize, organize, and display data in an accessible manner while avoiding making sweeping generalizations about the whole population. It aids in discovering patterns, trends, and distributions within the collection.

How is the mean computed in descriptive statistics?

Mean is computed by adding together all of the values in the dataset and dividing them by the total number of observations. It measures the dataset’s central tendency or average value.

What role do measures of variability play in descriptive statistics?

Measures of variability, such as range, standard deviation, and variance, aid in quantifying the spread or dispersion of data points around the mean. They give insights on the dataset’s variety and consistency.

Can you explain the median in descriptive statistics?

The median is the midpoint value of a dataset whether sorted ascending or descending. It measures central tendency and is important when dealing with skewed data or outliers.

How can frequency distribution measurements contribute to descriptive statistics?

Measures of frequency distribution summarize the incidence of various values or categories within a dataset. They give insights into the distribution pattern of the data and are commonly represented by graphs or tables.

How are inferential statistics distinguished from descriptive statistics?

Inferential statistics use sample data to draw inferences or make predictions about a wider population, whereas descriptive statistics summarize aspects of known data. Descriptive statistics concentrate on the present dataset, whereas inferential statistics go beyond the observable data.

Why are descriptive statistics necessary in data analysis?

Descriptive statistics give researchers and analysts a clear and straightforward summary of the dataset, helping them to identify patterns, trends, and distributions. It aids in making educated judgements and gaining valuable insights from data.

What are the four types of descriptive statistics?

There are four major types of descriptive statistics: Measures of Frequency Measures of Central Tendency Measures of Dispersion or Variation Measures of Position

Which is an example of descriptive statistics?

Descriptive statistics examples include the study of mean, median, and mode.

Please Login to comment...

Similar reads.

• School Learning
• Math-Statistics
• OpenAI o1 AI Model Launched: Explore o1-Preview, o1-Mini, Pricing & Comparison
• How to Merge Cells in Google Sheets: Step by Step Guide
• How to Lock Cells in Google Sheets : Step by Step Guide
• PS5 Pro Launched: Controller, Price, Specs & Features, How to Pre-Order, and More
• #geekstreak2024 – 21 Days POTD Challenge Powered By Deutsche Bank

Improve your Coding Skills with Practice

What kind of Experience do you want to share?

• Skip to main content
• Skip to primary sidebar
• Skip to footer
• QuestionPro

• Solutions Industries Gaming Automotive Sports and events Education Government Travel & Hospitality Financial Services Healthcare Cannabis Technology Use Case AskWhy Communities Audience Contactless surveys Mobile LivePolls Member Experience GDPR Positive People Science 360 Feedback Surveys
• Resources Blog eBooks Survey Templates Case Studies Training Help center

Home Market Research

Descriptive Research: Definition, Characteristics, Methods + Examples

Suppose an apparel brand wants to understand the fashion purchasing trends among New York’s buyers, then it must conduct a demographic survey of the specific region, gather population data, and then conduct descriptive research on this demographic segment.

The study will then uncover details on “what is the purchasing pattern of New York buyers,” but will not cover any investigative information about “ why ” the patterns exist. Because for the apparel brand trying to break into this market, understanding the nature of their market is the study’s main goal. Let’s talk about it.

What is descriptive research?

Descriptive research is a research method describing the characteristics of the population or phenomenon studied. This descriptive methodology focuses more on the “what” of the research subject than the “why” of the research subject.

The method primarily focuses on describing the nature of a demographic segment without focusing on “why” a particular phenomenon occurs. In other words, it “describes” the research subject without covering “why” it happens.

Characteristics of descriptive research

The term descriptive research then refers to research questions, the design of the study, and data analysis conducted on that topic. We call it an observational research method because none of the research study variables are influenced in any capacity.

Some distinctive characteristics of descriptive research are:

• Quantitative research: It is a quantitative research method that attempts to collect quantifiable information for statistical analysis of the population sample. It is a popular market research tool that allows us to collect and describe the demographic segment’s nature.
• Uncontrolled variables: In it, none of the variables are influenced in any way. This uses observational methods to conduct the research. Hence, the nature of the variables or their behavior is not in the hands of the researcher.
• Cross-sectional studies: It is generally a cross-sectional study where different sections belonging to the same group are studied.
• The basis for further research: Researchers further research the data collected and analyzed from descriptive research using different research techniques. The data can also help point towards the types of research methods used for the subsequent research.

Applications of descriptive research with examples

A descriptive research method can be used in multiple ways and for various reasons. Before getting into any survey , though, the survey goals and survey design are crucial. Despite following these steps, there is no way to know if one will meet the research outcome. How to use descriptive research? To understand the end objective of research goals, below are some ways organizations currently use descriptive research today:

• Define respondent characteristics: The aim of using close-ended questions is to draw concrete conclusions about the respondents. This could be the need to derive patterns, traits, and behaviors of the respondents. It could also be to understand from a respondent their attitude, or opinion about the phenomenon. For example, understand millennials and the hours per week they spend browsing the internet. All this information helps the organization researching to make informed business decisions.
• Measure data trends: Researchers measure data trends over time with a descriptive research design’s statistical capabilities. Consider if an apparel company researches different demographics like age groups from 24-35 and 36-45 on a new range launch of autumn wear. If one of those groups doesn’t take too well to the new launch, it provides insight into what clothes are like and what is not. The brand drops the clothes and apparel that customers don’t like.
• Conduct comparisons: Organizations also use a descriptive research design to understand how different groups respond to a specific product or service. For example, an apparel brand creates a survey asking general questions that measure the brand’s image. The same study also asks demographic questions like age, income, gender, geographical location, geographic segmentation , etc. This consumer research helps the organization understand what aspects of the brand appeal to the population and what aspects do not. It also helps make product or marketing fixes or even create a new product line to cater to high-growth potential groups.
• Validate existing conditions: Researchers widely use descriptive research to help ascertain the research object’s prevailing conditions and underlying patterns. Due to the non-invasive research method and the use of quantitative observation and some aspects of qualitative observation , researchers observe each variable and conduct an in-depth analysis . Researchers also use it to validate any existing conditions that may be prevalent in a population.
• Conduct research at different times: The analysis can be conducted at different periods to ascertain any similarities or differences. This also allows any number of variables to be evaluated. For verification, studies on prevailing conditions can also be repeated to draw trends.

Advantages of descriptive research

Some of the significant advantages of descriptive research are:

• Data collection: A researcher can conduct descriptive research using specific methods like observational method, case study method, and survey method. Between these three, all primary data collection methods are covered, which provides a lot of information. This can be used for future research or even for developing a hypothesis for your research object.
• Varied: Since the data collected is qualitative and quantitative, it gives a holistic understanding of a research topic. The information is varied, diverse, and thorough.
• Natural environment: Descriptive research allows for the research to be conducted in the respondent’s natural environment, which ensures that high-quality and honest data is collected.
• Quick to perform and cheap: As the sample size is generally large in descriptive research, the data collection is quick to conduct and is inexpensive.

Descriptive research methods

There are three distinctive methods to conduct descriptive research. They are:

Observational method

The observational method is the most effective method to conduct this research, and researchers make use of both quantitative and qualitative observations.

A quantitative observation is the objective collection of data primarily focused on numbers and values. It suggests “associated with, of or depicted in terms of a quantity.” Results of quantitative observation are derived using statistical and numerical analysis methods. It implies observation of any entity associated with a numeric value such as age, shape, weight, volume, scale, etc. For example, the researcher can track if current customers will refer the brand using a simple Net Promoter Score question .

Qualitative observation doesn’t involve measurements or numbers but instead just monitoring characteristics. In this case, the researcher observes the respondents from a distance. Since the respondents are in a comfortable environment, the characteristics observed are natural and effective. In a descriptive research design, the researcher can choose to be either a complete observer, an observer as a participant, a participant as an observer, or a full participant. For example, in a supermarket, a researcher can from afar monitor and track the customers’ selection and purchasing trends. This offers a more in-depth insight into the purchasing experience of the customer.

Case study method

Case studies involve in-depth research and study of individuals or groups. Case studies lead to a hypothesis and widen a further scope of studying a phenomenon. However, case studies should not be used to determine cause and effect as they can’t make accurate predictions because there could be a bias on the researcher’s part. The other reason why case studies are not a reliable way of conducting descriptive research is that there could be an atypical respondent in the survey. Describing them leads to weak generalizations and moving away from external validity.

Survey research

In survey research, respondents answer through surveys or questionnaires or polls . They are a popular market research tool to collect feedback from respondents. A study to gather useful data should have the right survey questions. It should be a balanced mix of open-ended questions and close ended-questions . The survey method can be conducted online or offline, making it the go-to option for descriptive research where the sample size is enormous.

Examples of descriptive research

Some examples of descriptive research are:

• A specialty food group launching a new range of barbecue rubs would like to understand what flavors of rubs are favored by different people. To understand the preferred flavor palette, they conduct this type of research study using various methods like observational methods in supermarkets. By also surveying while collecting in-depth demographic information, offers insights about the preference of different markets. This can also help tailor make the rubs and spreads to various preferred meats in that demographic. Conducting this type of research helps the organization tweak their business model and amplify marketing in core markets.
• Another example of where this research can be used is if a school district wishes to evaluate teachers’ attitudes about using technology in the classroom. By conducting surveys and observing their comfortableness using technology through observational methods, the researcher can gauge what they can help understand if a full-fledged implementation can face an issue. This also helps in understanding if the students are impacted in any way with this change.

Some other research problems and research questions that can lead to descriptive research are:

• Market researchers want to observe the habits of consumers.
• A company wants to evaluate the morale of its staff.
• A school district wants to understand if students will access online lessons rather than textbooks.
• To understand if its wellness questionnaire programs enhance the overall health of the employees.

LEARN MORE         FREE TRIAL

MORE LIKE THIS

Participant Engagement: Strategies + Improving Interaction

Sep 12, 2024

Employee Recognition Programs: A Complete Guide

Sep 11, 2024

A guide to conducting agile qualitative research for rapid insights with Digsite 

Cultural Insights: What it is, Importance + How to Collect?

Sep 10, 2024

Other categories

• Academic Research
• Artificial Intelligence
• Assessments
• Brand Awareness
• Case Studies
• Communities
• Consumer Insights
• Customer effort score
• Customer Engagement
• Customer Experience
• Customer Loyalty
• Customer Research
• Customer Satisfaction
• Employee Benefits
• Employee Engagement
• Employee Retention
• Friday Five
• General Data Protection Regulation
• Insights Hub
• Life@QuestionPro
• Market Research
• Mobile diaries
• Mobile Surveys
• New Features
• Online Communities
• Question Types
• Questionnaire
• QuestionPro Products
• Release Notes
• Research Tools and Apps
• Revenue at Risk
• Survey Templates
• Training Tips
• Tuesday CX Thoughts (TCXT)
• Uncategorized
• What’s Coming Up
• Workforce Intelligence

Once the data has been coded and double-checked, the next step is to calculate Descriptive Statistics. The three main types of descriptive statistics are frequencies, measures of central tendency (also called averages), and measures of variability. Frequency statistics simply count the number of times that each variable occurs, such as the number of males and females within the sample. Measures of central tendency give one number that represents the entire set of scores, such as the mean. Measures of variability indicate the degree to which scores differ around the average.

Descriptive research designs typically only require descriptive statistics. However, all other types of research designs will require both descriptive and inferential statistics. Since it is important for the reader to have a good understanding of the sample that the study was conducted on, the first statistics for all research designs should include descriptive statistics of the personal information for the sample. The types of personal information to be included will vary depending on the type of research study. All studies should report descriptive statistics on gender and age. Other variables might include grade level, marital status, years of work experience, educational qualifications, socio-economic status, etc. It is up to the researcher to thoughtfully consider what the reader needs to know about the sample to make an informed decision about whether the sample is representative of the overall population.

Frequency and percentage statistics should be used to represent most personal information variables. However, if participants reported their exact age, then the mean and standard deviation should be calculated for the age variable. Frequency statistics should be reported whenever the data is discrete, meaning that there are separate categories that the participant can tick. For example, marital status can have categories of single, married, divorced, widowed, and separated. Educational qualifications can have categories of secondary school, diploma, degree, post-graduate diploma, masters, and doctorate.

However, measures of central tendency and variability should be reported for variables that have continuous data, meaning that the scores can vary along a continuum of numbers. For example, age is on a continuum from 0 to 100 or so, academic achievement generally varies from 0 to 100, and number of pages a student reads in a week can vary from 0 to maybe 300. These are all continuous variables, so a measure of central tendency and variability should be reported to represent these variables.

Recall that a frequency is simply the number of participants who indicated that category (aka "Male"). However, it is oftentimes difficult to interpret frequency distributions because the frequency by itself is meaningless unless there is a reference point to interpret the number. Percentages are easier to understand than frequencies because the percentage can be interpreted as follows. Imagine there were exactly 100 participants in the sample. How many participants out of those 100 would fall in that category? In Table 3, if there were 100 participants in the study, 55 would be female. Percentage is calculated by taking the frequency in the category divided by the total number of participants and multiplying by 100%. To calculate the percentage of males in Table 3, take the frequency for males (80) divided by the total number in the sample (200). Then take this number times 100%, resulting in 40%. At this point, a simple table with the frequency and Percentage of personal information variables will suffice. In the Tables and Figures page, I will describe how to convert these tables into APA format or graphically represent it in a figure.

Once descriptive statistics for the personal information have been calculated, then it is time to move onto the variables under study. In most cases, a total score for each variable will have been calculated in the previous step, Coding the Data . APA standards require that researchers report descriptive statistics on the major variables under study, even for studies that will use inferential statistics, so the nature of any effect can be understood by the reader. This means that all research studies must report the mean and standard deviation for all variables under study. The mean is necessary to summarize that variable across all participants; the standard deviation is necessary to understand how much each participant varies around that mean.

At the moment, it is enough to calculate the mean and standard deviation and combine them all in one table. If a causal-comparative design is used that compares two or more groups on these variables (aka compares males and females on academic achievement), then it is necessary to calculate the mean and standard deviation separately for each group. If a pre- post-test design is used, then the mean and standard deviation will need to be calculated separately for the pre-test and the post-test. Table 4 gives the means and standard deviations for a study that compares teachers in private and public schools on three variables associated with early literacy practices. Recall that the mean is calculated by summing the scores, and then dividing this sum by the number of scores. Calculating the standard deviation is a bit more complicated. Microsoft Excel will quickly and automatically calculate each statistic using the =average and =stdev functions. For examples of how to calculate frequencies, averages, and variation by hand, click here .

When reporting frequencies, do not add any places after the decimal point; only report whole numbers. When reporting percentages, means, and standard deviations, typically include two decimal points.

At this point, we cannot say that there is a significant difference between Public or Private school teachers on any of these variables. There will always be differences between scores for different groups of people. Inferential statistics are necessary to determine whether these differences are big enough to be considered significant. In other words, to determine if the differences between groups are large enough to say that there is any meaningful difference between the two, one must calculate an inferential statistic, described in the next chapter.

If a research study has Research Questions, then either a percentage or a mean will likely be calculated to answer the research question. Once the descriptive statistics for the personal information and key variables have been calculated, then it is time to answer any research questions. Refer to the Research Questions that were developed. Calculate the appropriate statistic to answer each research question separately. Refer to the Methods of Data Analysis to determine which statistics should be calculated to answer each research question.

Again, it is very important that the researcher is very careful when calculating statistics to avoid careless errors. Incorrect calculations can lead a researcher to draw incorrect conclusions, making the study invalid and untrue. Therefore, check every calculation multiple times in order to maintain the highest ethical standards in research.

For a step-by-step example of a descriptive research study and how to calculate descriptive statistics, click here .

Copyright 2013, Katrina A. Korb, All Rights Reserved

• Search Search Please fill out this field.

What Are Descriptive Statistics?

• How They Work

Univariate vs. Bivariate

Descriptive statistics and visualizations, descriptive statistics and outliers.

• Descriptive vs. Inferential

The Bottom Line

• Corporate Finance
• Financial Analysis

Descriptive Statistics: Definition, Overview, Types, and Examples

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and behavioral finance. Adam received his master's in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology. He is a CFA charterholder as well as holding FINRA Series 7, 55 & 63 licenses. He currently researches and teaches economic sociology and the social studies of finance at the Hebrew University in Jerusalem.

Descriptive statistics are brief informational coefficients that summarize a given data set, which can be either a representation of the entire population or a sample of a population. Descriptive statistics are broken down into measures of central tendency and measures of variability (spread). Measures of central tendency include the mean , median , and mode , while measures of variability include standard deviation , variance , minimum and maximum variables, kurtosis , and skewness .

Key Takeaways

• Descriptive statistics summarizes or describes the characteristics of a data set.
• Descriptive statistics consists of three basic categories of measures: measures of central tendency, measures of variability (or spread), and frequency distribution.
• Measures of central tendency describe the center of the data set (mean, median, mode).
• Measures of variability describe the dispersion of the data set (variance, standard deviation).
• Measures of frequency distribution describe the occurrence of data within the data set (count).

Jessica Olah

Understanding Descriptive Statistics

Descriptive statistics help describe and explain the features of a specific data set by giving short summaries about the sample and measures of the data. The most recognized types of descriptive statistics are measures of center. For example, the mean, median, and mode, which are used at almost all levels of math and statistics, are used to define and describe a data set. The mean, or the average, is calculated by adding all the figures within the data set and then dividing by the number of figures within the set.

For example, the sum of the following data set is 20: (2, 3, 4, 5, 6). The mean is 4 (20/5). The mode of a data set is the value appearing most often, and the median is the figure situated in the middle of the data set. It is the figure separating the higher figures from the lower figures within a data set. However, there are less common types of descriptive statistics that are still very important.

People use descriptive statistics to repurpose hard-to-understand quantitative insights across a large data set into bite-sized descriptions. A student's grade point average (GPA), for example, provides a good understanding of descriptive statistics. The idea of a GPA is that it takes data points from a range of individual course grades, and averages them together to provide a general understanding of a student's overall academic performance. A student's personal GPA reflects their mean academic performance.

Descriptive statistics, especially in fields such as medicine, often visually depict data using scatter plots, histograms, line graphs, or stem and leaf displays. We'll talk more about visuals later in this article.

Types of Descriptive Statistics

All descriptive statistics are either measures of central tendency or measures of variability , also known as measures of dispersion.

Central Tendency

Measures of central tendency focus on the average or middle values of data sets, whereas measures of variability focus on the dispersion of data. These two measures use graphs, tables, and general discussions to help people understand the meaning of the analyzed data.

Measures of central tendency describe the center position of a distribution for a data set. A person analyzes the frequency of each data point in the distribution and describes it using the mean, median, or mode, which measures the most common patterns of the analyzed data set.

Measures of Variability

Measures of variability (or measures of spread) aid in analyzing how dispersed the distribution is for a set of data. For example, while the measures of central tendency may give a person the average of a data set, it does not describe how the data is distributed within the set.

So while the average of the data might be 65 out of 100, there can still be data points at both 1 and 100. Measures of variability help communicate this by describing the shape and spread of the data set. Range, quartiles , absolute deviation, and variance are all examples of measures of variability.

Consider the following data set: 5, 19, 24, 62, 91, 100. The range of that data set is 95, which is calculated by subtracting the lowest number (5) in the data set from the highest (100).

Distribution

Distribution (or frequency distribution) refers to the number of times a data point occurs. Alternatively, it can be how many times a data point fails to occur. Consider this data set: male, male, female, female, female, other. The distribution of this data can be classified as:

• The number of males in the data set is 2.
• The number of females in the data set is 3.
• The number of individuals identifying as other is 1.
• The number of non-males is 4.

In descriptive statistics, univariate data analyzes only one variable. It is used to identify characteristics of a single trait and is not used to analyze any relationships or causations.

For example, imagine a room full of high school students. Say you wanted to gather the average age of the individuals in the room. This univariate data is only dependent on one factor: each person's age. By gathering this one piece of information from each person and dividing by the total number of people, you can determine the average age.

Bivariate data, on the other hand, attempts to link two variables by searching for correlation. Two types of data are collected, and the relationship between the two pieces of information is analyzed together. Because multiple variables are analyzed, this approach may also be referred to as multivariate .

Let's say each high school student in the example above takes a college assessment test, and we want to see whether older students are testing better than younger students. In addition to gathering the ages of the students, we need to find out each student's test score. Then, using data analytics, we mathematically or graphically depict whether there is a relationship between student age and test scores.

The preparation and reporting of financial statements is an example of descriptive statistics. Analyzing that financial information to make decisions on the future is inferential statistics.

One essential aspect of descriptive statistics is graphical representation. Visualizing data distributions effectively can be incredibly powerful, and this is done in several ways.

Histograms are tools for displaying the distribution of numerical data. They divide the data into bins or intervals and represent the frequency or count of data points falling into each bin through bars of varying heights. Histograms help identify the shape of the distribution, central tendency, and variability of the data.

Another visualization is boxplots. Boxplots, also known as box-and-whisker plots, provide a concise summary of a data distribution by highlighting key summary statistics including the median (middle line inside the box), quartiles (edges of the box), and potential outliers (points outside, or the "whiskers"). Boxplots visually depict the spread and skewness of the data and are particularly useful for comparing distributions across different groups or variables.

Whenever descriptive statistics are being discussed, it's important to note outliers. Outliers are data points that significantly differ from other observations in a dataset. These could be errors, anomalies, or rare events within the data.

Detecting and managing outliers is a step in descriptive statistics to ensure accurate and reliable data analysis. To identify outliers, you can use graphical techniques (such as boxplots or scatter plots) or statistical methods (such as Z-score or IQR method). These approaches help pinpoint observations that deviate substantially from the overall pattern of the data.

The presence of outliers can have a notable impact on descriptive statistics, skewing results and affecting the interpretation of data. Outliers can disproportionately influence measures of central tendency, such as the mean, pulling it towards their extreme values. For example, the dataset of (1, 1, 1, 997) is 250, even though that is hardly representative of the dataset. This distortion can lead to misleading conclusions about the typical behavior of the dataset.

Depending on the context, outliers can often be treated by removing them (if they are genuinely erroneous or irrelevant). Alternatively, outliers may hold important information and should be kept for the value they may be able to demonstrate. As you analyze your data, consider the relevance of what outliers can contribute and whether it makes more sense to just strike those data points from your descriptive statistic calculations.

Descriptive Statistics vs. Inferential Statistics

Descriptive statistics have a different function from inferential statistics, which are data sets that are used to make decisions or apply characteristics from one data set to another.

Imagine another example where a company sells hot sauce. The company gathers data such as the count of sales , average quantity purchased per transaction , and average sale per day of the week. All of this information is descriptive, as it tells a story of what actually happened in the past. In this case, it is not being used beyond being informational.

Now let's say that the company wants to roll out a new hot sauce. It gathers the same sales data above, but it uses the information to make predictions about what the sales of the new hot sauce will be. The act of using descriptive statistics and applying characteristics to a different data set makes the data set inferential statistics. We are no longer simply summarizing data; we are using it to predict what will happen regarding an entirely different body of data (in this case, the new hot sauce product).

What Is Descriptive Statistics?

Descriptive statistics is a means of describing features of a data set by generating summaries about data samples. For example, a population census may include descriptive statistics regarding the ratio of men and women in a specific city.

What Are Examples of Descriptive Statistics?

In recapping a Major League Baseball season, for example, descriptive statistics might include team batting averages, the number of runs allowed per team, and the average wins per division.

What Is the Main Purpose of Descriptive Statistics?

The main purpose of descriptive statistics is to provide information about a data set. In the example above, there are dozens of baseball teams, hundreds of players, and thousands of games. Descriptive statistics summarizes large amounts of data into useful bits of information.

What Are the Types of Descriptive Statistics?

The three main types of descriptive statistics are frequency distribution, central tendency, and variability of a data set. The frequency distribution records how often data occurs, central tendency records the data's center point of distribution, and variability of a data set records its degree of dispersion.

Can Descriptive Statistics Be Used to Make Inferences or Predictions?

Technically speaking, descriptive statistics only serves to help understand historical data attributes. Inferential statistics—a separate branch of statistics—is used to understand how variables interact with one another in a data set and possibly predict what might happen in the future.

Descriptive statistics refers to the analysis, summary, and communication of findings that describe a data set. Often not useful for decision-making, descriptive statistics still hold value in explaining high-level summaries of a set of information such as the mean, median, mode, variance, range, and count of information.

Purdue Online Writing Lab. " Writing with Statistics: Descriptive Statistics ."

National Library of Medicine. " Descriptive Statistics for Summarizing Data ."

CSUN.edu. " Measures of Variability, Descriptive Statistics Part 2 ."

Math.Kent.edu. " Summary: Differences Between Univariate and Bivariate Data ."

Purdue Online Writing Lab. " Writing with Statistics: Basic Inferential Statistics: Theory and Application ."

• Terms of Service
• Editorial Policy
• Privacy Policy

Want to create or adapt books like this? Learn more about how Pressbooks supports open publishing practices.

Chapter 1. Descriptive Statistics and Frequency Distributions

This chapter is about describing populations and samples, a subject known as descriptive statistics. This will all make more sense if you keep in mind that the information you want to produce is a description of the population or sample as a whole, not a description of one member of the population. The first topic in this chapter is a discussion of distributions , essentially pictures of populations (or samples). Second will be the discussion of descriptive statistics. The topics are arranged in this order because the descriptive statistics can be thought of as ways to describe the picture of a population, the distribution.

Distributions

The first step in turning data into information is to create a distribution. The most primitive way to present a distribution is to simply list, in one column, each value that occurs in the population and, in the next column, the number of times it occurs. It is customary to list the values from lowest to highest. This simple listing is called a frequency distribution . A more elegant way to turn data into information is to draw a graph of the distribution. Customarily, the values that occur are put along the horizontal axis and the frequency of the value is on the vertical axis.

Ann is the equipment manager for the Chargers athletic teams at Camosun College, located in Victoria, British Columbia. She called the basketball and volleyball team managers and collected the following data on sock sizes used by their players. Ann found out that last year the basketball team used 14 pairs of size 7 socks, 18 pairs of size 8, 15 pairs of size 9, and 6 pairs of size 10 were used. The volleyball team used 3 pairs of size 6, 10 pairs of size 7, 15 pairs of size 8, 5 pairs of size 9, and 11 pairs of size 10. Ann arranged her data into a distribution and then drew a graph called a histogram. Ann could have created a relative frequency distribution as well as a frequency distribution. The difference is that instead of listing how many times each value occurred, Ann would list what proportion of her sample was made up of socks of each size.

You can use the Excel template below (Figure 1.1) to see all the histograms and frequencies she has created. You may also change her numbers in the yellow cells to see how the graphs will change automatically.

Notice that Ann has drawn the graphs differently. In the first graph, she has used bars for each value, while on the second, she has drawn a point for the relative frequency of each size, and then “connected the dots”. While both methods are correct, when you have values that are continuous, you will want to do something more like the “connect the dots” graph. Sock sizes are discrete , they only take on a limited number of values. Other things have continuous values; they can take on an infinite number of values, though we are often in the habit of rounding them off. An example is how much students weigh. While we usually give our weight in whole kilograms in Canada (“I weigh 60 kilograms”), few have a weight that is exactly so many kilograms. When you say “I weigh 60”, you actually mean that you weigh between 59 1/2 and 60 1/2 kilograms. We are heading toward a graph of a distribution of a continuous variable where the relative frequency of any exact value is very small, but the relative frequency of observations between two values is measurable. What we want to do is to get used to the idea that the total area under a “connect the dots” relative frequency graph, from the lowest to the highest possible value, is one. Then the part of the area under the graph between two values is the relative frequency of observations with values within that range. The height of the line above any particular value has lost any direct meaning, because it is now the area under the line between two values that is the relative frequency of an observation between those two values occurring.

You can get some idea of how this works if you go back to the bar graph of the distribution of sock sizes, but draw it with relative frequency on the vertical axis. If you arbitrarily decide that each bar has a width of one, then the area under the curve between 7.5 and 8.5 is simply the height times the width of the bar for sock size 8: .3510*1 . If you wanted to find the relative frequency of sock sizes between 6.5 and 8.5, you could simply add together the area of the bar for size 7 (that’s between 6.5 and 7.5) and the bar for size 8 (between 7.5 and 8.5).

Descriptive statistics

Now that you see how a distribution is created, you are ready to learn how to describe one. There are two main things that need to be described about a distribution: its location and its shape. Generally, it is best to give a single measure as the description of the location and a single measure as the description of the shape.

To describe the location of a distribution, statisticians use a typical value from the distribution. There are a number of different ways to find the typical value, but by far the most used is the arithmetic mean , usually simply called the mean . You already know how to find the arithmetic mean, you are just used to calling it the average . Statisticians use average more generally — the arithmetic mean is one of a number of different averages. Look at the formula for the arithmetic mean:

[latex]\mu = \dfrac{\sum{x}}{N}[/latex]

All you do is add up all of the members of the population, [latex]\sum{x}[/latex], and divide by how many members there are, N . The only trick is to remember that if there is more than one member of the population with a certain value, to add that value once for every member that has it. To reflect this, the equation for the mean sometimes is written:

[latex]\mu = \dfrac{\sum{f_i(x_i)}}{N}[/latex]

where f i is the frequency of members of the population with the value x i .

This is really the same formula as above. If there are seven members with a value of ten, the first formula would have you add seven ten times. The second formula simply has you multiply seven by ten — the same thing as adding together ten sevens.

Other measures of location are the median and the mode. The median is the value of the member of the population that is in the middle when the members are sorted from smallest to largest. Half of the members of the population have values higher than the median, and half have values lower. The median is a better measure of location if there are one or two members of the population that are a lot larger (or a lot smaller) than all the rest. Such extreme values can make the mean a poor measure of location, while they have little effect on the median. If there are an odd number of members of the population, there is no problem finding which member has the median value. If there are an even number of members of the population, then there is no single member in the middle. In that case, just average together the values of the two members that share the middle.

The third common measure of location is the mode . If you have arranged the population into a frequency or relative frequency distribution, the mode is easy to find because it is the value that occurs most often. While in some sense, the mode is really the most typical member of the population, it is often not very near the middle of the population. You can also have multiple modes. I am sure you have heard someone say that “it was a bimodal distribution “. That simply means that there were two modes, two values that occurred equally most often.

If you think about it, you should not be surprised to learn that for bell-shaped distributions, the mean, median, and mode will be equal. Most of what statisticians do when describing or inferring the location of a population is done with the mean. Another thing to think about is using a spreadsheet program, like Microsoft Excel, when arranging data into a frequency distribution or when finding the median or mode. By using the sort and distribution commands in 1-2-3, or similar commands in Excel, data can quickly be arranged in order or placed into value classes and the number in each class found. Excel also has a function, =AVERAGE(…), for finding the arithmetic mean. You can also have the spreadsheet program draw your frequency or relative frequency distribution.

One of the reasons that the arithmetic mean is the most used measure of location is because the mean of a sample is an unbiased estimator of the population mean. Because the sample mean is an unbiased estimator of the population mean, the sample mean is a good way to make an inference about the population mean. If you have a sample from a population, and you want to guess what the mean of that population is, you can legitimately guess that the population mean is equal to the mean of your sample. This is a legitimate way to make this inference because the mean of all the sample means equals the mean of the population, so if you used this method many times to infer the population mean, on average you’d be correct.

All of these measures of location can be found for samples as well as populations, using the same formulas. Generally, μ is used for a population mean, and x is used for sample means. Upper-case N , really a Greek nu , is used for the size of a population, while lower case n is used for sample size. Though it is not universal, statisticians tend to use the Greek alphabet for population characteristics and the Roman alphabet for sample characteristics.

Measuring population shape

Measuring the shape of a distribution is more difficult. Location has only one dimension (“where?”), but shape has a lot of dimensions. We will talk about two,and you will find that most of the time, only one dimension of shape is measured. The two dimensions of shape discussed here are the width and symmetry of the distribution. The simplest way to measure the width is to do just that—the range is the distance between the lowest and highest members of the population. The range is obviously affected by one or two population members that are much higher or lower than all the rest.

The most common measures of distribution width are the standard deviation and the variance. The standard deviation is simply the square root of the variance, so if you know one (and have a calculator that does squares and square roots) you know the other. The standard deviation is just a strange measure of the mean distance between the members of a population and the mean of the population. This is easiest to see if you start out by looking at the formula for the variance:

[latex]\sigma^2 = \dfrac{\sum{(x-\mu)^2}}{N}[/latex]

Look at the numerator. To find the variance, the first step (after you have the mean, μ ) is to take each member of the population, and find the difference between its value and the mean; you should have N differences. Square each of those, and add them together, dividing the sum by N , the number of members of the population. Since you find the mean of a group of things by adding them together and then dividing by the number in the group, the variance is simply the mean of the squared distances between members of the population and the population mean.

Notice that this is the formula for a population characteristic, so we use the Greek σ and that we write the variance as σ 2 , or sigma square because the standard deviation is simply the square root of the variance, its symbol is simply sigma , σ .

One of the things statisticians have discovered is that 75 per cent of the members of any population are within two standard deviations of the mean of the population. This is known as Chebyshev’s theorem . If the mean of a population of shoe sizes is 9.6 and the standard deviation is 1.1, then 75 per cent of the shoe sizes are between 7.4 (two standard deviations below the mean) and 11.8 (two standard deviations above the mean). This same theorem can be stated in probability terms: the probability that anything is within two standard deviations of the mean of its population is .75.

It is important to be careful when dealing with variances and standard deviations. In later chapters, there are formulas using the variance, and formulas using the standard deviation. Be sure you know which one you are supposed to be using. Here again, spreadsheet programs will figure out the standard deviation for you. In Excel, there is a function, =STDEVP(…), that does all of the arithmetic. Most calculators will also compute the standard deviation. Read the little instruction booklet, and find out how to have your calculator do the numbers before you do any homework or have a test.

The other measure of shape we will discuss here is the measure of skewness. Skewness is simply a measure of whether or not the distribution is symmetric or if it has a long tail on one side, but not the other. There are a number of ways to measure skewness, with many of the measures based on a formula much like the variance. The formula looks a lot like that for the variance, except the distances between the members and the population mean are cubed, rather than squared, before they are added together:

[latex]sk = \dfrac{\sum{(x-\mu)^3}}{N}[/latex]

At first, it might not seem that cubing rather than squaring those distances would make much difference. Remember, however, that when you square either a positive or negative number, you get a positive number, but when you cube a positive, you get a positive and when you cube a negative you get a negative. Also remember that when you square a number, it gets larger, but that when you cube a number, it gets a whole lot larger. Think about a distribution with a long tail out to the left. There are a few members of that population much smaller than the mean, members for which (x – μ) is large and negative. When these are cubed, you end up with some really big negative numbers. Because there are no members with such large, positive (x – μ) , there are no corresponding really big positive numbers to add in when you sum up the (x – μ) 3 , and the sum will be negative. A negative measure of skewness means that there is a tail out to the left, a positive measure means a tail to the right. Take a minute and convince yourself that if the distribution is symmetric, with equal tails on the left and right, the measure of skew is zero.

To be really complete, there is one more thing to measure, kurtosis or peakedness . As you might expect by now, it is measured by taking the distances between the members and the mean and raising them to the fourth power before averaging them together.

Measuring sample shape

Measuring the location of a sample is done in exactly the way that the location of a population is done. However, measuring the shape of a sample is done a little differently than measuring the shape of a population. The reason behind the difference is the desire to have the sample measurement serve as an unbiased estimator of the population measurement. If we took all of the possible samples of a certain size, n , from a population and found the variance of each one, and then found the mean of those sample variances, that mean would be a little smaller than the variance of the population.

You can see why this is so if you think it through. If you knew the population mean, you could find [latex]\sum{\dfrac{(x-\mu)^2}{n}}[/latex] for each sample, and have an unbiased estimate for σ 2 . However, you do not know the population mean, so you will have to infer it. The best way to infer the population mean is to use the sample mean x . The variance of a sample will then be found by averaging together all of the [latex]\sum{\dfrac{(x-\bar{x})^2}{n}}[/latex].

The mean of a sample is obviously determined by where the members of that sample lie. If you have a sample that is mostly from the high (or right) side of a population’s distribution, then the sample mean will almost for sure be greater than the population mean. For such a sample, [latex]\sum{\dfrac{(x-\bar{x})^2}{n}}[/latex] would underestimate σ 2 . The same is true for samples that are mostly from the low (or left) side of the population. If you think about what kind of samples will have [latex]\sum{\dfrac{(x-\bar{x})^2}{n}}[/latex] that is greater than the population σ 2 , you will come to the realization that it is only those samples with a few very high members and a few very low members — and there are not very many samples like that. By now you should have convinced yourself that [latex]\sum{\dfrac{(x-\bar{x})^2}{n}}[/latex] will result in a biased estimate of σ 2 . You can see that, on average, it is too small.

How can an unbiased estimate of the population variance, σ 2 , be found? If [latex]\sum{\dfrac{(x-\bar{x})^2}{n}}[/latex] is on average too small, we need to do something to make it a little bigger. We want to keep the [latex]\sum{(x-\bar{x})^2}[/latex], but if we divide it by something a little smaller, the result will be a little larger. Statisticians have found out that the following way to compute the sample variance results in an unbiased estimator of the population variance:

[latex]s^2 = \dfrac{\sum{(x-\bar{x})^2}}{n-1}[/latex]

If we took all of the possible samples of some size, n , from a population, and found the sample variance for each of those samples, using this formula, the mean of those sample variances would equal the population variance, σ 2 .

Note that we use s 2 instead of σ 2 , and n instead of N (really nu , not en ) since this is for a sample and we want to use the Roman letters rather than the Greek letters, which are used for populations.

There is another way to see why you divide by n-1 . We also have to address something called degrees of freedom before too long, and the degrees of freedom are the key in the other explanation. As we go through this explanation, you should be able to see that the two explanations are related.

Imagine that you have a sample with 10 members, n=10 , and you want to use it to estimate the variance of the population from which it was drawn. You write each of the 10 values on a separate scrap of paper. If you know the population mean, you could start by computing all 10 (x – μ) 2 . However, in the usual case, you do not know μ , and you must start by finding x from the values on the 10 scraps to use as an estimate of m . Once you have found x , you could lose any one of the 10 scraps and still be able to find the value that was on the lost scrap from the other 9 scraps. If you are going to use x in the formula for sample variance, only 9 (or n-1 ) of the x ’s are free to take on any value. Because only n-1 of the  x ’s can vary freely, you should divide [latex]\sum{(x-\bar{x})^2}[/latex] by n-1 , the number of ( x ’s) that are really free. Once you use x in the formula for sample variance, you use up one degree of freedom, leaving only n-1 . Generally, whenever you use something you have previously computed from a sample within a formula, you use up a degree of freedom.

A little thought will link the two explanations. The first explanation is based on the idea that x , the estimator of μ , varies with the sample. It is because x varies with the sample that a degree of freedom is used up in the second explanation.

The sample standard deviation is found simply by taking the square root of the sample variance:

[latex]s=\surd[\dfrac{\sum{(x-\bar{x}})^2}{n-1}][/latex]

While the sample variance is an unbiased estimator of population variance, the sample standard deviation is not an unbiased estimator of the population standard deviation — the square root of the average is not the same as the average of the square roots. This causes statisticians to use variance where it seems as though they are trying to get at standard deviation. In general, statisticians tend to use variance more than standard deviation. Be careful with formulas using sample variance and standard deviation in the following chapters. Make sure you are using the right one. Also note that many calculators will find standard deviation using both the population and sample formulas. Some use σ and s to show the difference between population and sample formulas, some use s n and s n-1 to show the difference.

If Ann wanted to infer what the population distribution of volleyball players’ sock sizes looked like she could do so from her sample. If she is going to send volleyball coaches packages of socks for the players to try, she will want to have the packages contain an assortment of sizes that will allow each player to have a pair that fits. Ann wants to infer what the distribution of volleyball players’ sock sizes looks like. She wants to know the mean and variance of that distribution. Her data, again, are shown in Table 1.1.

The mean sock size can be found: [latex]=\dfrac{3*6+24*7+33*8+20*9+17*10}{97} = 8.25[/latex]

To find the sample standard deviation, Ann decides to use Excel. She lists the sock sizes that were in the sample in column A (see Table 1.2) , and the frequency of each of those sizes in column B. For column C, she has the computer find for each of [latex]\sum{(x-\bar{x})^2}[/latex] the sock sizes, using the formula (A1-8.25) 2 in the first row, and then copying it down to the other four rows. In D1, she multiplies C1, by the frequency using the formula =B1*C1, and copying it down into the other rows. Finally, she finds the sample standard deviation by adding up the five numbers in column D and dividing by n-1 = 96 using the Excel formula =sum(D1:D5)/96. The spreadsheet appears like this when she is done:

Ann now has an estimate of the variance of the sizes of socks worn by basketball and volleyball players, 1.22. She has inferred that the population of Chargers players’ sock sizes has a mean of 8.25 and a variance of 1.22.

Ann’s collected data can simply be added to the following Excel template. The calculations of both variance and standard deviation have been shown below. You can change her numbers to see how these two measures change.

To describe a population you need to describe the picture or graph of its distribution. The two things that need to be described about the distribution are its location and its shape. Location is measured by an average, most often the arithmetic mean. The most important measure of shape is a measure of dispersion, roughly width, most often the variance or its square root the standard deviation.

Samples need to be described, too. If all we wanted to do with sample descriptions was describe the sample, we could use exactly the same measures for sample location and dispersion that are used for populations. However, we want to use the sample describers for dual purposes: (a) to describe the sample, and (b) to make inferences about the description of the population that sample came from. Because we want to use them to make inferences, we want our sample descriptions to be unbiased estimators . Our desire to measure sample dispersion with an unbiased estimator of population dispersion means that the formula we use for computing sample variance is a little different from the one used for computing population variance.

Introductory Business Statistics with Interactive Spreadsheets - 1st Canadian Edition Copyright © 2015 by Mohammad Mahbobi and Thomas K. Tiemann is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

Share This Book

Copyright © SurveySparrow Inc. 2024 Privacy Policy Terms of Service SurveySparrow Inc.

Descriptive Research 101: Definition, Methods and Examples

Parvathi Vijayamohan

Last Updated: 16 July 2024

10 min read

Table Of Contents

• Descriptive Research 101: The Definitive Guide

What is Descriptive Research?

• Key Characteristics
• Observation
• Case Studies
• Types of Descriptive Research
• Question Examples
• Real-World Examples

Tips to Excel at Descriptive Research

• More Interesting Reads

Imagine you are a detective called to a crime scene. Your job is to study the scene and report whatever you find: whether that’s the half-smoked cigarette on the table or the large “RACHE” written in blood on the wall. That, in a nutshell, is  descriptive research .

Researchers often need to do descriptive research on a problem before they attempt to solve it. So in this guide, we’ll take you through:

• What is descriptive research + its characteristics
• Descriptive research methods
• Types of descriptive research
• Descriptive research examples
• Tips to excel at the descriptive method

Click to jump to the section that interests you.

Let’s begin by going through what descriptive studies can and cannot do.

Definition: As its name says, descriptive research  describes  the characteristics of the problem, phenomenon, situation, or group under study.

So the goal of all descriptive studies is to  explore  the background, details, and existing patterns in the problem to fully understand it. In other words, preliminary research.

However, descriptive research can be both  preliminary and conclusive . You can use the data from a descriptive study to make reports and get insights for further planning.

What descriptive research isn’t: Descriptive research finds the  what/when/where  of a problem, not the  why/how .

Because of this, we can’t use the descriptive method to explore cause-and-effect relationships where one variable (like a person’s job role) affects another variable (like their monthly income).

Key Characteristics of Descriptive Research

• Answers the “what,” “when,” and “where”  of a research problem. For this reason, it is popularly used in  market research ,  awareness surveys , and  opinion polls .
• Sets the stage  for a research problem. As an early part of the research process, descriptive studies help you dive deeper into the topic.
• Opens the door  for further research. You can use descriptive data as the basis for more profound research, analysis and studies.
• Qualitative and quantitative research . It is possible to get a balanced mix of numerical responses and open-ended answers from the descriptive method.
• No control or interference with the variables . The researcher simply observes and reports on them. However, specific research software has filters that allow her to zoom in on one variable.
• Done in natural settings . You can get the best results from descriptive research by talking to people, surveying them, or observing them in a suitable environment. For example, suppose you are a website beta testing an app feature. In that case, descriptive research invites users to try the feature, tracking their behavior and then asking their opinions .
• Can be applied to many research methods and areas. Examples include healthcare, SaaS, psychology, political studies, education, and pop culture.

Descriptive Research Methods: The Top Three You Need to Know!

In short, survey research is a brief interview or conversation with a set of prepared questions about a topic. So you create a questionnaire, share it, and analyze the data you collect for further action.

Read more : The difference between surveys vs questionnaires

• Surveys can be hyper-local, regional, or global, depending on your objectives.
• Share surveys in-person, offline, via SMS, email, or QR codes – so many options!
• Easy to automate if you want to conduct many surveys over a period.

FYI: If you’re looking for the perfect tool to conduct descriptive research, SurveySparrow’s got you covered. Our AI-powered text and sentiment analysis help you instantly capture detailed insights for your studies.

With 1,000+ customizable (and free) survey templates , 20+ question types, and 1500+ integrations , SurveySparrow makes research super-easy.

Want to try out our platform? Click on the template below to start using it.👇

Product Market Research Survey Template

Preview Template

2. Observation

The observational method is a type of descriptive research in which you, the researcher, observe ongoing behavior.

Now, there are several (non-creepy) ways you can observe someone. In fact, observational research has three main approaches:

• Covert observation: In true spy fashion, the researcher mixes in with the group undetected or observes from a distance.
• Overt observation : The researcher identifies himself as a researcher – “The name’s Bond. J. Bond.” – and explains the purpose of the study.
• Participatory observation : The researcher participates in what he is observing to understand his topic better.
• Observation is one of the most accurate ways to get data on a subject’s behavior in a natural setting.
• You don’t need to rely on people’s willingness to share information.
• Observation is a universal method that can be applied to any area of research.

3. Case Studies

In the case study method, you do a detailed study of a specific group, person, or event over a period.

This brings us to a frequently asked question: “What’s the difference between case studies and longitudinal studies?”

A case study will go  very in-depth into the subject with one-on-one interviews, observations, and archival research. They are also qualitative, though sometimes they will use numbers and stats.

An example of longitudinal research would be a study of the health of night shift employees vs. general shift employees over a decade. An example of a case study would involve in-depth interviews with Casey, an assistant director of nursing who’s handled the night shift at the hospital for ten years now.

• Due to the focus on a few people, case studies can give you a tremendous amount of information.
• Because of the time and effort involved, a case study engages both researchers and participants.
• Case studies are helpful for ethically investigating unusual, complex, or challenging subjects. An example would be a study of the habits of long-term cocaine users.

7 Types of Descriptive Research

Descriptive Research Question Examples

• How have teen social media habits changed in 10 years?
• What causes high employee turnover in tech?
• How do urban and rural diets differ in India?
• What are consumer preferences for electric vs. gasoline cars in Germany?
• How common is smartphone addiction among UK college students?
• What drives customer satisfaction in banking?
• How have adolescent mental health issues changed in 15 years?
• What leisure activities are popular among retirees in Japan?
• How do commute times vary in US metro areas?
• What makes e-commerce websites successful?

Descriptive Research: Real-World Examples To Build Your Next Study

1. case study: airbnb’s growth strategy.

In an excellent case study, Tam Al Saad, Principal Consultant, Strategy + Growth at Webprofits, deep dives into how Airbnb attracted and retained 150 million users .

“What Airbnb offers isn’t a cheap place to sleep when you’re on holiday; it’s the opportunity to experience your destination as a local would. It’s the chance to meet the locals, experience the markets, and find non-touristy places.

Sure, you can visit the Louvre, see Buckingham Palace, and climb the Empire State Building, but you can do it as if it were your hometown while staying in a place that has character and feels like a home.” – Tam al Saad, Principal Consultant, Strategy + Growth at Webprofits

2. Observation – Better Tech Experiences for the Elderly

We often think that our elders are so hopeless with technology. But we’re not getting any younger either, and tech is changing at a hair trigger! This article by Annemieke Hendricks shares a wonderful example where researchers compare the levels of technological familiarity between age groups and how that influences usage.

“It is generally assumed that older adults have difficulty using modern electronic devices, such as mobile telephones or computers. Because this age group is growing in most countries, changing products and processes to adapt to their needs is increasingly more important. “ – Annemieke Hendricks, Marketing Communication Specialist, Noldus

3. Surveys – Decoding Sleep with SurveySparrow

SRI International (formerly Stanford Research Institute) – an independent, non-profit research center – wanted to investigate the impact of stress on an adolescent’s sleep. To get those insights, two actions were essential: tracking sleep patterns through wearable devices and sending surveys at a pre-set time – the pre-sleep period.

“With SurveySparrow’s recurring surveys feature, SRI was able to share engaging surveys with their participants exactly at the time they wanted and at the frequency they preferred.”

Read more about this project : How SRI International decoded sleep patterns with SurveySparrow

1: Answer the six Ws –

• Who should we consider?
• What information do we need?
• When should we collect the information?
• Where should we collect the information?
• Why are we obtaining the information?
• Way to collect the information

#2: Introduce and explain your methodological approach

#3: Describe your methods of data collection and/or selection.

#4: Describe your methods of analysis.

#5: Explain the reasoning behind your choices.

#6: Collect data.

#7: Analyze the data. Use software to speed up the process and reduce overthinking and human error.

#8: Report your conclusions and how you drew the results.

Wrapping Up

Whether it’s social media habits, consumer preferences, or mental health trends, descriptive research provides a clear snapshot into what people actually think.

If you want to know more about feedback methodology, or research, check out some of our other articles below.

👉 Desk Research 101: Definition, Methods, and Examples

👉 Exploratory Research: Your Guide to Unraveling Insights

👉 Design Research: Types, Methods, and Importance

Content marketer at SurveySparrow.

Parvathi is a sociologist turned marketer. After 6 years as a copywriter, she pivoted to B2B, diving into growth marketing for SaaS. Now she uses content and conversion optimization to fuel growth - focusing on CX, reputation management and feedback methodology for businesses.

You Might Also Like

What is Chatbot? A Definitive guide

Customer Experience

How to Get Reviews on Facebook & Manage Them: A Quick Guide

Alternative

Top 7 NetSuite Alternatives That You Need to Switch To in 2024

Survey Tips

How AI Integrations in Surveys Can Boost CX

Turn every feedback into a growth opportunity.

14-day free trial • Cancel Anytime • No Credit Card Required • Need a Demo?

An official website of the United States government

The .gov means it’s official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings

Preview improvements coming to the PMC website in October 2024. Learn More or Try it out now .

• Advanced Search
• Journal List
• Indian J Anaesth
• v.60(9); 2016 Sep

Basic statistical tools in research and data analysis

Zulfiqar ali.

Department of Anaesthesiology, Division of Neuroanaesthesiology, Sheri Kashmir Institute of Medical Sciences, Soura, Srinagar, Jammu and Kashmir, India

S Bala Bhaskar

1 Department of Anaesthesiology and Critical Care, Vijayanagar Institute of Medical Sciences, Bellary, Karnataka, India

Statistical methods involved in carrying out a study include planning, designing, collecting data, analysing, drawing meaningful interpretation and reporting of the research findings. The statistical analysis gives meaning to the meaningless numbers, thereby breathing life into a lifeless data. The results and inferences are precise only if proper statistical tests are used. This article will try to acquaint the reader with the basic research tools that are utilised while conducting various studies. The article covers a brief outline of the variables, an understanding of quantitative and qualitative variables and the measures of central tendency. An idea of the sample size estimation, power analysis and the statistical errors is given. Finally, there is a summary of parametric and non-parametric tests used for data analysis.

INTRODUCTION

Statistics is a branch of science that deals with the collection, organisation, analysis of data and drawing of inferences from the samples to the whole population.[ 1 ] This requires a proper design of the study, an appropriate selection of the study sample and choice of a suitable statistical test. An adequate knowledge of statistics is necessary for proper designing of an epidemiological study or a clinical trial. Improper statistical methods may result in erroneous conclusions which may lead to unethical practice.[ 2 ]

Variable is a characteristic that varies from one individual member of population to another individual.[ 3 ] Variables such as height and weight are measured by some type of scale, convey quantitative information and are called as quantitative variables. Sex and eye colour give qualitative information and are called as qualitative variables[ 3 ] [ Figure 1 ].

Classification of variables

Quantitative variables

Quantitative or numerical data are subdivided into discrete and continuous measurements. Discrete numerical data are recorded as a whole number such as 0, 1, 2, 3,… (integer), whereas continuous data can assume any value. Observations that can be counted constitute the discrete data and observations that can be measured constitute the continuous data. Examples of discrete data are number of episodes of respiratory arrests or the number of re-intubations in an intensive care unit. Similarly, examples of continuous data are the serial serum glucose levels, partial pressure of oxygen in arterial blood and the oesophageal temperature.

A hierarchical scale of increasing precision can be used for observing and recording the data which is based on categorical, ordinal, interval and ratio scales [ Figure 1 ].

Categorical or nominal variables are unordered. The data are merely classified into categories and cannot be arranged in any particular order. If only two categories exist (as in gender male and female), it is called as a dichotomous (or binary) data. The various causes of re-intubation in an intensive care unit due to upper airway obstruction, impaired clearance of secretions, hypoxemia, hypercapnia, pulmonary oedema and neurological impairment are examples of categorical variables.

Ordinal variables have a clear ordering between the variables. However, the ordered data may not have equal intervals. Examples are the American Society of Anesthesiologists status or Richmond agitation-sedation scale.

Interval variables are similar to an ordinal variable, except that the intervals between the values of the interval variable are equally spaced. A good example of an interval scale is the Fahrenheit degree scale used to measure temperature. With the Fahrenheit scale, the difference between 70° and 75° is equal to the difference between 80° and 85°: The units of measurement are equal throughout the full range of the scale.

Ratio scales are similar to interval scales, in that equal differences between scale values have equal quantitative meaning. However, ratio scales also have a true zero point, which gives them an additional property. For example, the system of centimetres is an example of a ratio scale. There is a true zero point and the value of 0 cm means a complete absence of length. The thyromental distance of 6 cm in an adult may be twice that of a child in whom it may be 3 cm.

STATISTICS: DESCRIPTIVE AND INFERENTIAL STATISTICS

Descriptive statistics[ 4 ] try to describe the relationship between variables in a sample or population. Descriptive statistics provide a summary of data in the form of mean, median and mode. Inferential statistics[ 4 ] use a random sample of data taken from a population to describe and make inferences about the whole population. It is valuable when it is not possible to examine each member of an entire population. The examples if descriptive and inferential statistics are illustrated in Table 1 .

Example of descriptive and inferential statistics

Descriptive statistics

The extent to which the observations cluster around a central location is described by the central tendency and the spread towards the extremes is described by the degree of dispersion.

Measures of central tendency

The measures of central tendency are mean, median and mode.[ 6 ] Mean (or the arithmetic average) is the sum of all the scores divided by the number of scores. Mean may be influenced profoundly by the extreme variables. For example, the average stay of organophosphorus poisoning patients in ICU may be influenced by a single patient who stays in ICU for around 5 months because of septicaemia. The extreme values are called outliers. The formula for the mean is

where x = each observation and n = number of observations. Median[ 6 ] is defined as the middle of a distribution in a ranked data (with half of the variables in the sample above and half below the median value) while mode is the most frequently occurring variable in a distribution. Range defines the spread, or variability, of a sample.[ 7 ] It is described by the minimum and maximum values of the variables. If we rank the data and after ranking, group the observations into percentiles, we can get better information of the pattern of spread of the variables. In percentiles, we rank the observations into 100 equal parts. We can then describe 25%, 50%, 75% or any other percentile amount. The median is the 50 th percentile. The interquartile range will be the observations in the middle 50% of the observations about the median (25 th -75 th percentile). Variance[ 7 ] is a measure of how spread out is the distribution. It gives an indication of how close an individual observation clusters about the mean value. The variance of a population is defined by the following formula:

where σ 2 is the population variance, X is the population mean, X i is the i th element from the population and N is the number of elements in the population. The variance of a sample is defined by slightly different formula:

where s 2 is the sample variance, x is the sample mean, x i is the i th element from the sample and n is the number of elements in the sample. The formula for the variance of a population has the value ‘ n ’ as the denominator. The expression ‘ n −1’ is known as the degrees of freedom and is one less than the number of parameters. Each observation is free to vary, except the last one which must be a defined value. The variance is measured in squared units. To make the interpretation of the data simple and to retain the basic unit of observation, the square root of variance is used. The square root of the variance is the standard deviation (SD).[ 8 ] The SD of a population is defined by the following formula:

where σ is the population SD, X is the population mean, X i is the i th element from the population and N is the number of elements in the population. The SD of a sample is defined by slightly different formula:

where s is the sample SD, x is the sample mean, x i is the i th element from the sample and n is the number of elements in the sample. An example for calculation of variation and SD is illustrated in Table 2 .

Example of mean, variance, standard deviation

Normal distribution or Gaussian distribution

Most of the biological variables usually cluster around a central value, with symmetrical positive and negative deviations about this point.[ 1 ] The standard normal distribution curve is a symmetrical bell-shaped. In a normal distribution curve, about 68% of the scores are within 1 SD of the mean. Around 95% of the scores are within 2 SDs of the mean and 99% within 3 SDs of the mean [ Figure 2 ].

Normal distribution curve

Skewed distribution

It is a distribution with an asymmetry of the variables about its mean. In a negatively skewed distribution [ Figure 3 ], the mass of the distribution is concentrated on the right of Figure 1 . In a positively skewed distribution [ Figure 3 ], the mass of the distribution is concentrated on the left of the figure leading to a longer right tail.

Curves showing negatively skewed and positively skewed distribution

Inferential statistics

In inferential statistics, data are analysed from a sample to make inferences in the larger collection of the population. The purpose is to answer or test the hypotheses. A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. Hypothesis tests are thus procedures for making rational decisions about the reality of observed effects.

Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty).

In inferential statistics, the term ‘null hypothesis’ ( H 0 ‘ H-naught ,’ ‘ H-null ’) denotes that there is no relationship (difference) between the population variables in question.[ 9 ]

Alternative hypothesis ( H 1 and H a ) denotes that a statement between the variables is expected to be true.[ 9 ]

The P value (or the calculated probability) is the probability of the event occurring by chance if the null hypothesis is true. The P value is a numerical between 0 and 1 and is interpreted by researchers in deciding whether to reject or retain the null hypothesis [ Table 3 ].

P values with interpretation

If P value is less than the arbitrarily chosen value (known as α or the significance level), the null hypothesis (H0) is rejected [ Table 4 ]. However, if null hypotheses (H0) is incorrectly rejected, this is known as a Type I error.[ 11 ] Further details regarding alpha error, beta error and sample size calculation and factors influencing them are dealt with in another section of this issue by Das S et al .[ 12 ]

Illustration for null hypothesis

PARAMETRIC AND NON-PARAMETRIC TESTS

Numerical data (quantitative variables) that are normally distributed are analysed with parametric tests.[ 13 ]

Two most basic prerequisites for parametric statistical analysis are:

• The assumption of normality which specifies that the means of the sample group are normally distributed
• The assumption of equal variance which specifies that the variances of the samples and of their corresponding population are equal.

However, if the distribution of the sample is skewed towards one side or the distribution is unknown due to the small sample size, non-parametric[ 14 ] statistical techniques are used. Non-parametric tests are used to analyse ordinal and categorical data.

Parametric tests

The parametric tests assume that the data are on a quantitative (numerical) scale, with a normal distribution of the underlying population. The samples have the same variance (homogeneity of variances). The samples are randomly drawn from the population, and the observations within a group are independent of each other. The commonly used parametric tests are the Student's t -test, analysis of variance (ANOVA) and repeated measures ANOVA.

Student's t -test

Student's t -test is used to test the null hypothesis that there is no difference between the means of the two groups. It is used in three circumstances:

where X = sample mean, u = population mean and SE = standard error of mean

where X 1 − X 2 is the difference between the means of the two groups and SE denotes the standard error of the difference.

• To test if the population means estimated by two dependent samples differ significantly (the paired t -test). A usual setting for paired t -test is when measurements are made on the same subjects before and after a treatment.

The formula for paired t -test is:

where d is the mean difference and SE denotes the standard error of this difference.

The group variances can be compared using the F -test. The F -test is the ratio of variances (var l/var 2). If F differs significantly from 1.0, then it is concluded that the group variances differ significantly.

Analysis of variance

The Student's t -test cannot be used for comparison of three or more groups. The purpose of ANOVA is to test if there is any significant difference between the means of two or more groups.

In ANOVA, we study two variances – (a) between-group variability and (b) within-group variability. The within-group variability (error variance) is the variation that cannot be accounted for in the study design. It is based on random differences present in our samples.

However, the between-group (or effect variance) is the result of our treatment. These two estimates of variances are compared using the F-test.

A simplified formula for the F statistic is:

where MS b is the mean squares between the groups and MS w is the mean squares within groups.

Repeated measures analysis of variance

As with ANOVA, repeated measures ANOVA analyses the equality of means of three or more groups. However, a repeated measure ANOVA is used when all variables of a sample are measured under different conditions or at different points in time.

As the variables are measured from a sample at different points of time, the measurement of the dependent variable is repeated. Using a standard ANOVA in this case is not appropriate because it fails to model the correlation between the repeated measures: The data violate the ANOVA assumption of independence. Hence, in the measurement of repeated dependent variables, repeated measures ANOVA should be used.

Non-parametric tests

When the assumptions of normality are not met, and the sample means are not normally, distributed parametric tests can lead to erroneous results. Non-parametric tests (distribution-free test) are used in such situation as they do not require the normality assumption.[ 15 ] Non-parametric tests may fail to detect a significant difference when compared with a parametric test. That is, they usually have less power.

As is done for the parametric tests, the test statistic is compared with known values for the sampling distribution of that statistic and the null hypothesis is accepted or rejected. The types of non-parametric analysis techniques and the corresponding parametric analysis techniques are delineated in Table 5 .

Analogue of parametric and non-parametric tests

Median test for one sample: The sign test and Wilcoxon's signed rank test

The sign test and Wilcoxon's signed rank test are used for median tests of one sample. These tests examine whether one instance of sample data is greater or smaller than the median reference value.

This test examines the hypothesis about the median θ0 of a population. It tests the null hypothesis H0 = θ0. When the observed value (Xi) is greater than the reference value (θ0), it is marked as+. If the observed value is smaller than the reference value, it is marked as − sign. If the observed value is equal to the reference value (θ0), it is eliminated from the sample.

If the null hypothesis is true, there will be an equal number of + signs and − signs.

The sign test ignores the actual values of the data and only uses + or − signs. Therefore, it is useful when it is difficult to measure the values.

Wilcoxon's signed rank test

There is a major limitation of sign test as we lose the quantitative information of the given data and merely use the + or – signs. Wilcoxon's signed rank test not only examines the observed values in comparison with θ0 but also takes into consideration the relative sizes, adding more statistical power to the test. As in the sign test, if there is an observed value that is equal to the reference value θ0, this observed value is eliminated from the sample.

Wilcoxon's rank sum test ranks all data points in order, calculates the rank sum of each sample and compares the difference in the rank sums.

Mann-Whitney test

It is used to test the null hypothesis that two samples have the same median or, alternatively, whether observations in one sample tend to be larger than observations in the other.

Mann–Whitney test compares all data (xi) belonging to the X group and all data (yi) belonging to the Y group and calculates the probability of xi being greater than yi: P (xi > yi). The null hypothesis states that P (xi > yi) = P (xi < yi) =1/2 while the alternative hypothesis states that P (xi > yi) ≠1/2.

Kolmogorov-Smirnov test

The two-sample Kolmogorov-Smirnov (KS) test was designed as a generic method to test whether two random samples are drawn from the same distribution. The null hypothesis of the KS test is that both distributions are identical. The statistic of the KS test is a distance between the two empirical distributions, computed as the maximum absolute difference between their cumulative curves.

Kruskal-Wallis test

The Kruskal–Wallis test is a non-parametric test to analyse the variance.[ 14 ] It analyses if there is any difference in the median values of three or more independent samples. The data values are ranked in an increasing order, and the rank sums calculated followed by calculation of the test statistic.

Jonckheere test

In contrast to Kruskal–Wallis test, in Jonckheere test, there is an a priori ordering that gives it a more statistical power than the Kruskal–Wallis test.[ 14 ]

Friedman test

The Friedman test is a non-parametric test for testing the difference between several related samples. The Friedman test is an alternative for repeated measures ANOVAs which is used when the same parameter has been measured under different conditions on the same subjects.[ 13 ]

Tests to analyse the categorical data

Chi-square test, Fischer's exact test and McNemar's test are used to analyse the categorical or nominal variables. The Chi-square test compares the frequencies and tests whether the observed data differ significantly from that of the expected data if there were no differences between groups (i.e., the null hypothesis). It is calculated by the sum of the squared difference between observed ( O ) and the expected ( E ) data (or the deviation, d ) divided by the expected data by the following formula:

A Yates correction factor is used when the sample size is small. Fischer's exact test is used to determine if there are non-random associations between two categorical variables. It does not assume random sampling, and instead of referring a calculated statistic to a sampling distribution, it calculates an exact probability. McNemar's test is used for paired nominal data. It is applied to 2 × 2 table with paired-dependent samples. It is used to determine whether the row and column frequencies are equal (that is, whether there is ‘marginal homogeneity’). The null hypothesis is that the paired proportions are equal. The Mantel-Haenszel Chi-square test is a multivariate test as it analyses multiple grouping variables. It stratifies according to the nominated confounding variables and identifies any that affects the primary outcome variable. If the outcome variable is dichotomous, then logistic regression is used.

SOFTWARES AVAILABLE FOR STATISTICS, SAMPLE SIZE CALCULATION AND POWER ANALYSIS

Numerous statistical software systems are available currently. The commonly used software systems are Statistical Package for the Social Sciences (SPSS – manufactured by IBM corporation), Statistical Analysis System ((SAS – developed by SAS Institute North Carolina, United States of America), R (designed by Ross Ihaka and Robert Gentleman from R core team), Minitab (developed by Minitab Inc), Stata (developed by StataCorp) and the MS Excel (developed by Microsoft).

There are a number of web resources which are related to statistical power analyses. A few are:

• StatPages.net – provides links to a number of online power calculators
• G-Power – provides a downloadable power analysis program that runs under DOS
• Power analysis for ANOVA designs an interactive site that calculates power or sample size needed to attain a given power for one effect in a factorial ANOVA design
• SPSS makes a program called SamplePower. It gives an output of a complete report on the computer screen which can be cut and paste into another document.

It is important that a researcher knows the concepts of the basic statistical methods used for conduct of a research study. This will help to conduct an appropriately well-designed study leading to valid and reliable results. Inappropriate use of statistical techniques may lead to faulty conclusions, inducing errors and undermining the significance of the article. Bad statistics may lead to bad research, and bad research may lead to unethical practice. Hence, an adequate knowledge of statistics and the appropriate use of statistical tests are important. An appropriate knowledge about the basic statistical methods will go a long way in improving the research designs and producing quality medical research which can be utilised for formulating the evidence-based guidelines.

Financial support and sponsorship

Conflicts of interest.

There are no conflicts of interest.

Descriptive Statistics (Psychology)

Contents Toggle Main Menu 1 Introduction 2 Sampling 3 Measures of Location 3.1 The Arithmetic Mean 3.2 The Mode 3.3 The Median 4 Measures of Spread 4.1 The Range 4.2 The Sample Variance $(s^2)$ 4.3 The Population Variance $(\sigma^2)$ 4.4 The Sample Standard Deviation $(s)$ 4.5 The Population Standard Deviation $(\sigma)$ 4.6 The Interquartile Range (IQR) 4.7 The Standard Error (SE) of the Mean 4.8 Notation in the above formulas explained: 5 Workbook 6 Test Yourself 7 See Also

Introduction

Given a dataset, your task may be to try to describe the main features of the data, or descriptive statistics , which could be influential in making decisions. For example, you may want to know how widely dispersed the data are about a central location; this will give you an idea of the variability of the dataset. You will have a choice of measures of central location and variability, you choose the ones that give you the most information depending on the type of data you have and in relation to the decisions you want to make.

If all the dataset information is available to you and you have sufficient software to analyse it e.g. R, SPSS or Minitab, then your task is to put the information into the program and choose the appropriate descriptive statistics.

However, the dataset information you want may not be fully available to you. This is particularly true for large populations where it is not feasible to extract all the data , e.g. for the the UK population; voting preferences, number of cars per household etc. In this case the usual method is to sample the population.

Sampling involves taking a small amount, or sample, of the entire population to draw conclusions and test hypotheses. For example, if you wanted to answer the question, “How many hours after school do children do homework in England?” it would be almost impossible and very time consuming to question every child in the country, so you instead take a sample of the population and test them, to make inferences about the overall population. There are different types of sampling: random and non-random , which both have advantages and disadvantages. For more information on this, see sampling .

Measures of Location

The following are ways of representing a representative value of the set of data.

The Arithmetic Mean

This is calculated by summing all of the data values and dividing by the total number of data items you have. It is normally called the mean or the average. If you have a data consisting of $n$ observations $(x_1,...,x_n)$ then the mean $(\bar{x})$ is given by the formula:

\begin{equation} \bar {x} = \frac{1}{n}\sum\limits_{i=1}^{n}\ x_i. \end{equation}

• A sample mean is the mean of a sample taken from the population you are considering.
• The population mean , often denoted by $\mu$, is the mean for the entire population you are studying. Often you do not know the population mean and have to estimate it from a sample mean.

The mode is the most frequently occurring value in the data set. For instance in the set of data $3,4,4,5,4,6,7,8$ the modal value of the set is $4$, as $4$ occurs most frequently.

The median can be viewed as the middle value for a set of numeric data. To calculate this value, order the data values by increasing size:

For an odd number of points the median is the value that is in the middle i.e. for $n$ observations the middle number is the $\bigg(\dfrac{n+1}{2}\bigg)^\text{th}$term. For example, in the ordered set $1,3,4,4,5,6,7,7,8$ the median is the fifth number in this set which is $5$.

If you have an even number ($n$) of observations then there is no one middle number so you average the middle two values i.e. $\big(\frac{n}{2}\big)^\text{th}$ and $\big( \frac{n}{2} +1\big)^\text{th}$ values.

For example in the ordered set $10,13,14,14,16,17,17,17,18,19$, the median is the average of the middle two numbers; the fifth, $16$ and the sixth, $17$. Hence the median is $\dfrac{16 + 17}{2} = 16.5$.

See Mean, median and mode and Weighted averages for more information and more complex examples.

Measures of Spread

For a numeric dataset the range measures the difference between the greatest and least values.

We calculate this using the formula:

\begin{equation} \text{Range} =\text{Greatest value}- \text{ least value}. \end{equation}

The Sample Variance $(s^2)$

Is the square of the sample standard deviation. and measures the spread of the sample data values about the sample mean. The formula for the sample variance is therefore:

\begin{equation} s^2 = \frac{1}{n-1}\sum\limits_{i=1}^n(x_i - \bar {x})^2. \end{equation}

The Population Variance $(\sigma^2)$

The population variance measures the spread of the whole population. Note carefully that the population variance differs from the sample variance in that instead of dividing by $n-1$ we divide by $n$ so the formula becomes :

\begin{equation} \sigma^2 = \frac{1}{n}\sum\limits_{i=1}^n(x_i - \bar {x})^2. \end{equation}

The Sample Standard Deviation $(s)$

If we have taken a sample from a population, the sample standard deviation (SD) measures by how much the sample data deviates from the sample mean. The standard deviation is the positive square root of the variance. It is calculated using the formula:

\begin{equation} s = \sqrt{\frac{1}{n-1}\sum\limits_{i=1}^n(x_i - \bar {x})^2}. \end{equation}

The Population Standard Deviation $(\sigma)$

The population standard deviation (SD) measures by how much the population data deviates from the mean of the whole population. The formula is slightly different from that of the sample standard deviation.

\begin{equation} \sigma = \sqrt{\frac{1}{n}\sum\limits_{i=1}^n(x_i - \bar {x})^2}. \end{equation}

The Interquartile Range (IQR)

The IQR measures the range of the middle half of the data, and so is less affected by extreme observations. It is given by $Q3 - Q1$, where:

\begin{equation} \begin{split} &&Q1 = \frac{(n+1)}{4}^\text{th} \text{ smallest observation} \\&& Q3 = \frac{3(n+1)}{4}^\text{th} \text {smallest observation}. \end{split} \end{equation}

The Standard Error (SE) of the Mean

The sample mean is an estimator of the population mean. If we keep on taking samples and then obtain a dataset comprising these sample means, then the standard error is a measure of the spread of the sample means from the population mean. It is calculated using the following formula:

\begin{equation} \text{Standard Error (SE)} = \frac{\sigma}{\sqrt{n}}. \end{equation}

Note that of we take large samples,i.e. increase $n$, then the standard error of the mean becomes smaller.

For more information see Variance and standard deviation

Notation in the above formulas explained:

\begin{equation} \begin{split} \bar{x}&& = \text{Arithmetic mean} \\ x &&= \text {Individual data value} \\ s&& = \text{ Sample standard deviation} \\ \sigma &&= \text{ Population standard deviation} \\ s^2&&= \text{ Sample variance} \\ \sigma^2&&= \text{ Population variance} \\ n &&= \text{Sample size} \\ \sum \limits_{i=1}^n{x_i}&& = \text{Sum of of the data values} (x_1,\ldots,x_n). \end{split} \end{equation}

This workbook produced by HELM is a good revision aid, containing key points for revision and many worked examples.

• Descriptive statistics including work on measures of location.

Test Yourself

Try testing yourself on descriptive statistics .

You can also take this test on identifying parts of statistical formulas .

For more information on the topics covered in this section see descriptive statistics .