defining variables in research

Scale: Nominal and ordinal.

The confounding variable could be the   and compels people to drink a lot of water and a cold drink to reduce heat and thirst caused due to the heat.

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Frequently Asked Questions

What are the 10 types of variables in research.

The 10 types of variables in research are:

• Independent
• Confounding
• Categorical
• Extraneous.

What is an independent variable?

An independent variable, often termed the predictor or explanatory variable, is the variable manipulated or categorized in an experiment to observe its effect on another variable, called the dependent variable. It’s the presumed cause in a cause-and-effect relationship, determining if changes in it produce changes in the observed outcome.

What is a variable?

In research, a variable is any attribute, quantity, or characteristic that can be measured or counted. It can take on various values, making it “variable.” Variables can be classified as independent (manipulated), dependent (observed outcome), or control (kept constant). They form the foundation for hypotheses, observations, and data analysis in studies.

What is a dependent variable?

A dependent variable is the outcome or response being studied in an experiment or investigation. It’s what researchers measure to determine the effect of changes in the independent variable. In a cause-and-effect relationship, the dependent variable is presumed to be influenced or caused by the independent variable.

What is a variable in programming?

In programming, a variable is a symbolic name for a storage location that holds data or values. It allows data storage and retrieval for computational operations. Variables have types, like integer or string, determining the nature of data they can hold. They’re fundamental in manipulating and processing information in software.

What is a control variable?

A control variable in research is a factor that’s kept constant to ensure that it doesn’t influence the outcome. By controlling these variables, researchers can isolate the effects of the independent variable on the dependent variable, ensuring that other factors don’t skew the results or introduce bias into the experiment.

What is a controlled variable in science?

In science, a controlled variable is a factor that remains constant throughout an experiment. It ensures that any observed changes in the dependent variable are solely due to the independent variable, not other factors. By keeping controlled variables consistent, researchers can maintain experiment validity and accurately assess cause-and-effect relationships.

How many independent variables should an investigation have?

Ideally, an investigation should have one independent variable to clearly establish cause-and-effect relationships. Manipulating multiple independent variables simultaneously can complicate data interpretation.

However, in advanced research, experiments with multiple independent variables (factorial designs) are used, but they require careful planning to understand interactions between variables.

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Neag School of Education

Educational Research Basics by Del Siegle

Each person/thing we collect data on is called an OBSERVATION (in our work these are usually people/subjects. Currently, the term participant rather than subject is used when describing the people from whom we collect data).

OBSERVATIONS (participants) possess a variety of CHARACTERISTICS .

If a CHARACTERISTIC of an OBSERVATION (participant) is the same for every member of the group (doesn’t vary) it is called a CONSTANT .

If a CHARACTERISTIC of an OBSERVATION (participant) differs for group members it is called a VARIABLE . In research we don’t get excited about CONSTANTS (since everyone is the same on that characteristic); we’re more interested in VARIABLES. Variables can be classified as QUANTITATIVE or QUALITATIVE (also known as CATEGORICAL).

QUANTITATIVE variables are ones that exist along a continuum that runs from low to high. Ordinal, interval, and ratio variables are quantitative.  QUANTITATIVE variables are sometimes called CONTINUOUS VARIABLES because they have a variety (continuum) of characteristics. Height in inches and scores on a test would be examples of quantitative variables.

QUALITATIVE variables do not express differences in amount, only differences. They are sometimes referred to as CATEGORICAL variables because they classify by categories. Nominal variables such as gender, religion, or eye color are CATEGORICAL variables. Generally speaking, categorical variables

A special case of a CATEGORICAL variable is a DICHOTOMOUS VARIABLE. DICHOTOMOUS variables have only two CHARACTERISTICS (male or female). When naming QUALITATIVE variables, it is important to name the category rather than the levels (i.e., gender is the variable name, not male and female).

Variables have different purposes or roles…

Independent (Experimental, Manipulated, Treatment, Grouping) Variable- That factor which is measured, manipulated, or selected by the experimenter to determine its relationship to an observed phenomenon. “In a research study, independent variables are antecedent conditions that are presumed to affect a dependent variable. They are either manipulated by the researcher or are observed by the researcher so that their values can be related to that of the dependent variable. For example, in a research study on the relationship between mosquitoes and mosquito bites, the number of mosquitoes per acre of ground would be an independent variable” (Jaeger, 1990, p. 373)

While the independent variable is often manipulated by the researcher, it can also be a classification where subjects are assigned to groups. In a study where one variable causes the other, the independent variable is the cause. In a study where groups are being compared, the independent variable is the group classification.

Dependent (Outcome) Variable- That factor which is observed and measured to determine the effect of the independent variable, i.e., that factor that appears, disappears, or varies as the experimenter introduces, removes, or varies the independent variable. “In a research study, the independent variable defines a principal focus of research interest. It is the consequent variable that is presumably affected by one or more independent variables that are either manipulated by the researcher or observed by the researcher and regarded as antecedent conditions that determine the value of the dependent variable. For example, in a study of the relationship between mosquitoes and mosquito bites, the number of mosquito bites per hour would be the dependent variable” (Jaeger, 1990, p. 370). The dependent variable is the participant’s response.

The dependent variable is the outcome. In an experiment, it may be what was caused or what changed as a result of the study. In a comparison of groups, it is what they differ on.

Moderator Variable- That factor which is measured, manipulated, or selected by the experimenter to discover whether it modifies the relationship of the independent variable to an observed phenomenon. It is a special type of independent variable.

The independent variable’s relationship with the dependent variable may change under different conditions. That condition is the moderator variable. In a study of two methods of teaching reading, one of the methods of teaching reading may work better with boys than girls. Method of teaching reading is the independent variable and reading achievement is the dependent variable. Gender is the moderator variable because it moderates or changes the relationship between the independent variable (teaching method) and the dependent variable (reading achievement).

Suppose we do a study of reading achievement where we compare whole language with phonics, and we also include students’ social economic status (SES) as a variable. The students are randomly assigned to either whole language instruction or phonics instruction. There are students of high and low SES in each group.

Let’s assume that we found that whole language instruction worked better than phonics instruction with the high SES students, but phonics instruction worked better than whole language instruction with the low SES students. Later you will learn in statistics that this is an interaction effect. In this study, language instruction was the independent variable (with two levels: phonics and whole language). SES was the moderator variable (with two levels: high and low). Reading achievement was the dependent variable (measured on a continuous scale so there aren’t levels).

With a moderator variable, we find the type of instruction did make a difference, but it worked differently for the two groups on the moderator variable. We select this moderator variable because we think it is a variable that will moderate the effect of the independent on the dependent. We make this decision before we start the study.

If the moderator had not been in the study above, we would have said that there was no difference in reading achievement between the two types of reading instruction. This would have happened because the average of the high and low scores of each SES group within a reading instruction group would cancel each other an produce what appears to be average reading achievement in each instruction group (i.e., Phonics: Low—6 and High—2; Whole Language:   Low—2 and High—6; Phonics has an average of 4 and Whole Language has an average of 4. If we just look at the averages (without regard to the moderator), it appears that the instruction types produced similar results).

Extraneous Variable- Those factors which cannot be controlled. Extraneous variables are independent variables that have not been controlled. They may or may not influence the results. One way to control an extraneous variable which might influence the results is to make it a constant (keep everyone in the study alike on that characteristic). If SES were thought to influence achievement, then restricting the study to one SES level would eliminate SES as an extraneous variable.

Here are some examples similar to your homework:

Null Hypothesis: Students who receive pizza coupons as a reward do not read more books than students who do not receive pizza coupon rewards. Independent Variable: Reward Status Dependent Variable: Number of Books Read

High achieving students do not perform better than low achieving student when writing stories regardless of whether they use paper and pencil or a word processor. Independent Variable: Instrument Used for Writing Moderator Variable: Ability Level of the Students Dependent Variable:  Quality of Stories Written When we are comparing two groups, the groups are the independent variable. When we are testing whether something influences something else, the influence (cause) is the independent variable. The independent variable is also the one we manipulate. For example, consider the hypothesis “Teachers given higher pay will have more positive attitudes toward children than teachers given lower pay.” One approach is to ask ourselves “Are there two or more groups being compared?” The answer is “Yes.” “What are the groups?” Teachers who are given higher pay and teachers who are given lower pay. Therefore, the independent variable is teacher pay (it has two levels– high pay and low pay). The dependent variable (what the groups differ on) is attitude towards school.

We could also approach this another way. “Is something causing something else?” The answer is “Yes.” “What is causing what?” Teacher pay is causing attitude towards school. Therefore, teacher pay is the independent variable (cause) and attitude towards school is the dependent variable (outcome).

Research Questions and Hypotheses

The research question drives the study. It should specifically state what is being investigated. Statisticians often convert their research questions to null and alternative hypotheses. The null hypothesis states that no relationship (correlation study) or difference (experimental study) exists. Converting research questions to hypotheses is a simple task. Take the questions and make it a positive statement that says a relationship exists (correlation studies) or a difference exists (experiment study) between the groups and we have the alternative hypothesis. Write a statement  that a relationship does not exist or a difference does not exist and we have the null hypothesis.

Format for sample research questions and accompanying hypotheses:

Research Question for Relationships: Is there a relationship between height and weight? Null Hypothesis:  There is no relationship between height and weight. Alternative Hypothesis:   There is a relationship between height and weight.

When a researcher states a nondirectional hypothesis in a study that compares the performance of two groups, she doesn’t state which group she believes will perform better. If the word “more” or “less” appears in the hypothesis, there is a good chance that we are reading a directional hypothesis. A directional hypothesis is one where the researcher states which group she believes will perform better.  Most researchers use nondirectional hypotheses.

We usually write the alternative hypothesis (what we believe might happen) before we write the null hypothesis (saying it won’t happen).

Directional Research Question for Differences: Do boys like reading more than girls? Null Hypothesis:   Boys do not like reading more than girls. Alternative Hypothesis:   Boys do like reading more than girls.

Nondirectional Research Question for Differences: Is there a difference between boys’ and girls’ attitude towards reading? –or– Do boys’ and girls’ attitude towards reading differ? Null Hypothesis:   There is no difference between boys’ and girls’ attitude towards reading.  –or–  Boys’ and girls’ attitude towards reading do not differ. Alternative Hypothesis:   There is a difference between boys’ and girls’ attitude towards reading.  –or–  Boys’ and girls’ attitude towards reading differ.

Del Siegle, Ph.D. Neag School of Education – University of Connecticut [email protected] www.delsiegle.com

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• v.10(1); Jan-Feb 2019

Types of Variables, Descriptive Statistics, and Sample Size

Feroze kaliyadan.

Department of Dermatology, King Faisal University, Al Hofuf, Saudi Arabia

Vinay Kulkarni

1 Department of Dermatology, Prayas Amrita Clinic, Pune, Maharashtra, India

This short “snippet” covers three important aspects related to statistics – the concept of variables , the importance, and practical aspects related to descriptive statistics and issues related to sampling – types of sampling and sample size estimation.

What is a variable?[ 1 , 2 ] To put it in very simple terms, a variable is an entity whose value varies. A variable is an essential component of any statistical data. It is a feature of a member of a given sample or population, which is unique, and can differ in quantity or quantity from another member of the same sample or population. Variables either are the primary quantities of interest or act as practical substitutes for the same. The importance of variables is that they help in operationalization of concepts for data collection. For example, if you want to do an experiment based on the severity of urticaria, one option would be to measure the severity using a scale to grade severity of itching. This becomes an operational variable. For a variable to be “good,” it needs to have some properties such as good reliability and validity, low bias, feasibility/practicality, low cost, objectivity, clarity, and acceptance. Variables can be classified into various ways as discussed below.

Quantitative vs qualitative

A variable can collect either qualitative or quantitative data. A variable differing in quantity is called a quantitative variable (e.g., weight of a group of patients), whereas a variable differing in quality is called a qualitative variable (e.g., the Fitzpatrick skin type)

A simple test which can be used to differentiate between qualitative and quantitative variables is the subtraction test. If you can subtract the value of one variable from the other to get a meaningful result, then you are dealing with a quantitative variable (this of course will not apply to rating scales/ranks).

Quantitative variables can be either discrete or continuous

Discrete variables are variables in which no values may be assumed between the two given values (e.g., number of lesions in each patient in a sample of patients with urticaria).

Continuous variables, on the other hand, can take any value in between the two given values (e.g., duration for which the weals last in the same sample of patients with urticaria). One way of differentiating between continuous and discrete variables is to use the “mid-way” test. If, for every pair of values of a variable, a value exactly mid-way between them is meaningful, the variable is continuous. For example, two values for the time taken for a weal to subside can be 10 and 13 min. The mid-way value would be 11.5 min which makes sense. However, for a number of weals, suppose you have a pair of values – 5 and 8 – the midway value would be 6.5 weals, which does not make sense.

Under the umbrella of qualitative variables, you can have nominal/categorical variables and ordinal variables

Nominal/categorical variables are, as the name suggests, variables which can be slotted into different categories (e.g., gender or type of psoriasis).

Ordinal variables or ranked variables are similar to categorical, but can be put into an order (e.g., a scale for severity of itching).

Dependent and independent variables

In the context of an experimental study, the dependent variable (also called outcome variable) is directly linked to the primary outcome of the study. For example, in a clinical trial on psoriasis, the PASI (psoriasis area severity index) would possibly be one dependent variable. The independent variable (sometime also called explanatory variable) is something which is not affected by the experiment itself but which can be manipulated to affect the dependent variable. Other terms sometimes used synonymously include blocking variable, covariate, or predictor variable. Confounding variables are extra variables, which can have an effect on the experiment. They are linked with dependent and independent variables and can cause spurious association. For example, in a clinical trial for a topical treatment in psoriasis, the concomitant use of moisturizers might be a confounding variable. A control variable is a variable that must be kept constant during the course of an experiment.

Descriptive Statistics

Statistics can be broadly divided into descriptive statistics and inferential statistics.[ 3 , 4 ] Descriptive statistics give a summary about the sample being studied without drawing any inferences based on probability theory. Even if the primary aim of a study involves inferential statistics, descriptive statistics are still used to give a general summary. When we describe the population using tools such as frequency distribution tables, percentages, and other measures of central tendency like the mean, for example, we are talking about descriptive statistics. When we use a specific statistical test (e.g., Mann–Whitney U-test) to compare the mean scores and express it in terms of statistical significance, we are talking about inferential statistics. Descriptive statistics can help in summarizing data in the form of simple quantitative measures such as percentages or means or in the form of visual summaries such as histograms and box plots.

Descriptive statistics can be used to describe a single variable (univariate analysis) or more than one variable (bivariate/multivariate analysis). In the case of more than one variable, descriptive statistics can help summarize relationships between variables using tools such as scatter plots.

Descriptive statistics can be broadly put under two categories:

• Sorting/grouping and illustration/visual displays
• Summary statistics.

Sorting and grouping

Sorting and grouping is most commonly done using frequency distribution tables. For continuous variables, it is generally better to use groups in the frequency table. Ideally, group sizes should be equal (except in extreme ends where open groups are used; e.g., age “greater than” or “less than”).

Another form of presenting frequency distributions is the “stem and leaf” diagram, which is considered to be a more accurate form of description.

Suppose the weight in kilograms of a group of 10 patients is as follows:

56, 34, 48, 43, 87, 78, 54, 62, 61, 59

The “stem” records the value of the “ten's” place (or higher) and the “leaf” records the value in the “one's” place [ Table 1 ].

Stem and leaf plot

Illustration/visual display of data

The most common tools used for visual display include frequency diagrams, bar charts (for noncontinuous variables) and histograms (for continuous variables). Composite bar charts can be used to compare variables. For example, the frequency distribution in a sample population of males and females can be illustrated as given in Figure 1 .

Composite bar chart

A pie chart helps show how a total quantity is divided among its constituent variables. Scatter diagrams can be used to illustrate the relationship between two variables. For example, global scores given for improvement in a condition like acne by the patient and the doctor [ Figure 2 ].

Scatter diagram

Summary statistics

The main tools used for summary statistics are broadly grouped into measures of central tendency (such as mean, median, and mode) and measures of dispersion or variation (such as range, standard deviation, and variance).

Imagine that the data below represent the weights of a sample of 15 pediatric patients arranged in ascending order:

30, 35, 37, 38, 38, 38, 42, 42, 44, 46, 47, 48, 51, 53, 86

Just having the raw data does not mean much to us, so we try to express it in terms of some values, which give a summary of the data.

The mean is basically the sum of all the values divided by the total number. In this case, we get a value of 45.

The problem is that some extreme values (outliers), like “'86,” in this case can skew the value of the mean. In this case, we consider other values like the median, which is the point that divides the distribution into two equal halves. It is also referred to as the 50 th percentile (50% of the values are above it and 50% are below it). In our previous example, since we have already arranged the values in ascending order we find that the point which divides it into two equal halves is the 8 th value – 42. In case of a total number of values being even, we choose the two middle points and take an average to reach the median.

The mode is the most common data point. In our example, this would be 38. The mode as in our case may not necessarily be in the center of the distribution.

The median is the best measure of central tendency from among the mean, median, and mode. In a “symmetric” distribution, all three are the same, whereas in skewed data the median and mean are not the same; lie more toward the skew, with the mean lying further to the skew compared with the median. For example, in Figure 3 , a right skewed distribution is seen (direction of skew is based on the tail); data values' distribution is longer on the right-hand (positive) side than on the left-hand side. The mean is typically greater than the median in such cases.

Location of mode, median, and mean

Measures of dispersion

The range gives the spread between the lowest and highest values. In our previous example, this will be 86-30 = 56.

A more valuable measure is the interquartile range. A quartile is one of the values which break the distribution into four equal parts. The 25 th percentile is the data point which divides the group between the first one-fourth and the last three-fourth of the data. The first one-fourth will form the first quartile. The 75 th percentile is the data point which divides the distribution into a first three-fourth and last one-fourth (the last one-fourth being the fourth quartile). The range between the 25 th percentile and 75 th percentile is called the interquartile range.

Variance is also a measure of dispersion. The larger the variance, the further the individual units are from the mean. Let us consider the same example we used for calculating the mean. The mean was 45.

For the first value (30), the deviation from the mean will be 15; for the last value (86), the deviation will be 41. Similarly we can calculate the deviations for all values in a sample. Adding these deviations and averaging will give a clue to the total dispersion, but the problem is that since the deviations are a mix of negative and positive values, the final total becomes zero. To calculate the variance, this problem is overcome by adding squares of the deviations. So variance would be the sum of squares of the variation divided by the total number in the population (for a sample we use “n − 1”). To get a more realistic value of the average dispersion, we take the square root of the variance, which is called the “standard deviation.”

The box plot

The box plot is a composite representation that portrays the mean, median, range, and the outliers [ Figure 4 ].

The concept of skewness and kurtosis

Skewness is a measure of the symmetry of distribution. Basically if the distribution curve is symmetric, it looks the same on either side of the central point. When this is not the case, it is said to be skewed. Kurtosis is a representation of outliers. Distributions with high kurtosis tend to have “heavy tails” indicating a larger number of outliers, whereas distributions with low kurtosis have light tails, indicating lesser outliers. There are formulas to calculate both skewness and kurtosis [Figures ​ [Figures5 5 – 8 ].

Positive skew

High kurtosis (positive kurtosis – also called leptokurtic)

Negative skew

Low kurtosis (negative kurtosis – also called “Platykurtic”)

Sample Size

In an ideal study, we should be able to include all units of a particular population under study, something that is referred to as a census.[ 5 , 6 ] This would remove the chances of sampling error (difference between the outcome characteristics in a random sample when compared with the true population values – something that is virtually unavoidable when you take a random sample). However, it is obvious that this would not be feasible in most situations. Hence, we have to study a subset of the population to reach to our conclusions. This representative subset is a sample and we need to have sufficient numbers in this sample to make meaningful and accurate conclusions and reduce the effect of sampling error.

We also need to know that broadly sampling can be divided into two types – probability sampling and nonprobability sampling. Examples of probability sampling include methods such as simple random sampling (each member in a population has an equal chance of being selected), stratified random sampling (in nonhomogeneous populations, the population is divided into subgroups – followed be random sampling in each subgroup), systematic (sampling is based on a systematic technique – e.g., every third person is selected for a survey), and cluster sampling (similar to stratified sampling except that the clusters here are preexisting clusters unlike stratified sampling where the researcher decides on the stratification criteria), whereas nonprobability sampling, where every unit in the population does not have an equal chance of inclusion into the sample, includes methods such as convenience sampling (e.g., sample selected based on ease of access) and purposive sampling (where only people who meet specific criteria are included in the sample).

An accurate calculation of sample size is an essential aspect of good study design. It is important to calculate the sample size much in advance, rather than have to go for post hoc analysis. A sample size that is too less may make the study underpowered, whereas a sample size which is more than necessary might lead to a wastage of resources.

We will first go through the sample size calculation for a hypothesis-based design (like a randomized control trial).

The important factors to consider for sample size calculation include study design, type of statistical test, level of significance, power and effect size, variance (standard deviation for quantitative data), and expected proportions in the case of qualitative data. This is based on previous data, either based on previous studies or based on the clinicians' experience. In case the study is something being conducted for the first time, a pilot study might be conducted which helps generate these data for further studies based on a larger sample size). It is also important to know whether the data follow a normal distribution or not.

Two essential aspects we must understand are the concept of Type I and Type II errors. In a study that compares two groups, a null hypothesis assumes that there is no significant difference between the two groups, and any observed difference being due to sampling or experimental error. When we reject a null hypothesis, when it is true, we label it as a Type I error (also denoted as “alpha,” correlating with significance levels). In a Type II error (also denoted as “beta”), we fail to reject a null hypothesis, when the alternate hypothesis is actually true. Type II errors are usually expressed as “1- β,” correlating with the power of the test. While there are no absolute rules, the minimal levels accepted are 0.05 for α (corresponding to a significance level of 5%) and 0.20 for β (corresponding to a minimum recommended power of “1 − 0.20,” or 80%).

Effect size and minimal clinically relevant difference

For a clinical trial, the investigator will have to decide in advance what clinically detectable change is significant (for numerical data, this is could be the anticipated outcome means in the two groups, whereas for categorical data, it could correlate with the proportions of successful outcomes in two groups.). While we will not go into details of the formula for sample size calculation, some important points are as follows:

In the context where effect size is involved, the sample size is inversely proportional to the square of the effect size. What this means in effect is that reducing the effect size will lead to an increase in the required sample size.

Reducing the level of significance (alpha) or increasing power (1-β) will lead to an increase in the calculated sample size.

An increase in variance of the outcome leads to an increase in the calculated sample size.

A note is that for estimation type of studies/surveys, sample size calculation needs to consider some other factors too. This includes an idea about total population size (this generally does not make a major difference when population size is above 20,000, so in situations where population size is not known we can assume a population of 20,000 or more). The other factor is the “margin of error” – the amount of deviation which the investigators find acceptable in terms of percentages. Regarding confidence levels, ideally, a 95% confidence level is the minimum recommended for surveys too. Finally, we need an idea of the expected/crude prevalence – either based on previous studies or based on estimates.

Sample size calculation also needs to add corrections for patient drop-outs/lost-to-follow-up patients and missing records. An important point is that in some studies dealing with rare diseases, it may be difficult to achieve desired sample size. In these cases, the investigators might have to rework outcomes or maybe pool data from multiple centers. Although post hoc power can be analyzed, a better approach suggested is to calculate 95% confidence intervals for the outcome and interpret the study results based on this.

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Conflicts of interest.

There are no conflicts of interest.

Independent and Dependent Variables

This guide discusses how to identify independent and dependent variables effectively and incorporate their description within the body of a research paper.

A variable can be anything you might aim to measure in your study, whether in the form of numerical data or reflecting complex phenomena such as feelings or reactions. Dependent variables change due to the other factors measured, especially if a study employs an experimental or semi-experimental design. Independent variables are stable: they are both presumed causes and conditions in the environment or milieu being manipulated.

Identifying Independent and Dependent Variables

Even though the definitions of the terms independent and dependent variables may appear to be clear, in the process of analyzing data resulting from actual research, identifying the variables properly might be challenging. Here is a simple rule that you can apply at all times: the independent variable is what a researcher changes, whereas the dependent variable is affected by these changes. To illustrate the difference, a number of examples are provided below.

• The purpose of Study 1 is to measure the impact of different plant fertilizers on how many fruits apple trees bear. Independent variable : plant fertilizers (chosen by researchers) Dependent variable : fruits that the trees bear (affected by choice of fertilizers)
• The purpose of Study 2 is to find an association between living in close vicinity to hydraulic fracturing sites and respiratory diseases. Independent variable: proximity to hydraulic fracturing sites (a presumed cause and a condition of the environment) Dependent variable: the percentage/ likelihood of suffering from respiratory diseases

Confusion is possible in identifying independent and dependent variables in the social sciences. When considering psychological phenomena and human behavior, it can be difficult to distinguish between cause and effect. For example, the purpose of Study 3 is to establish how tactics for coping with stress are linked to the level of stress-resilience in college students. Even though it is feasible to speculate that these variables are interdependent, the following factors should be taken into account in order to clearly define which variable is dependent and which is interdependent.

• The dependent variable is usually the objective of the research. In the study under examination, the levels of stress resilience are being investigated.
• The independent variable precedes the dependent variable. The chosen stress-related coping techniques help to build resilience; thus, they occur earlier.

Writing Style and Structure

Usually, the variables are first described in the introduction of a research paper and then in the method section. No strict guidelines for approaching the subject exist; however, academic writing demands that the researcher make clear and concise statements. It is only reasonable not to leave readers guessing which of the variables is dependent and which is independent. The description should reflect the literature review, where both types of variables are identified in the context of the previous research. For instance, in the case of Study 3, a researcher would have to provide an explanation as to the meaning of stress resilience and coping tactics.

In properly organizing a research paper, it is essential to outline and operationalize the appropriate independent and dependent variables. Moreover, the paper should differentiate clearly between independent and dependent variables. Finding the dependent variable is typically the objective of a study, whereas independent variables reflect influencing factors that can be manipulated. Distinguishing between the two types of variables in social sciences may be somewhat challenging as it can be easy to confuse cause with effect. Academic format calls for the author to mention the variables in the introduction and then provide a detailed description in the method section.

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Home » Dependent Variable – Definition, Types and Example

Dependent Variable – Definition, Types and Example

Table of Contents

Dependent Variable

Definition:

Dependent variable is a variable in a study or experiment that is being measured or observed and is affected by the independent variable. In other words, it is the variable that researchers are interested in understanding, predicting, or explaining based on the changes made to the independent variable.

Types of Dependent Variables

Types of Dependent Variables are as follows:

• Continuous dependent variable : A continuous variable is a variable that can take on any value within a certain range. Examples include height, weight, and temperature.
• Discrete dependent variable: A discrete variable is a variable that can only take on certain values within a certain range. Examples include the number of children in a family, the number of pets someone has, and the number of cars owned by a household.
• Categorical dependent variable: A categorical variable is a variable that can take on values that belong to specific categories or groups. Examples include gender, race, and marital status.
• Dichotomous dependent variable: A dichotomous variable is a categorical variable that can take on only two values. Examples include whether someone is a smoker or non-smoker, or whether someone has a certain medical condition or not.
• Ordinal dependent variable: An ordinal variable is a categorical variable that has a specific order or ranking to its categories. Examples include education level (e.g., high school diploma, college degree, graduate degree), or socioeconomic status (e.g., low, middle, high).
• Interval dependent variable: An interval variable is a continuous variable that has a specific measurement scale with equal intervals between the values. Examples include temperature measured in degrees Celsius or Fahrenheit.
• Ratio dependent variable : A ratio variable is a continuous variable that has a true zero point and equal intervals between the values. Examples include height, weight, and income.
• Count dependent variable: A count variable is a discrete variable that represents the number of times an event occurs within a specific time period. Examples include the number of times a customer visits a store, or the number of times a student misses a class.
• Time-to-event dependent variable: A time-to-event variable is a type of continuous variable that measures the time it takes for an event to occur. Examples include the time until a customer makes a purchase, or the time until a patient recovers from an illness.
• Latent dependent variable: A latent variable is a variable that cannot be directly observed or measured, but is inferred from other observable variables. Examples include intelligence, personality traits, and motivation.
• Binary dependent variable: A binary variable is a dichotomous variable with only two possible outcomes, usually represented by 0 or 1. Examples include whether a customer will make a purchase or not, or whether a patient will respond to a treatment or not.
• Multinomial dependent variable: A multinomial variable is a categorical variable with more than two possible outcomes. Examples include political affiliation, type of employment, or type of transportation used to commute.
• Longitudinal dependent variable : A longitudinal variable is a type of continuous variable that measures change over time. Examples include academic performance, income, or health status.

Examples of Dependent Variable

Here are some examples of dependent variables in different fields:

• In physics : The velocity of an object is a dependent variable as it changes in response to the force applied to it.
• In psychology : The level of happiness or satisfaction of a person can be a dependent variable as it may change in response to different factors such as the level of stress or social support.
• I n medicine: The effectiveness of a new drug can be a dependent variable as it may be measured in relation to the symptoms of a disease.
• In education : The grades of a student can be a dependent variable as they may be influenced by factors such as teaching methods or amount of studying.
• In economics : The demand for a product can be a dependent variable as it may change in response to factors such as the price or availability of the product.
• In biology : The growth rate of a plant can be a dependent variable as it may change in response to factors such as sunlight, water, or soil nutrients.
• In sociology: The level of social support for an individual can be a dependent variable as it may change in response to factors such as the availability of community resources or the strength of social networks.
• In marketing : The sales of a product can be a dependent variable as they may change in response to factors such as advertising, pricing, or consumer trends.
• In environmental science : The biodiversity of an ecosystem can be a dependent variable as it may change in response to factors such as climate change, pollution, or habitat destruction.
• I n political science : The outcome of an election can be a dependent variable as it may change in response to factors such as campaign strategies, political advertising, or voter turnout.
• I n criminology : The likelihood of a person committing a crime can be a dependent variable as it may change in response to factors such as poverty, education, or socialization.
• In engineering : The efficiency of a machine can be a dependent variable as it may change in response to factors such as the materials used, the design of the machine, or the operating conditions.
• In linguistics: The speed and accuracy of language processing can be a dependent variable as they may change in response to factors such as linguistic complexity, language experience, or cognitive ability.
• In history : The outcome of a historical event, such as a battle or a revolution, can be a dependent variable as it may change in response to factors such as leadership, strategy, or external forces.
• In sports science : The performance of an athlete can be a dependent variable as it may change in response to factors such as training methods, nutrition, or psychological factors.

Applications of Dependent Variable

• Experimental studies: In experimental studies, the dependent variable is used to test the effect of one or more independent variables on the outcome variable. For example, in a study on the effect of a new drug on blood pressure, the dependent variable is the blood pressure.
• Observational studies : In observational studies, the dependent variable is used to explore the relationship between two or more variables. For example, in a study on the relationship between physical activity and depression, the dependent variable is the level of depression.
• Psychology : In psychology, dependent variables are used to measure the response or behavior of individuals in response to different experimental or natural conditions.
• Predictive modeling : In predictive modeling, the dependent variable is used to predict the outcome of a future event or situation. For example, in financial modeling, the dependent variable can be used to predict the future value of a stock or currency.
• Regression analysis : In regression analysis, the dependent variable is used to predict the value of one or more independent variables based on their relationship with the dependent variable. For example, in a study on the relationship between income and education, the dependent variable is income.
• Machine learning : In machine learning, the dependent variable is used to train the model to predict the value of the dependent variable based on the values of one or more independent variables. For example, in image recognition, the dependent variable can be used to identify the object in an image.
• Quality control : In quality control, the dependent variable is used to monitor the performance of a product or process. For example, in a manufacturing process, the dependent variable can be used to measure the quality of the product and identify any defects.
• Marketing research : In marketing research, the dependent variable is used to understand consumer behavior and preferences. For example, in a study on the effectiveness of a new advertising campaign, the dependent variable can be used to measure consumer response to the ad.
• Social sciences research : In social sciences research, the dependent variable is used to study human behavior and attitudes. For example, in a study on the impact of social media on mental health, the dependent variable can be used to measure the level of anxiety or depression.
• Epidemiological studies: In epidemiological studies, the dependent variable is used to investigate the prevalence and incidence of diseases or health conditions. For example, in a study on the risk factors for heart disease, the dependent variable can be used to measure the occurrence of heart disease.
• Environmental studies : In environmental studies, the dependent variable is used to assess the impact of environmental factors on ecosystems and natural resources. For example, in a study on the effect of pollution on aquatic life, the dependent variable can be used to measure the health and survival of aquatic organisms.
• Educational research: In educational research, the dependent variable is used to study the effectiveness of different teaching methods and instructional strategies. For example, in a study on the impact of a new teaching program on student achievement, the dependent variable can be used to measure student performance.

Purpose of Dependent Variable

The purpose of the dependent variable is to help researchers understand the relationship between the independent variable and the outcome they are studying. By measuring the changes in the dependent variable, researchers can determine the effects of different variables on the outcome of interest.

When to use Dependent Variable

Following are some situations When to use Dependent Variable:

• When conducting scientific research or experiments, the dependent variable is the factor that is being measured or observed to determine its relationship with other factors or variables.
• In statistical analysis, the dependent variable is the outcome or response variable that is being predicted or explained by one or more independent variables.
• When formulating hypotheses, the dependent variable is the variable that is being predicted or explained by the independent variable(s).
• When writing a research paper or report, it is important to clearly define the dependent variable(s) in order to provide a clear understanding of the research question and methods used to answer it.
• In social sciences, such as psychology or sociology, the dependent variable may refer to behaviors, attitudes, or other measurable aspects of individuals or groups.
• In natural sciences, such as biology or physics, the dependent variable may refer to physical properties or characteristics, such as temperature, speed, or mass.
• The dependent variable is often contrasted with the independent variable, which is the variable that is being manipulated or changed in order to observe its effects on the dependent variable.

Characteristics of Dependent Variable

Some Characteristics of Dependent Variable are as follows:

• The dependent variable is the outcome or response variable in the study.
• Its value depends on the values of one or more independent variables.
• The dependent variable is typically measured or observed, rather than manipulated by the researcher.
• It can be continuous (e.g., height, weight) or categorical (e.g., yes/no, red/green/blue).
• The dependent variable should be relevant to the research question and meaningful to the study participants.
• It should have a clear and consistent definition and be measured or observed consistently across all participants in the study.
• The dependent variable should be valid and reliable, meaning that it measures what it is intended to measure and produces consistent results over time.

Advantages of Dependent Variable

Some Advantages of Dependent Variable are as follows:

• Allows for the testing of hypotheses: By measuring the dependent variable in response to changes in the independent variable, researchers can test hypotheses and draw conclusions about cause-and-effect relationships.
• Provides insight into the relationship between variables: The dependent variable can provide insight into how one variable is related to another, allowing researchers to identify patterns and make predictions about future outcomes.
• Enables the evaluation of interventions : By measuring changes in the dependent variable over time, researchers can evaluate the effectiveness of interventions and determine whether they have a meaningful impact on the outcome being studied.
• Enables the comparison of groups: The dependent variable can be used to compare groups of participants or populations, helping researchers to identify differences or similarities and draw conclusions about underlying factors that may be contributing to those differences.
• Enables the calculation of statistical measures: By measuring the dependent variable, researchers can calculate statistical measures such as means, variances, and standard deviations, which are used to make statistical inferences about the population being studied.

Disadvantages of Dependent Variable

• Limited in scope: The dependent variable is limited to the specific outcome being studied, which may not capture the full complexity of the system or phenomenon being investigated.
• Vulnerable to confounding variables: Confounding variables, or factors that are not controlled for in the study, can influence the dependent variable and obscure the relationship between the independent and dependent variables.
• Prone to measurement error: The dependent variable may be subject to measurement error due to issues with data collection methods or measurement instruments, which can lead to inaccurate or unreliable results.
• Limited to observable variables : The dependent variable is typically limited to variables that can be measured or observed, which may not capture underlying or latent variables that may be important for understanding the phenomenon being studied.
• Ethical concerns: In some cases, measuring the dependent variable may raise ethical concerns, such as in studies of sensitive topics or vulnerable populations.
• Limited to specific time periods : The dependent variable is typically measured at specific time points or over specific time periods, which may not capture changes or fluctuations in the outcome over longer periods of time.

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Variables in Quantitative Research: A Beginner's Guide (COUN)

Quantitative variables.

Because quantitative methodology requires measurement, the concepts being investigated need to be defined in a way that can be measured. Organizational change, reading comprehension, emergency response, or depression are concepts, but they cannot be measured as such. Frequency of organizational change, reading comprehension scores, emergency response time, or types of depression can be measured. They are variables (concepts that can vary).

• Independent variables (IV).
• Dependent variables (DV).
• Sample variables.
• Extraneous variables.

Independent Variables (IV)

Independent variables (IV) are those that are suspected of being the cause in a causal relationship. If you are asking a cause and effect question, your IV will be the variable (or variables) that you suspect causes the effect.

There are two main sorts of IV—active independent variables and attribute independent variables:

• Active IV are interventions or conditions that are being applied to the participants. A special tutorial for the third graders, a new therapy for clients, or a new training program being tested on employees would be active IVs.
• Attribute IV are intrinsic characteristics of the participants that are suspected of causing a result. For example, if you are examining whether gender which is intrinsic to the participants results in higher or lower scores on some skill, gender is an attribute IV.
• Both types of IV can have what are called levels. For example:
• In the example above, the active IV special tutorial , receiving the tutorial is one level, and tutorial withheld (control) is a second level.
• In the same example, being a third grader would be an attribute IV. It could be defined as only one level—being in third grade or you might wish to define it with more than one level, such as first half of third grade and second half of third grade. Indeed, that attribute IV could take many more, for example, if you wished to look at each month of third grade.

Independent variables are frequently called different things depending on the nature of the research question. In predictive questions, where a variable is thought to predict another but it is not yet appropriate to ask whether it causes the other, the IV is usually called a predictor or criterion variable rather than an independent variable.

Dependent Variables (DV)

• Dependent variables are variables that depend on or are influenced by the independent variables.
• They are outcomes or results of the influence of the independent variable.
• Dependent variables answer the question, "What do I observe happening when I apply the intervention?"
• The dependent variable receives the intervention.

In questions where full clausation is not assumed, such as a predictive question or a question about differences between groups but no manipulation of an IV, the dependent variables are usually called outcome variable s, and the independent variables are usually called the predictor or criterion variables.

Sample Variables

In some studies, some characteristic of the participants must be measured for some reason, but that characteristic is not the IV or the DV. In this case, these are called sample variables. For example, suppose you are investigating whether amount of sleep affects level of concentration in depressed people. In order to obtain a sample of depressed people, a standard test of depression will be given. So the presence or absence of depression will be a sample variable. That score is not used as an IV or a DV, but simply to get the appropriate people into the sample.

When there is no measure of a characteristic of the participants, the characteristic is called a sample characteristic . When the characteristic must be measured, it is called a sample variable .

Extraneous Variables

Extraneous variables are not of interest to the study, but may influence the dependent variable. For this reason, most quantitative studies attempt to control extraneous variables. The literature should inform you what extraneous variables to account for. For example, in the study of third graders' reading scores, variables such as noise levels in the testing room, the size or lighting or temperature of the room, and whether the children had had a good breakfast might be extraneous variables.

There is a special class of extraneous variables called confounding variables. These are variables that can cause the effect we are looking for if they are not controlled for, resulting in a false finding that the IV is effective when it is not. In a study of changes in skill levels in a group of caseworkers after a training program, if the follow-up measure is taken relatively late after the training, the simple effect of practicing the skills might explain improved scores, and the training might be mistakenly thought to be successful when it was not.

There are many details about variables not covered in this handout. Please consult any text on research methods for a more comprehensive review.

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Types of Variables in Research – Definition & Examples

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A fundamental component in statistical investigations is the methodology you employ in selecting your research variables. The careful selection of appropriate variable types can significantly enhance the robustness of your experimental design . This piece explores the diverse array of variable classifications within the field of statistical research. Additionally, understanding the different types of variables in research can greatly aid in shaping your experimental hypotheses and outcomes.

Inhaltsverzeichnis

• 1 Types of Variables in Research – In a Nutshell
• 2 Definition: Types of variables in research
• 3 Types of variables in research – Quantitative vs. Categorical
• 4 Types of variables in research – Independent vs. Dependent
• 5 Other useful types of variables in research

Types of Variables in Research – In a Nutshell

• A variable is an attribute of an item of analysis in research.
• The types of variables in research can be categorized into: independent vs. dependent , or categorical vs. quantitative .
• The types of variables in research (correlational) can be classified into predictor or outcome variables.
• Other types of variables in research are confounding variables , latent variables , and composite variables.

Definition: Types of variables in research

A variable is a trait of an item of analysis in research. Types of variables in research are imperative, as they describe and measure places, people, ideas , or other research objects . There are many types of variables in research. Therefore, you must choose the right types of variables in research for your study.

Note that the correct variable will help with your research design , test selection, and result interpretation.

In a study testing whether some genders are more stress-tolerant than others, variables you can include are the level of stressors in the study setting, male and female subjects, and productivity levels in the presence of stressors.

Also, before choosing which types of variables in research to use, you should know how the various types work and the ideal statistical tests and result interpretations you will use for your study. The key is to determine the type of data the variable contains and the part of the experiment the variable represents.

Types of variables in research – Quantitative vs. Categorical

Data is the precise extent of a variable in statistical research that you record in a data sheet. It is generally divided into quantitative and categorical classes.

Quantitative or numerical data represents amounts, while categorical data represents collections or groupings.

The type of data contained in your variable will determine the types of variables in research. For instance, variables consisting of quantitative data are called quantitative variables, while those containing categorical data are called categorical variables. The section below explains these two types of variables in research better.

Quantitative variables

The scores you record when collecting quantitative data usually represent real values you can add, divide , subtract , or multiply . There are two types of quantitative variables: discrete variables and continuous variables .

The table below explains the elements that set apart discrete and continuous types of variables in research:

Categorical variables

Categorical variables contain data representing groupings. Additionally, the data in categorical variables is sometimes recorded as numbers . However, the numbers represent categories instead of real amounts.

There are three categorical types of variables in research: nominal variables, ordinal variables , and binary variables . Here is a tabular summary.

It is worth mentioning that some categorical variables can function as multiple types. For example, in some studies, you can use ordinal variables as quantitative variables if the scales are numerical and not discrete.

Data sheet of quantitative and categorical variables

A data sheet is where you record the data on the variables in your experiment.

In a study of the salt-tolerance levels of various plant species, you can record the data on salt addition and how the plant responds in your datasheet.

The key is to gather the information and draw a conclusion over a specific period and filling out a data sheet along the process.

Below is an example of a data sheet containing binary, nominal, continuous , and ordinal types of variables in research.

Types of variables in research – Independent vs. Dependent

The purpose of experiments is to determine how the variables affect each other. As stated in our experiment above, the study aims to find out how the quantity of salt introduce in the water affects the plant’s growth and survival.

Therefore, the researcher manipulates the independent variables and measures the dependent variables . Additionally, you may have control variables that you hold constant.

The table below summarizes independent variables, dependent variables , and control variables .

Data sheet of independent and dependent variables

In salt-tolerance research, there is one independent variable (salt amount) and three independent variables. All other variables are neither dependent nor independent.

Below is a data sheet based on our experiment:

Types of variables in correlational research

The types of variables in research may differ depending on the study.

In correlational research , dependent and independent variables do not apply because the study objective is not to determine the cause-and-effect link between variables.

However, in correlational research, one variable may precede the other, as illness leads to death, and not vice versa. In such an instance, the preceding variable, like illness, is the predictor variable, while the other one is the outcome variable.

Other useful types of variables in research

The key to conducting effective research is to define your types of variables as independent and dependent. Next, you must determine if they are categorical or numerical types of variables in research so you can choose the proper statistical tests for your study.

Below are other types of variables in research worth understanding.

What is the definition for independent and dependent variables?

An autonomous or independent variable is the one you believe is the origin of the outcome, while the dependent variable is the one you believe affects the outcome of your study.

What are quantitative and categorical variables?

Knowing the types of variables in research that you can work with will help you choose the best statistical tests and result representation techniques. It will also help you with your study design.

Discrete and continuous variables: What is their difference?

Discrete variables are types of variables in research that represent counts, like the quantities of objects. In contrast, continuous variables are types of variables in research that represent measurable quantities like age, volume, and weight.

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What are Variables and Why are They Important in Research?

In research, variables are crucial components that help to define and measure the concepts and phenomena under investigation. Variables are defined as any characteristic or attribute that can vary or change in some way. They can be measured, manipulated, or controlled to investigate the relationship between different factors and their impact on the research outcomes. In this essay, I will discuss the importance of variables in research, highlighting their role in defining research questions, designing studies, analyzing data, and drawing conclusions.

Defining Research Questions

Variables play a critical role in defining research questions. Research questions are formulated based on the variables that are under investigation. These questions guide the entire research process, including the selection of research methods, data collection procedures, and data analysis techniques. Variables help researchers to identify the key concepts and phenomena that they wish to investigate, and to formulate research questions that are specific, measurable, and relevant to the research objectives.

For example, in a study on the relationship between exercise and stress, the variables would be exercise and stress. The research question might be: “What is the relationship between the frequency of exercise and the level of perceived stress among young adults?”

Designing Studies

Variables also play a crucial role in the design of research studies. The selection of variables determines the type of research design that will be used, as well as the methods and procedures for collecting and analyzing data. Variables can be independent, dependent, or moderator variables, depending on their role in the research design.

Independent variables are the variables that are manipulated or controlled by the researcher. They are used to determine the effect of a particular factor on the dependent variable. Dependent variables are the variables that are measured or observed to determine the impact of the independent variable. Moderator variables are the variables that influence the relationship between the independent and dependent variables.

For example, in a study on the effect of caffeine on athletic performance, the independent variable would be caffeine, and the dependent variable would be athletic performance. The moderator variables could include factors such as age, gender, and fitness level.

Analyzing Data

Variables are also essential in the analysis of research data. Statistical methods are used to analyze the data and determine the relationships between the variables. The type of statistical analysis that is used depends on the nature of the variables, their level of measurement, and the research design.

For example, if the variables are categorical or nominal, chi-square tests or contingency tables can be used to determine the relationships between them. If the variables are continuous, correlation analysis or regression analysis can be used to determine the strength and direction of the relationship between them.

Drawing Conclusions

Finally, variables are crucial in drawing conclusions from research studies. The results of the study are based on the relationship between the variables and the conclusions drawn depend on the validity and reliability of the research methods and the accuracy of the statistical analysis. Variables help to establish the cause-and-effect relationships between different factors and to make predictions about the outcomes of future events.

For example, in a study on the effect of smoking on lung cancer, the independent variable would be smoking, and the dependent variable would be lung cancer. The conclusion would be that smoking is a risk factor for lung cancer, based on the strength and direction of the relationship between the variables.

In conclusion, variables play a crucial role in research across different fields and disciplines. They help to define research questions, design studies, analyze data, and draw conclusions. By understanding the importance of variables in research, researchers can design studies that are relevant, accurate, and reliable, and can provide valuable insights into the phenomena under investigation. Therefore, it is essential to consider variables carefully when designing, conducting, and interpreting research studies.

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4.1 Introduction to Probability and Random Variables

Learning Objectives

By the end of this chapter, the student should be able to:

• Understand the terminology and basic rules of probability
• Handle general discrete random variables
• Recognize and apply the binomial distribution
• Understand general continuous random variables
• Recognize and apply special cases of continuous random variables (uniform, normal)
• Use the normal distribution to approximate the binomial

More than likely, you have used probability. In fact, you probably have an intuitive sense of probability. Probability deals with the chance of an event occurring. Whenever you weigh the odds of whether or not to do your homework or to study for an exam, you are using probability. In this chapter, you will learn how to solve probability problems using a systematic approach.

Probability

Probability is a measure that is associated with how certain we are of outcomes of a particular experiment or activity. An experiment is a planned operation carried out under controlled conditions. If the result is not predetermined, then the experiment is said to be a probability experiment . Flipping one fair coin twice is an example of an experiment.

A result of an experiment is called an outcome . The sample space of an experiment is the set of all possible outcomes. Three ways to represent a sample space are listing the possible outcomes, creating a tree diagram, or creating a Venn diagram. The uppercase letter S is used to denote the sample space. For example, if you flip one fair coin, S = { H , T } where H ( heads) and T (tails) are the outcomes.

An event is any combination of outcomes. Upper case letters like A and B represent events. For example, if the experiment is to flip one fair coin, event A might be getting at most one head. The probability of an event A is written P ( A ).

The probability of any outcome is the long-term relative frequency of that outcome. Probabilities are between zero and one, inclusive (that is, zero, one, and all numbers between these values). P ( A ) = 0 means that event A can never happen. P ( A ) = 1 means that event A always happens. P ( A ) = 0.5 means that event A is equally likely to occur or not to occur. For example, if you flip one fair coin repeatedly (from 20 to 2,000 to 20,000 times), the relative frequency of heads approaches 0.5 (the probability of heads).

A probability model is a mathematical representation of a random process that lists all possible outcomes and assigns probabilities to each of them. This type of model is our ultimately our goal when moving forward in our study of statistics.

The Law of Large Numbers

An important characteristic of probability experiments known as the law of large numbers states that, as the number of repetitions of an experiment increases, the relative frequency obtained in the experiment tends to become closer and closer to the theoretical probability. Even though the outcomes do not happen according to any set pattern or order, overall, the long-term observed relative frequency will approach the theoretical probability. (The word “empirical” is often used instead of the word “observed.”)

If you toss a coin and record the result, what is the probability that the result is heads? If you flip a coin two times, does probability tell you that these flips will result in one heads and one tail? You might toss a fair coin ten times and record nine heads. Probability does not describe the short-term results of an experiment; rather, it gives information about what can be expected in the long term. To demonstrate this, Karl Pearson once tossed a fair coin 24,000 times! He recorded the results of each toss, obtaining heads 12,012 times. In his experiment, Pearson illustrated the law of large numbers.

The Axioms of Probability

Finding probabilities in more complicated situations starts with the three axioms of probability:

• 0 ≤ P(E) ≤ 1
• For each two events E 1 and E 2 with E 1 ∩ E 2 = Ø, P(E 1 U E 2 ) = P(E 1 ) + P(E 2 )

The first two axioms should be fairly intuitive. Axiom 1 says that the probabilities of all outcomes in a sample space will always add up to 1. Axiom 2 says the probability of any event must be between 0 and 1. For now, the third axiom, called the disjoint addition rule, isn’t that important, but the upcoming ideas are based on the first two axioms.

The Complement

Suppose we know the probability of an event occurring but want to know the probability it does not occur, or vice versa? We can easily find this from the first two axioms of probability.

There are several useful forms of the complement rule:

• P ( A ) + P ( A′ ) = 1
• 1 – P ( A ) = P ( A′ )
• 1 – P ( A’ ) = P ( A )

Random Variables

Random variables (RVs) are probability models quantifying situations. A random variable describes the outcomes of a statistical experiment in words or as a function that assigns each element of a sample space a unique real number. Uppercase letters such as X or Y typically denote a random variable. Lowercase letters like x or y denote a specific value of that random variable. If X is a random variable, then X is written in words, and x is given as a number. For example, the probability of the random variable X being equal to 3 is denoted as P(X=3).

There are both continuous and discrete random variables depending on the type of data that situation would produce. We will begin with discrete random variables (DRVs) and revisit continuous random variables (CRVs) in the future.

Click here for more multimedia resources, including podcasts, videos, lecture notes, and worked examples.

Figure References

Figure 4.1: Ed Sweeney (2009). 2009 Leonid Meteor. CC BY 2.0. https://flic.kr/p/7girE8

The study of randomness; a number between zero and one, inclusive, that gives the likelihood that a specific event will occur

A random experiment where the result is not predetermined

A particular result of an experiment

The set of all possible outcomes of an experiment

An outcome or subset of outcomes of an experiment in which you are interested

A mathematical representation of a random process that lists all possible outcomes and assigns probabilities to each

As the number of trials in a probability experiment increases, the relative frequency of an event approaches the theoretical probability

The complement of an event consists of all outcomes in a sample space that are NOT in the event.

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Research Variables: Types, Uses and Definition of Terms

The purpose of research is to describe and explain variance in the world, that is, variance that occurs naturally in the world or change that we create due to manipulation. Variables are therefore the names that are given to the variance we wish to explain and it is very critical to the research because the way the researcher uses or handles them in the research process could determine the nature and direction of the research (Nwankwo and Emunemu, 2014). Closely related to the understanding of what a variable is, is the idea of definition of terms. This chapter explores the use of variables in research, types of variables and the definition of terms, so as to help some of the students who have a problem identifying and clarifying the variables they are working on in their project work.

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George Argyrous , Glyze Abella

This book aims to help people analyze quantitative information. Before detailing the 'hands-on' analysis we will explore in later chapters, this introductory chapter will discuss some of the background conceptual issues that are precursors to statistical analysis. The chapter begins where most research in fact begins; with research questions. A research question states the aim of a research project in terms of cases of interest and the variables upon which these cases are thought to differ. A few examples of research questions are: 'What is the age distribution of the students in my statistics class?' 'Is there a relationship between the health status of my statistics students and their sex?' 'Is any relationship between the health status and the sex of students in my statistics class affected by the age of the students?' We begin with very clear, precisely stated research questions such as these that will guide the way we conduct research and ensure that we do not end up with a jumble of information that does not create any real knowledge. We need a clear research question (or questions) in mind before undertaking statistical analysis to avoid the situation where huge amounts of data are gathered unnecessarily, and which do not lead to any meaningful results. I suspect that a great deal of the confusion associated with statistical analysis actually arises from imprecision in the research questions that are meant to guide it. It is very difficult to select the relevant type of analysis to undertake, given the many possible analyses we could employ on a given set of data, if we are uncertain of our objectives. If we don't know why we are undertaking research in the first place, then it follows we will not know what to do with research data once we have gathered them. Conversely, if we are clear about the research question(s) we are addressing the statistical techniques to apply follow almost as a matter of course. We can see that each of the research questions above identifies the entities that I wish to investigate. In each question these entities are students in my statistics class, who are thus the units of analysis – the cases of interest – to my study.

Abimbola Awotedu

International Journal of Methodology

Akaawase Mchi

This paper discusses the importance of variable conceptualisation and measurement in environmental research. The paper explains how wrong application of concepts can mislead the researcher when conducting research, and the resultant effects on each stage of the environmental research process. The paper is motivated by the problems behind many research students pursuing their masters or doctoral degree programmes face, especially with change in dissertations or theses titles and methods to match the contents of their reports. In this paper, the authors demystify the challenges encountered by unskilful researchers and students when trying to make their readers have a clear understanding of their research reports (dissertations or theses). Therefore, the paper may serve as a guide in planning and conducting environmental research by university degree students and early career researchers.

Faith Musango

Symeou, L. & Lamprianou, J.

Loizos Symeou , Iasonas Lamprianou

Santo Di Nuovo

The article deals with the use of variables in quantitative psychological research. Topics as the choice of variables, their measurement and statistical analysis, the deductions based on data, are briefly reviewed. All variables can be misleading if used in a misleading way, but the Author contends that the psychology based on the variables has not the possibility to represent selected samples of inner processes and contents. Quantitative analyses based on linear causality and probabilistic inference pose many problems, but some alternative approaches devised to cope with these problems are indicated. An hermeneutic approach aware of the constructivist ground of the scientific knowledge is proposed.

Rahul Pilani

Environmental Policy Convergence in Europe

Stephan Heichel

International Journal of Religion

José Mario Ochoa-Pachas , Luis Pajuelo , JOSE MARIO OCHOA PACHAS

It is common to use Bloom's taxonomy to write research objectives; however, it is often forgotten that this Bloomian classification corresponds to the teaching-learning process. Likewise, is not usual to include the levels or scope of research since so many classifications have been proposed, suggesting that science can be fragmented and that qualitative studies have nothing to do with quantitative studies and vice versa. Regardless of the coincidences and discrepancies that may exist, researchers require a guideline that is based on the principles of science to be able to organize and structure their studies and that allows for growth and development, removing biases and partialities from analysis. It is necessary to remember that a taxonomy is valid if it adheres to the criteria that scientific knowledge itself indicates. This research is an exploratory and observational study whose purpose is to identify its objectives according to its levels with their respective study variables.

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Prediction models for perioperative blood transfusion in patients undergoing gynecologic surgery: a systematic review.

1. Introduction

2. materials and methods, 2.1. eligibility criteria, 2.1.1. population/participants, 2.1.2. interventions and comparators (models), 2.1.3. outcomes, 2.1.4. timing, 2.1.5. setting, 2.2. information sources and search strategy, 2.3. study selection, 2.4. data collection, 2.5. risk of bias assessment, 2.6. summary measures of the model’s predictive performance, 2.7. visualization, 3.1. results of the search, 3.2. included studies, 3.2.1. participants, 3.2.2. predictors, 3.2.3. outcome, 3.2.4. prediction model development and validation, 3.3. risk of bias and applicability concerns, 3.3.1. model development, participants, 3.3.2. model external validation, 3.4. models’ predictive performances ( table 2 ), 4. discussion, 4.1. summary of findings, 4.2. relevant literature, 4.3. strengths and limitations, 4.4. implications for research, 5. conclusions, supplementary materials, author contributions, institutional review board statement, informed consent statement, data availability statement, conflicts of interest.

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Pan, Z.; Charoenkwan, K. Prediction Models for Perioperative Blood Transfusion in Patients Undergoing Gynecologic Surgery: A Systematic Review. Diagnostics 2024 , 14 , 2018. https://doi.org/10.3390/diagnostics14182018

Pan Z, Charoenkwan K. Prediction Models for Perioperative Blood Transfusion in Patients Undergoing Gynecologic Surgery: A Systematic Review. Diagnostics . 2024; 14(18):2018. https://doi.org/10.3390/diagnostics14182018

Pan, Zhongmian, and Kittipat Charoenkwan. 2024. "Prediction Models for Perioperative Blood Transfusion in Patients Undergoing Gynecologic Surgery: A Systematic Review" Diagnostics 14, no. 18: 2018. https://doi.org/10.3390/diagnostics14182018

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