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A Beginner’s Guide to Hypothesis Testing in Business
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- 30 Mar 2021
Becoming a more data-driven decision-maker can bring several benefits to your organization, enabling you to identify new opportunities to pursue and threats to abate. Rather than allowing subjective thinking to guide your business strategy, backing your decisions with data can empower your company to become more innovative and, ultimately, profitable.
If you’re new to data-driven decision-making, you might be wondering how data translates into business strategy. The answer lies in generating a hypothesis and verifying or rejecting it based on what various forms of data tell you.
Below is a look at hypothesis testing and the role it plays in helping businesses become more data-driven.
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What Is Hypothesis Testing?
To understand what hypothesis testing is, it’s important first to understand what a hypothesis is.
A hypothesis or hypothesis statement seeks to explain why something has happened, or what might happen, under certain conditions. It can also be used to understand how different variables relate to each other. Hypotheses are often written as if-then statements; for example, “If this happens, then this will happen.”
Hypothesis testing , then, is a statistical means of testing an assumption stated in a hypothesis. While the specific methodology leveraged depends on the nature of the hypothesis and data available, hypothesis testing typically uses sample data to extrapolate insights about a larger population.
Hypothesis Testing in Business
When it comes to data-driven decision-making, there’s a certain amount of risk that can mislead a professional. This could be due to flawed thinking or observations, incomplete or inaccurate data , or the presence of unknown variables. The danger in this is that, if major strategic decisions are made based on flawed insights, it can lead to wasted resources, missed opportunities, and catastrophic outcomes.
The real value of hypothesis testing in business is that it allows professionals to test their theories and assumptions before putting them into action. This essentially allows an organization to verify its analysis is correct before committing resources to implement a broader strategy.
As one example, consider a company that wishes to launch a new marketing campaign to revitalize sales during a slow period. Doing so could be an incredibly expensive endeavor, depending on the campaign’s size and complexity. The company, therefore, may wish to test the campaign on a smaller scale to understand how it will perform.
In this example, the hypothesis that’s being tested would fall along the lines of: “If the company launches a new marketing campaign, then it will translate into an increase in sales.” It may even be possible to quantify how much of a lift in sales the company expects to see from the effort. Pending the results of the pilot campaign, the business would then know whether it makes sense to roll it out more broadly.
Related: 9 Fundamental Data Science Skills for Business Professionals
Key Considerations for Hypothesis Testing
1. alternative hypothesis and null hypothesis.
In hypothesis testing, the hypothesis that’s being tested is known as the alternative hypothesis . Often, it’s expressed as a correlation or statistical relationship between variables. The null hypothesis , on the other hand, is a statement that’s meant to show there’s no statistical relationship between the variables being tested. It’s typically the exact opposite of whatever is stated in the alternative hypothesis.
For example, consider a company’s leadership team that historically and reliably sees $12 million in monthly revenue. They want to understand if reducing the price of their services will attract more customers and, in turn, increase revenue.
In this case, the alternative hypothesis may take the form of a statement such as: “If we reduce the price of our flagship service by five percent, then we’ll see an increase in sales and realize revenues greater than $12 million in the next month.”
The null hypothesis, on the other hand, would indicate that revenues wouldn’t increase from the base of $12 million, or might even decrease.
Check out the video below about the difference between an alternative and a null hypothesis, and subscribe to our YouTube channel for more explainer content.
2. Significance Level and P-Value
Statistically speaking, if you were to run the same scenario 100 times, you’d likely receive somewhat different results each time. If you were to plot these results in a distribution plot, you’d see the most likely outcome is at the tallest point in the graph, with less likely outcomes falling to the right and left of that point.
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With this in mind, imagine you’ve completed your hypothesis test and have your results, which indicate there may be a correlation between the variables you were testing. To understand your results' significance, you’ll need to identify a p-value for the test, which helps note how confident you are in the test results.
In statistics, the p-value depicts the probability that, assuming the null hypothesis is correct, you might still observe results that are at least as extreme as the results of your hypothesis test. The smaller the p-value, the more likely the alternative hypothesis is correct, and the greater the significance of your results.
3. One-Sided vs. Two-Sided Testing
When it’s time to test your hypothesis, it’s important to leverage the correct testing method. The two most common hypothesis testing methods are one-sided and two-sided tests , or one-tailed and two-tailed tests, respectively.
Typically, you’d leverage a one-sided test when you have a strong conviction about the direction of change you expect to see due to your hypothesis test. You’d leverage a two-sided test when you’re less confident in the direction of change.
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4. Sampling
To perform hypothesis testing in the first place, you need to collect a sample of data to be analyzed. Depending on the question you’re seeking to answer or investigate, you might collect samples through surveys, observational studies, or experiments.
A survey involves asking a series of questions to a random population sample and recording self-reported responses.
Observational studies involve a researcher observing a sample population and collecting data as it occurs naturally, without intervention.
Finally, an experiment involves dividing a sample into multiple groups, one of which acts as the control group. For each non-control group, the variable being studied is manipulated to determine how the data collected differs from that of the control group.
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Learn How to Perform Hypothesis Testing
Hypothesis testing is a complex process involving different moving pieces that can allow an organization to effectively leverage its data and inform strategic decisions.
If you’re interested in better understanding hypothesis testing and the role it can play within your organization, one option is to complete a course that focuses on the process. Doing so can lay the statistical and analytical foundation you need to succeed.
Do you want to learn more about hypothesis testing? Explore Business Analytics —one of our online business essentials courses —and download our Beginner’s Guide to Data & Analytics .
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What Is Hypothesis Testing?
Step 1: define the hypothesis, step 2: set the criteria, step 3: calculate the statistic, step 4: reach a conclusion, types of errors, the bottom line.
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Hypothesis Testing in Finance: Concept and Examples
Charlene Rhinehart is a CPA , CFE, chair of an Illinois CPA Society committee, and has a degree in accounting and finance from DePaul University.
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Your investment advisor proposes you a monthly income investment plan that promises a variable return each month. You will invest in it only if you are assured of an average $180 monthly income. Your advisor also tells you that for the past 300 months, the scheme had investment returns with an average value of $190 and a standard deviation of $75. Should you invest in this scheme? Hypothesis testing comes to the aid for such decision-making.
Key Takeaways
- Hypothesis testing is a mathematical tool for confirming a financial or business claim or idea.
- Hypothesis testing is useful for investors trying to decide what to invest in and whether the instrument is likely to provide a satisfactory return.
- Despite the existence of different methodologies of hypothesis testing, the same four steps are used: define the hypothesis, set the criteria, calculate the statistic, and reach a conclusion.
- This mathematical model, like most statistical tools and models, has limitations and is prone to certain errors, necessitating investors also considering other models in conjunction with this one
Hypothesis or significance testing is a mathematical model for testing a claim, idea or hypothesis about a parameter of interest in a given population set, using data measured in a sample set. Calculations are performed on selected samples to gather more decisive information about the characteristics of the entire population, which enables a systematic way to test claims or ideas about the entire dataset.
Here is a simple example: A school principal reports that students in their school score an average of 7 out of 10 in exams. To test this “hypothesis,” we record marks of say 30 students (sample) from the entire student population of the school (say 300) and calculate the mean of that sample. We can then compare the (calculated) sample mean to the (reported) population mean and attempt to confirm the hypothesis.
To take another example, the annual return of a particular mutual fund is 8%. Assume that mutual fund has been in existence for 20 years. We take a random sample of annual returns of the mutual fund for, say, five years (sample) and calculate its mean. We then compare the (calculated) sample mean to the (claimed) population mean to verify the hypothesis.
This article assumes readers' familiarity with concepts of a normal distribution table, formula, p-value and related basics of statistics.
Different methodologies exist for hypothesis testing, but the same four basic steps are involved:
Usually, the reported value (or the claim statistics) is stated as the hypothesis and presumed to be true. For the above examples, the hypothesis will be:
- Example A: Students in the school score an average of 7 out of 10 in exams.
- Example B: The annual return of the mutual fund is 8% per annum.
This stated description constitutes the “ Null Hypothesis (H 0 ) ” and is assumed to be true – the way a defendant in a jury trial is presumed innocent until proven guilty by the evidence presented in court. Similarly, hypothesis testing starts by stating and assuming a “ null hypothesis ,” and then the process determines whether the assumption is likely to be true or false.
The important point to note is that we are testing the null hypothesis because there is an element of doubt about its validity. Whatever information that is against the stated null hypothesis is captured in the Alternative Hypothesis (H 1 ). For the above examples, the alternative hypothesis will be:
- Students score an average that is not equal to 7.
- The annual return of the mutual fund is not equal to 8% per annum.
In other words, the alternative hypothesis is a direct contradiction of the null hypothesis.
As in a trial, the jury assumes the defendant's innocence (null hypothesis). The prosecutor has to prove otherwise (alternative hypothesis). Similarly, the researcher has to prove that the null hypothesis is either true or false. If the prosecutor fails to prove the alternative hypothesis, the jury has to let the defendant go (basing the decision on the null hypothesis). Similarly, if the researcher fails to prove an alternative hypothesis (or simply does nothing), then the null hypothesis is assumed to be true.
The decision-making criteria have to be based on certain parameters of datasets.
The decision-making criteria have to be based on certain parameters of datasets and this is where the connection to normal distribution comes into the picture.
As per the standard statistics postulate about sampling distribution , “For any sample size n, the sampling distribution of X̅ is normal if the population X from which the sample is drawn is normally distributed.” Hence, the probabilities of all other possible sample mean that one could select are normally distributed.
For e.g., determine if the average daily return, of any stock listed on XYZ stock market , around New Year's Day is greater than 2%.
H 0 : Null Hypothesis: mean = 2%
H 1 : Alternative Hypothesis: mean > 2% (this is what we want to prove)
Take the sample (say of 50 stocks out of total 500) and compute the mean of the sample.
For a normal distribution, 95% of the values lie within two standard deviations of the population mean. Hence, this normal distribution and central limit assumption for the sample dataset allows us to establish 5% as a significance level. It makes sense as, under this assumption, there is less than a 5% probability (100-95) of getting outliers that are beyond two standard deviations from the population mean. Depending upon the nature of datasets, other significance levels can be taken at 1%, 5% or 10%. For financial calculations (including behavioral finance), 5% is the generally accepted limit. If we find any calculations that go beyond the usual two standard deviations, then we have a strong case of outliers to reject the null hypothesis.
Graphically, it is represented as follows:
In the above example, if the mean of the sample is much larger than 2% (say 3.5%), then we reject the null hypothesis. The alternative hypothesis (mean >2%) is accepted, which confirms that the average daily return of the stocks is indeed above 2%.
However, if the mean of the sample is not likely to be significantly greater than 2% (and remains at, say, around 2.2%), then we CANNOT reject the null hypothesis. The challenge comes on how to decide on such close range cases. To make a conclusion from selected samples and results, a level of significance is to be determined, which enables a conclusion to be made about the null hypothesis. The alternative hypothesis enables establishing the level of significance or the "critical value” concept for deciding on such close range cases.
According to the textbook standard definition , “A critical value is a cutoff value that defines the boundaries beyond which less than 5% of sample means can be obtained if the null hypothesis is true. Sample means obtained beyond a critical value will result in a decision to reject the null hypothesis." In the above example, if we have defined the critical value as 2.1%, and the calculated mean comes to 2.2%, then we reject the null hypothesis. A critical value establishes a clear demarcation about acceptance or rejection.
This step involves calculating the required figure(s), known as test statistics (like mean, z-score , p-value , etc.), for the selected sample. (We'll get to these in a later section.)
With the computed value(s), decide on the null hypothesis. If the probability of getting a sample mean is less than 5%, then the conclusion is to reject the null hypothesis. Otherwise, accept and retain the null hypothesis.
There can be four possible outcomes in sample-based decision-making, with regard to the correct applicability to the entire population:
The “Correct” cases are the ones where the decisions taken on the samples are truly applicable to the entire population. The cases of errors arise when one decides to retain (or reject) the null hypothesis based on the sample calculations, but that decision does not really apply for the entire population. These cases constitute Type 1 ( alpha ) and Type 2 ( beta ) errors, as indicated in the table above.
Selecting the correct critical value allows eliminating the type-1 alpha errors or limiting them to an acceptable range.
Alpha denotes the error on the level of significance and is determined by the researcher. To maintain the standard 5% significance or confidence level for probability calculations, this is retained at 5%.
According to the applicable decision-making benchmarks and definitions:
- “This (alpha) criterion is usually set at 0.05 (a = 0.05), and we compare the alpha level to the p-value. When the probability of a Type I error is less than 5% (p < 0.05), we decide to reject the null hypothesis; otherwise, we retain the null hypothesis.”
- The technical term used for this probability is the p-value . It is defined as “the probability of obtaining a sample outcome, given that the value stated in the null hypothesis is true. The p-value for obtaining a sample outcome is compared to the level of significance."
- A Type II error, or beta error, is defined as the probability of incorrectly retaining the null hypothesis, when in fact it is not applicable to the entire population.
A few more examples will demonstrate this and other calculations.
A monthly income investment scheme exists that promises variable monthly returns. An investor will invest in it only if they are assured of an average $180 monthly income. The investor has a sample of 300 months’ returns which has a mean of $190 and a standard deviation of $75. Should they invest in this scheme?
Let’s set up the problem. The investor will invest in the scheme if they are assured of the investor's desired $180 average return.
H 0 : Null Hypothesis: mean = 180
H 1 : Alternative Hypothesis: mean > 180
Method 1: Critical Value Approach
Identify a critical value X L for the sample mean, which is large enough to reject the null hypothesis – i.e. reject the null hypothesis if the sample mean >= critical value X L
P (identify a Type I alpha error) = P(reject H 0 given that H 0 is true),
This would be achieved when the sample mean exceeds the critical limits.
= P (given that H 0 is true) = alpha
Graphically, it appears as follows:
Taking alpha = 0.05 (i.e. 5% significance level), Z 0.05 = 1.645 (from the Z-table or normal distribution table)
= > X L = 180 +1.645*(75/sqrt(300)) = 187.12
Since the sample mean (190) is greater than the critical value (187.12), the null hypothesis is rejected, and the conclusion is that the average monthly return is indeed greater than $180, so the investor can consider investing in this scheme.
Method 2: Using Standardized Test Statistics
One can also use standardized value z.
Test Statistic, Z = (sample mean – population mean) / (std-dev / sqrt (no. of samples).
Then, the rejection region becomes the following:
Z= (190 – 180) / (75 / sqrt (300)) = 2.309
Our rejection region at 5% significance level is Z> Z 0.05 = 1.645.
Since Z= 2.309 is greater than 1.645, the null hypothesis can be rejected with a similar conclusion mentioned above.
Method 3: P-value Calculation
We aim to identify P (sample mean >= 190, when mean = 180).
= P (Z >= (190- 180) / (75 / sqrt (300))
= P (Z >= 2.309) = 0.0084 = 0.84%
The following table to infer p-value calculations concludes that there is confirmed evidence of average monthly returns being higher than 180:
A new stockbroker (XYZ) claims that their brokerage fees are lower than that of your current stock broker's (ABC). Data available from an independent research firm indicates that the mean and std-dev of all ABC broker clients are $18 and $6, respectively.
A sample of 100 clients of ABC is taken and brokerage charges are calculated with the new rates of XYZ broker. If the mean of the sample is $18.75 and std-dev is the same ($6), can any inference be made about the difference in the average brokerage bill between ABC and XYZ broker?
H 0 : Null Hypothesis: mean = 18
H 1 : Alternative Hypothesis: mean <> 18 (This is what we want to prove.)
Rejection region: Z <= - Z 2.5 and Z>=Z 2.5 (assuming 5% significance level, split 2.5 each on either side).
Z = (sample mean – mean) / (std-dev / sqrt (no. of samples))
= (18.75 – 18) / (6/(sqrt(100)) = 1.25
This calculated Z value falls between the two limits defined by:
- Z 2.5 = -1.96 and Z 2.5 = 1.96.
This concludes that there is insufficient evidence to infer that there is any difference between the rates of your existing broker and the new broker.
Alternatively, The p-value = P(Z< -1.25)+P(Z >1.25)
= 2 * 0.1056 = 0.2112 = 21.12% which is greater than 0.05 or 5%, leading to the same conclusion.
Graphically, it is represented by the following:
Criticism Points for the Hypothetical Testing Method:
- A statistical method based on assumptions
- Error-prone as detailed in terms of alpha and beta errors
- Interpretation of p-value can be ambiguous, leading to confusing results
Hypothesis testing allows a mathematical model to validate a claim or idea with a certain confidence level. However, like the majority of statistical tools and models, it is bound by a few limitations. The use of this model for making financial decisions should be considered with a critical eye, keeping all dependencies in mind. Alternate methods like Bayesian Inference are also worth exploring for similar analysis.
Sage Publications. " Introduction to Hypothesis Testing ," Page 13.
Sage Publications. " Introduction to Hypothesis Testing ," Page 11.
Sage Publications. " Introduction to Hypothesis Testing ," Page 7.
Sage Publications. " Introduction to Hypothesis Testing ," Pages 10-11.
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Some results uranium dioxide powder structure investigation
- Processes of Obtaining and Properties of Powders
- Published: 28 June 2009
- Volume 50 , pages 281–285, ( 2009 )
Cite this article
- E. I. Andreev 1 ,
- K. V. Glavin 2 ,
- A. V. Ivanov 3 ,
- V. V. Malovik 3 ,
- V. V. Martynov 3 &
- V. S. Panov 2
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Features of the macrostructure and microstructure of uranium dioxide powders are considered. Assumptions are made on the mechanisms of the behavior of powders of various natures during pelletizing. Experimental data that reflect the effect of these powders on the quality of fuel pellets, which is evaluated by modern procedures, are presented. To investigate the structure of the powders, modern methods of electron microscopy, helium pycnometry, etc., are used. The presented results indicate the disadvantages of wet methods for obtaining the starting UO 2 powders by the ammonium diuranate (ADU) flow sheet because strong agglomerates and conglomerates, which complicate the process of pelletizing, are formed. The main directions of investigation that can lead to understanding the regularities of formation of the structure of starting UO 2 powders, which will allow one to control the process of their fabrication and stabilize the properties of powders and pellets, are emphasized.
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Investigation of the Influence of the Energy of Thermal Plasma on the Morphology and Phase Composition of Aluminosilicate Microspheres
Evaluation of the possibility of fabricating uranium-molybdenum fuel for vver by powder metallurgy methods.
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E. I. Andreev
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Original Russian Text © E.I. Andreev, K.V. Glavin, A.V. Ivanov, V.V. Malovik, V.V. Martynov, V.S. Panov, 2009, published in Izvestiya VUZ. Poroshkovaya Metallurgiya i Funktsional’nye Pokrytiya, 2008, No. 4, pp. 19–24.
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Andreev, E.I., Glavin, K.V., Ivanov, A.V. et al. Some results uranium dioxide powder structure investigation. Russ. J. Non-ferrous Metals 50 , 281–285 (2009). https://doi.org/10.3103/S1067821209030183
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Published : 28 June 2009
Issue Date : June 2009
DOI : https://doi.org/10.3103/S1067821209030183
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Features of the macrostructure and microstructure of uranium dioxide powders are considered. Assumptions are made on the mechanisms of the behavior of powders of various natures during pelletizing. Experimental data that reflect the effect of these powders on the quality of fuel pellets, which is evaluated by modern procedures, are presented. To investigate the structure of the powders, modern ...