# Test Statistic – Definition, Types & Examples

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In research, the primary goal is to come up with conclusions. Also, you must decide whether to support or reject the null hypothesis. This is where you use a test statistic, which we will explain in-depth in this post.

## Test statistic- In a Nutshell

• A test statistic is a part of a hypothesis test that helps you decide whether to reject or support your null hypothesis.
• A null hypothesis projects that the means of two specific sample sets are equal.
• After finding your test statistic, you have to report it in your paper’s results section of your t-test.

## Definition: Test statistic

A test statistic is a number that describes how much the research results differ from the null hypothesis. Therefore, the test statistic is a hypothesis test that helps you determine whether to support or reject a null hypothesis in your study. You achieve this by using a test statistic to calculate the p-value of your results.1

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## Types of test statistic

There are four primary types of test statistics used in different statistical tests. The table below summarizes the four basic types, their hypotheses, and the types of statistical tests that apply each type.

 Type Hypotheses Tests that use it in statistics t-score • Null: The two sets are equal • Alternative: The two sets are not equal Regression and t-tests z-score • Null: The two sets are equal • Alternative: Both sets are not equal Z-tests f-score statistic • Null: The disparities between two or more trials are greater than or equal to the distinctions between the sets • Alternative: The disparity between two or more groups is smaller than that between the sets ANOVA, ANCOVA, and MANOVA tests X2/chi-square statistic • Null: Two models are autonomous • Alternative: Two models are linked Chi-squared and non-paramedic correlation tests1

## Interpreting test statistic

A statistical test helps produce a predicted distribution for a test statistic for sample size combination and various predictor variables. The test shows the probable range of scores that will occur if your figures follow the null hypothesis.

Also, the more extreme the product of your hypothesis test, the further your observations are to the edge of the range of projected test cores. Therefore, your data is less probable to be produced under the null hypothesis.2

The correlation between your projected test values and the calculated test statistic is called the p-value. Therefore, a smaller p-value means that your results are less likely to occur under the null hypothesis and vice versa.

Note: The test statistic is usually calculated from the observed scores in your studies. This is why a small p-value means that your data is less probable to occur if the projected null hypothesis is factual.

## Reporting test statistic

It is usually reported in the result section of a research paper. In addition to the test statistic, the section should also consist of the sample size (n), the p-value, and other elements of your data that will help put the conclusions of your study into context.3

However, not all research papers need a report on the test statistic. Therefore, the type of test you want to report will determine whether you need it or not.

Below is a summary of the test types that need statistical test reporting.

 Type of Study Type of statistic you need to report Correlation and regression studies • The reversion coefficient for each predictor variable • The p-value for each forecaster Studies to determine the differences between specific groups • Test statistic • Freedom degree • The p-value

## Test statistic example

In this test, you will perform a regression test which produces a coefficient of 0.35.

The test also produces a t-value comparing the regression coefficient to the predicted coefficient ranges under the null hypothesis.

Suppose your t-value shows no relationship between your RC and the predicted regression coefficients.

Therefore, the t-value for the regression study is also the test statistic. In this example, the t-value is 2.35.3

You can use a statistical program like SPSS or Excel to calculate the p-value in your statistical test. However, you can also go the longer route of using the formulas available online.

### Example: Testing the hypothesis

While testing the hypothesis, you need to follow the steps below:

Teenage males are, on average, not taller than teenage females.

• Collect data in a uniquely designed way for testing the hypothesis:

Use a sample of equal teenage females and males and test their height differences. You can organize the data depending on the age.

You can also use medical records or census data as the source of your data if you do not want to conduct height tests.

• Perform the appropriate statistical test:

Perform a t-test to see if the male teenagers are shorter than the female teenagers by finding the estimated differences in average heights between each group and the p-value.

Your test shows that the height average is 175.2 for males and 167.6 for females. Therefore, the difference is 7.6 to infinity. So, the p-value is 0.002.

• Decide if you want to reject or support the null hypothesis:

The 0.002 p-value in your statistical test is below the 0.05 cutoff of your study. Therefore, you can decide to reject your null hypothesis.

Once you have completed the steps above, you can present or report your findings in the results or discussion section of your research paper.4

### Example: Interpretation

With a t-value of 2.35, the range is far from the projected values under your null hypothesis. The same study may have a p-value of less than 0.1. This is because, for such a study, you would not expect to see the flowering date as 0 (not a date).

Instead, according to your null hypothesis, you would expect a t-value of less than 1% or larger than 2.35. Therefore, the interpretation is that it is statistically unlikely that your results could have arisen under the null hypothesis.

So, you can say that the result is statistically significant.

### Example: Report

In a t-test researching the differences between two sets, you must report the test statistic, freedom degrees, and the p-value. Below is an example of how you can do this.

In our comparison of vitamin supplement A and vitamin supplement B, we found that the user’ lifespan on vitamin supplement A was notably shorter than the users’ lifespan on vitamin supplement B, with a disparity range of 6 months.3

Vitamin supplement A:

• Mean = 2.9 years
• Standard deviation = 0.22

Vitamin supplement B:

• Mean = 3.1 years
• Standard deviation = 0.2

T-Value:

• t (75) = -13.25; p less than 0.01

## FAQs

#### What is a test statistic in statistics?

It is a number derived from a statistical test that shows you how close your experiential scores match the distribution projected under the null hypothesis of a statistical test.

#### What is the p-value?

The p-value is the level of marginal significance calculated from a statistical hypothesis test that represents the probability of a specific event occurring.5

#### What is the difference between test statistics and p-value?

P-value is a result of test statistics. For instance, a statistical test allows you to calculate the p-value that will tell you if the results of your observations support your theory or not.5

#### What is the purpose of the statistical test?

It shows how close your data’s distribution matches the predicted distribution in your null hypothesis.

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## Sources

1 Glen, Stephanie. “Test Statistics: Definition, Types of Test Statistics.” StatisticsHowTo.com. Accessed September 02, 2022. https://www.statisticshowto.com/test-statistic/.

2 Frost, Jim. “Test Statistics: Definition, Types & Formulas.” Statistics by Jim. Accessed September 02, 2022. https://statisticsbyjim.com/hypothesis-testing/test-statistic/.

3 Indeed Editorial Team. “How To Calculate a Test Statistics (With Types and Examples).” Indeed. July 01, 2022. https://www.indeed.com/career-advice/career-development/how-to-calculate-test-statistic.

4 Glen, Stephanie. “Hypothesis Testing.” StatisticsHowTo.com. Accessed September 02, 2022. https://www.statisticshowto.com/probability-and-statistics/hypothesis-testing/.

5 Beers, Brian. “P-Value: What It Is, How to Calculate It, and Why It Matters.” Investopedia. May 18, 2022. https://www.investopedia.com/terms/p/p-value.asp.

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