The Traditional t-Test

Posted May 10, 2018

Ah, the -test—staple of many an introductory statistics class. Also known as the Student’s t-test; it was developed by William Sealy Gosset under the pseudonym of “Student”, hence the name. Because it is a basic significance test often taught in introductory statistics classes, some eschew it as elementary. However, the t-test is based on mathematics and theory just as much as any other statistical test, and it can be appropriate to answer certain research questions. If your research design, research question, and data call for it, there is no need complicate things—use the t-test! Whether you just need a refresher, or you are learning about the t-test for the first time, read on to discover more about the different types of t-tests you can utilize to answer your research questions.

There are two basic types of t-tests: one for independent samples and one for paired samples. Independent samples means that, in your research design, all of your data or measurements belong to unique individuals. You would use the independent samples t-test in this design to determine if there is a significant difference in some score between two groups of participants. For example, say you wanted to see if men and women scored similarly on an anxiety scale. You could test each participant to record their gender and anxiety score. You could then input gender as your independent variable for your t-test, and the anxiety score as the dependent variable. If you have a significant t-test, your two groups are significantly different on your measured variable! You could then look at the means to see which group scored higher or lower. Prior to running this analysis, you will want to test the assumptions of normality and equality of variances.

Paired samples means that, in your research design, you measured each participant on some variable more than once. So, for example, testing anxiety scores on the same participants before and after an intervention. You could use the paired samples t-test (also known as the repeated measures t-test) to see if your participants’ anxiety scores improved after your intervention. A significant paired samples t-test means that your two scores are significantly different from each other. You could then look at the means to see which score (e.g., pre or post) was higher. Prior to running this analysis, you will want to test the assumption of normality.

But what if you do not have a continuous measurement? What if you have a Likert-type scale, or some other ordinal variable? First, check this blog for more information on when you can use ordinal measurements as continuous variables. However; if you have a Likert-type scale with fewer than five categories, or you have a true ordinal measurement, you may need to use a non-parametric analysis. Luckily, there are some non-parametric equivalents to the two types of t-tests. The Mann-Whitney U is similar to the independent sample t-test, and the Wilcoxon Signed-Rank test is similar to the paired samples t-test. These may also be used if your data does not meet the normality assumption.

To recap: for an independent samples t-test, you want two different groups of unrelated participants. That is your independent variable. Then, you want a continuous score for your dependent variable. For a paired samples t-test, you want the same participants measured more than once. For your variable inputs, you would need two continuous measurements for each participant. If you need to run a non-parametric test, consider the Mann-Whitney U or the Wilcoxon Signed-Rank test.

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