The Paired-Samples t Test
We use a paired-samples t test when we have two samples, and the same participants are in both samples; to conduct the test, we calculate a difference score for every individual in the study. The comparison distribution is a distribution of mean difference scores instead of the distribution of means that we used with a single-sample t test. Aside from the comparison distribution, the steps of hypothesis testing are similar to those for a single-sample t test. As we can with a z test and a single-sample t test, we can calculate a confidence interval and an effect size (Cohen’s d) for a paired-samples t test.
Beyond Hypothesis Testing
As we can with a z test and a single-sample t test, we can calculate a confidence interval for a paired-samples t test. The confidence interval gives us an interval estimate rather than a point estimate. Its results match that of the hypothesis test. When we reject the null hypothesis, we know that the confidence interval will not include 0. We also can calculate an effect size (Cohen’s d) for a paired-samples t test. This provides information about the size of the observed effect and can let us know if a statistically significant finding is likely to be practically important.
Paired-samples t tests are used when we compare two groups using a within-groups design, a situation in which we must be aware of order effects, also called practice effects. Order effects occur when participants’ behavior changes when a dependent variable, such as a test or measure, is presented a second time. Researchers use counterbalancing to reduce order effects: they vary the order in which the different levels of the independent variable are presented from one participant to the next.