Paired Samples T Test (Dependent Samples T Test)

Paired samples t test, also known as dependent samples t test, is used when there are two groups to compare, wherein the scores in one group are linked or paired with scores in the other group. In this situation, the assumption of independence has been violated, so an independent t test cannot be used.

An example of when to use a paired samples t test is a study examining happiness of twins (based on a survey with a composite score ranging from 1 to 100), with both twins involved in the study. Because the scores are paired or dependent (each twin's score is related to the other twin's score), these data would be analyzed using a paired samples t test. This is the best choice of statistic to use because the scores from one twin are linked, or might be similar, to the scores from the other twin.

Another example of when it would be appropriate to use the paired samples t test is with repeated measures. For example, to understand if a teaching method is effective, a pretest could be given on the first day of class and then again on the last day of class. The scores from these tests (the data) would be considered linked for each student. Therefore, in the case of repeated measures with two sets of scores, the paired samples t test would be an appropriate choice for a statistic.

Table 1 shows an example of data that would be appropriate on which to use the paired samples t test. The first variable is “twin 1 happiness scores” and the second variable is “twin 2 happiness scores.” Happiness is measured on a scale of 1 to 100, where 1 is very unhappy and 100 is extremely happy.

Research Hypothesis

The null hypothesis analyzed with the paired samples t test is similar to the hypothesis used with the independent samples t test:

This hypothesis is testing that the means are equal. The alternative hypothesis would be that the means are not equal:

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Computing the Value for the Paired Samples t Test

The formula for the paired samples t test is as follows:

where X¯ is the mean for the first variable and Y¯ is the mean for the second variable. The denominator, sD¯ is the standard error of the difference between the means. It is calculated with the following formula:

The sD¯ is the standard error of the difference between the means. The sD is the standard deviation of the difference between the means, the D is the difference between each paired score (X − Y), and N is the number of paired scores.

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