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The dependent-samples $$t$$-test, sometimes called the paired-samples $$t$$-test, is used to compare two means obtained from the same sample tested at two different times or under two distinct conditions. This statistical comparison is particularly appropriate for analyzing data from pretest-posttest designs or within-subjects experiments. Conceptually, it functions as a special case of the one-sample $$t$$-test.

Dependent-Samples t-Test

Study that involves multiple measures of the same variable taken on the same or matched subjects either under different conditions or over two or more time periods.
Example: repeated measurements are collected in a longitudinal study in which change over time is assessed.

Repeated Measures Designs

In a dependent-samples $$t$$-test, the initial analysis step involves reducing the two paired scores recorded for each participant into a single value known as a difference score. This is achieved by subtracting one score from the other. It does not matter whether the first set of scores is subtracted from the second or vice versa, provided the order of subtraction is applied consistently across all participants. Often, researchers choose the direction of subtraction so that positive or negative difference scores intuitively align with the expected outcome (e.g., subtracting pretest scores from posttest scores so that a positive difference indicates an increase). Once these difference scores are calculated, the dependent-samples $$t$$-test functions exactly as a one-sample $$t$$-test performed directly on these new values.

Difference Score

To illustrate a dependent-samples $$t$$-test, consider a pretest-posttest study evaluating a training program designed to improve calorie estimates. A sample of $$10$$ participants estimates calories in a cookie both before and after the training. Subtracting the pretest estimates from the posttest estimates yields a set of $$10$$ difference scores with a mean ($$M$$) of $$8.50$$ and a standard deviation ($$SD$$) of $$24.27$$. Using the one-sample $$t$$-test formula on these difference scores against a hypothetical population mean of $$0$$, the computed $$t$$ score is $$1.11$$. For a one-tailed test with $$9$$ degrees of freedom ($$10 - 1$$), the critical value is $$1.833$$. Because the calculated $$t$$ score ($$1.11$$) is less extreme than this critical value, the researcher fails to reject the null hypothesis, concluding that the training program does not significantly increase calorie estimates. The corresponding $$p$$-value is $$.148$$, which is greater than the standard $$.05$$ alpha level.

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