Question: Explain why difference scores are computed for the related-samples t test.
• To test the null hypothesis, we state the mean difference between paired scores in the population and compare this to the difference between paired scores in a sample. A related-samples t test is different from a two-independent-sample t test in that we first find the difference between the paired scores and then compute the test statistic. The difference between two scores in a pair is called a difference score.
• Computing difference scores eliminates between-persons error. This error is associated with differences associated with observing different participants in each group or treatment. Because we observe the same (or matched) participants in each treatment, not different participants, we can eliminate this source of error before computing the test statistic. Removing this error reduces the value of the estimate of standard error, which increases the power to detect an effect.