t Test, Paired Samples

A paired samples t test is a hypothesis test for determining whether the population means of two dependent groups are the same. The researcher begins by selecting a sample of paired observations from the two groups. Thus, each observation in each group is paired (matched) with another observation from the other group. The researcher then calculates the difference between each of these paired observations and conducts a one-sample t test on these difference scores via the formula

where d is the sample mean difference score, sd is the standard deviation of the sample difference scores, and nd is the number of paired observations in the sample (i.e., the number of difference scores). This t value can then be used to determine the likelihood that any difference ...