The t test (III) is also used with two groups. This test's concern is to find out if the mean of one group is actually different from the mean of the other group . The difference between the t test (II) and the t test (III) has to do with the nature of the two groups. The t test (III) is used only in cases where the two groups are related. When we talk about related groups, we mean groups that are matched on some variable or in which the subjects are used more than once. The requirements for the t test (III) are as follows :
Two groups related
At least interval level of measurement
Populations both normally distributed
Populations having the same variances
Samples drawn at random
The formula used to evaluate whether the difference between these two groups is significant is different from the one used for the t (II). You compute the differences between each pair of scores and then use this difference to estimate the population standard error of the difference.
where = mean of the difference, & pound ; D 2 = square the differences, then find the sum, ( D) 2 = sum the differences, then square the sum, and N = number of pairs of scores.