Question

when do we to use the pooled, non-pooled, or paired inference to compare means of two populations. please be specific.

Answer 1

We use the pooled test when there is a homogeneity of variance among the groups. We use the non-pooled test when there is no homogeneity of variance among the groups. We perform the F-test to check if there is a homogeneity of variance among the groups. As a standard rule, the ratio of the largest to smallest standard deviation should be less than 2 in order to meet the homogeneity of variance assumption among the groups.

We use the paired inference when each subject is tested twice and the pooled or the non-pooled test is used when the subjects are independent of each other.