If homogeneity of variance is violated for a correlated-groups t-test, what nonparametric test should be considered?

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Laaibah Pitt · Accepted Answer

Step 1   Introduction:   A correlated-groups t-test, also known as the paired t-test, is used to compare whether there is significant mean difference between two sets of observations, when the two sets are correlated, that is, not independent.   In order to apply the paired t-test, the assumptions that must be satisfied are that, the observations must be measured on an interval or ratio scale, the data must be collected such that the sampled units are independent of one another, the observations must have at least an approximate normal distribution, there should not be any outliers, the two sets of observations must be homogeneous in variance.   If any one or more of these assumptions are not satisfied, then the paired t-test cannot be used. In such a situation, if two correlated sets of observations are to be compared, then an alternative non-parametric test is to be used.   Step 2   Explanation:   The Wilcoxon signed-rank test is a non-parametric test. It is used to test whether the mean ra of two correlated populations are significantly different or not, with the help of random samples taken from each of the two populations.   Clearly, the aim of the Wilcoxon signed-rank test is similar to the aim of the paired t-test. However, the added advantage is that, this test can be conducted even when one or more of the assumptions of the paired t-test are not satisfied.   Hence, if the assumption of homogeneity of variance for a correlated groups t-test is violated, the non-parametric test that can be considered is Wilcoxon signed-rank test.

If homogeneity of variance is violated for a correlated-groups t-test, what nonp

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