A Modified Normal Scores Test for Paired Data

Abstract

For the dependent-samples problem it is known that nonparametric tests such as the Wilcoxon signed-ranks test should be used instead of the paired t-test if the normality assumption is violated. The present study extends a family of tests for correlated samples by incorporating the concept of expected normal scores. This fusion leads to a promising significance test for paired non-normal samples, especially when distributions are highly skewed. In a simulation study we show that this modified normal scores test is robust for a wide range of non-normal distributions. Also, in most situations the test proved more powerful than traditional tests such as the paired t-test, the Wilcoxon signed-ranks test, or the Fraser normal scores test. For skewed distributions the test is also more powerful than applying the modified test to original measures or on ranks.