Comparing Two Samples from an Individual Likert Question

Abstract

For two independent samples there is much debate in the literature whether parametric or non-parametric methods should be used for the comparison of Likert question responses. The comparison of paired responses has received less attention in the literature. In this paper, parametric and non-parametric tests are assessed in the comparison of two samples from a paired design on a five point Likert question. The tests considered are the independent samples t-test, the Mann-Whitney test, the paired samples t-test and the Wilcoxon test. Pratt’s modified Wilcoxon test for dealing with zero differences is also included. The Type I error rate and power of the test statistics are assessed using Monte-Carlo methods. The parameters varied are; sample size, correlation between paired observations, and the distribution of the responses. The results show that the independent samples t-test and the Mann-Whitney test are not Type I error robust when there is correlation between the two groups compared. Pratt’s test more closely maintains the Type I error rate than the standard Wilcoxon test does. The paired samples t-test is Type I error robust across the simulation design. As the correlation between the paired samples increases, the power of the test statistics making use of the paired information increases. The paired samples t-test is more powerful than Pratt’s test when the correlation is weak. The power differential between the test statistics is exacerbated when sample sizes are small. Assuming equally spaced categories on a five point Likert item, the paired samples t-test is not inappropriate.