A Comparison on Performance of Tests for Equality of Means of Related Ordinal Data

Abstract

For hypothesis testing about more than one population mean when the data are related, parametric tests usually have been used. When using parametric tests, assumptions are required, the data have to be quantitative data and normally distributed. However, if the data are ordinal Likert scale and/or non-normally distributed, non-parametric tests are alternative. In this research, in case of testing two population means, t-test and Wilcoxon test are compared and for testing three population means, F-test and Friedman test are compared. The correlated ordinal data are generated from normal, uniform, left-skewed and right-skewed distributions. In addition, the correlation coefficients are 0.50 and 0.70. For testing two population means, sample sizes are 10, 20, 30, 50 and 100 and for testing three population means, sample sizes are 20, 30, 50 and 100. From the simulation study, when the sample sizes are small (10, 20 and 30 for two groups test, 20 and 30 for three groups test), parametric tests      (t-test and F-test) perform better than non-parametric tests (Wilcoxon test and Friedman test) in term of controlling the type I error rate and power. When the sample sizes are medium and large, both methods have similar performances. The power of both methods are increased as sample sizes and correlation increase and the distributions are completely difference. Keywords :  t-test, F-test, Wilcoxon test, Friedman test