Power Properties of Ordinal Regression Models for Likert Type Data

We discuss analysis of 5-grade Likert type data in the two-sample case. Analysis using two-sample t tests, nonparametric Wilcoxon tests, and ordinal regression methods, are compared using simulated data based on an ordinal regression paradigm. One thousand pairs of samples of size n=10 and n=30 were generated, with three different degrees of skewness. For all sample sizes and degrees of skewness, the ordinal probit model has highest power. This is not surprising since the data was generated with this model in mind. Slightly more surprising is that the t test has higher power than the Wilcoxon test in all studied situations, even for skewed data. For n=30, the differences between the methods are small.