Article

Five-Point Likert Items: t test versus Mann-Whitney-Wilcoxon (Addendum added October 2012)

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Abstract

Likert questionnaires are widely used in survey research, but it is unclear whether the item data should be investigated by means of parametric or nonparametric procedures. This study compared the Type I and II error rates of the t test versus the Mann-Whitney-Wilcoxon (MWW) for five-point Likert items. Fourteen population distributions were defined and pairs of samples were drawn from the populations and submitted to the t test and the t test on ranks, which yields the same results as MWW. The results showed that the two tests had equivalent power for most of the pairs. MWW had a power advantage when one of the samples was drawn from a skewed or peaked distribution. Strong power differences between the t test and MWW occurred when one of the samples was drawn from a multimodal distribution. Notably, the Type I error rate of both methods was never more than 3% above the nominal rate of 5%, even not when sample sizes were highly unequal. In conclusion, for five-point Likert items, the t test and MWW generally have similar power, and researchers do not have to worry about finding a difference whilst there is none in the population.Accessed 61,170 times on https://pareonline.net from October 06, 2010 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right.

Keywords: Evaluation Methods, Educational Research, Research Methodology, Statistical Analysis

How to Cite:

de Winter, J. & Dodou, D., (2010) “Five-Point Likert Items: t test versus Mann-Whitney-Wilcoxon (Addendum added October 2012)”, Practical Assessment, Research, and Evaluation 15(1): 11. doi: https://doi.org/10.7275/bj1p-ts64