Comparing with Relative Accuracy Two Independent Ordinal Samples

Abstract

Misuse of statistical techniques for analyzing ordinal data means that accuracy of resultant inferences are suspect. In an effort to examine the consequences of this issue, we investigate the relative accuracy of three hypothesis testing methods — two-sample t test with equal variances, the rank-sum test and ordered logit estimation — when applied to ordinal samples of five categories. Our most conclusive results are the following: Where ordinal samples are small and not bimodal, one should compare them with traditional nonparametric methods (rank-sum). Where observations have been made from bimodal populations on ordinal scales, and where samples are not so small, one should take care to compare them with theoretically appropriate techniques (ordered logit). Finally we present the proposed approach as a basis for comparing independent ordinal samples from the ABC Customer Satisfaction Survey dataset.

Key Words:

• Binomial
• Likert
• logit
• ordered
• proportional odds
• rank.

Additional information

Notes on contributors

Justin R. Chimka

Justin R Chimka is an Associate Professor of Industrial Engineering at the University of Arkansas. He received his Ph.D. in Industrial Engineering from the University of Pittsburgh. Justin teaches courses in applied statistics, generalized linear models, production, and regression analysis. His research interests include logistics and quality engineering.

Harvey Wolfe

Harvey Wolfe is a Professor of Industrial Engineering and has been a member of the faculty at the University of Pittsburgh since 1964. He served as the department chair from 1985 to 2000. He received his Ph.D. in Operations Research from the John Hopkins University, where he also earned a BES in industrial engineering and an MSE in operations research. His primary area of interest is operations research, with particular specialization in health applications and, more recently in Engineering Education systems.