A Note on Power and Sample Size Calculations for the Kruskal–Wallis Test for Ordered Categorical Data

Abstract

Although the Kruskal–Wallis test has been widely used to analyze ordered categorical data, power and sample size methods for this test have been investigated to a much lesser extent when the underlying multinomial distributions are unknown. This article generalizes the power and sample size procedures proposed by Fan et al. (2011) for continuous data to ordered categorical data, when estimates from a pilot study are used in the place of knowledge of the true underlying distribution. Simulations show that the proposed power and sample size formulas perform well. A myelin oligodendrocyte glycoprotein (MOG) induced experimental autoimmunce encephalomyelitis (EAE) mouse study is used to demonstrate the application of the methods.

Key Words:

• Ordinal data
• Rank test
• Ties

ACKNOWLEDGMENTS

The authors thank the anonymous referee for the constructive suggestions and comments that substantially improved the original version of this article.

Notes

^†: λ₁: λ₂: λ₃ = 0.2: 0.2: 0.6

^‡: λ₁: λ₂: λ₃: λ₄: λ₅ = 0.1:0.1:0.1:0.3:0.4

^{<sect >}:1,000 simulations.

^†: λ₁: λ₂: λ₃ = 0.2:0.2:0.6

^‡: λ₁: λ₂: λ₃: λ₄: λ₅ = 0.1:0.1:0.1:0.3:0.4

^{<sect >}:1,000 simulations.