Estimation of the Power of the Kruskal‐Wallis Test

Power calculations of a statistical test require that the underlying population distribution(s) be completely specified. Statisticians, in practice, may not have complete knowledge of the entire nature of the underlying distribution(s) and are at a loss for calculating the exact power of the test. In such cases, an estimate of the power would provide a suitable substitute. In this paper, we are interested in estimating the power of the Kruskal‐Wallis one‐way analysis of variance by ranks test for a location shift. We investigated an extension of a data‐based power estimation method presented by Collings and Hamilton (1988), which requires no prior knowledge of the underlying population distributions other than necessary to perform the Kruskal‐Wallis test for a location shift. This method utilizes bootstrapping techniques to produce a power estimate based on the empirical cumulative distribution functions of the sample data. We performed a simulation study of the extended power estimator under the conditions of k = 3 and k = 5 samples of equal sizes m = 10 and m = 20, with four underlying continuous distributions that possessed various location configurations. Our simulation study demonstates that the Extended Average × & Y power estimation method is a reliable estimator of the power of the Kruskal‐Wallis test for k = 3 samples, and a more conservative to a mild overestimator of the true power for k = 5 samples.