Modern sample size determination for unordered categorical data

Sample size determination is one of the most important practical tasks for statisticians. In this paper, we study sample size determination for unordered categorical data, with or without a pilot sample. With a pilot sample, we provide a minimal difference method, a first order correction, and bootstrap methods for sample size determination in the comparison of two multinomial distributions using the usual chi-squared test. We also propose a Bayesian approach that uses an extension of a posterior predictive p-value. The performance of these methods is investigated via both a simulation study and a real application to leukoplakia lesion data. We advocate a better performance measure than MSE when the sampling distribution is highly skewed. Practical recommendations are given. Some asymptotic results are also provided.

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