Statistics and Its Interface
Volume 7 (2014)
Modern sample size determination for unordered categorical data
Pages: 219 – 233
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.
bootstrap, calibrated posterior predictive p-value, multinomial distribution, pilot data, power calculation, practical recommendations
2010 Mathematics Subject Classification
Primary 62F10, 62F15. Secondary 62F40.