Sample size determination given data of preliminary experiment for Student's f-test, ANOVA and Tukey's multiple comparison

Abstract

The purpose of this article is to calculate the probability that a null hypothesis is rejected using data of preliminary experiment, and to determine an appropriate sample size based on that probability. The procedure to calculate that probability is as follows: (a) generate parameters from the posterior distribution of parameters given data of preliminary experiment; (b) generate test statistics from the conditional distribution given those parameters; (c) count how many of the generated test statistics exceed a critical value. Once the probability of rejecting null hypothesis is estimated, researchers can decide sample size corresponding to the desirable probability. Examples of the procedure are provided and compared with the traditional methods in the case of Student's t-test.