Sample size determination when the parameter of interest is the coefficient of variation under normality for the data

Abstract

This study considers classical and Bayesian inference approaches for the coefficient of variation under normality for the data, especially on the determination of the sample size of a random sample needed in a second stage of an experiment. This topic has been explored by many authors in the last decades. The first goal of the study is to present simple formulations to get the inferences of interest for the coefficient of variation under normality and usual frequentist approach based on the asymptotic normality of the maximum likelihood estimators for the mean and standard deviation of the normal distribution and using the delta method to get the inferences of interest for the coefficient of variation. Simple hypothesis tests and determination of the sample size are discussed under the frequentist approach.The second goal of the study is to present a sample size determination under a Bayesian approach, where it is assumed a Jeffreys non-informative prior distribution of the parameters of the normal distribution assumed for the data and using standard Markov Chain Monte Carlo (MCMC) methods to get the posterior summaries of interest.