On the Use of Bayes Factor and p-Value in Hypothesis Testing

Abstract

The focus in experimental data analysis is to assess treatments-mean structure and such decision is taken by the reported p-values from the corresponding F-tests. However, there are concerns about the use of p-value as a means of making decision in tests of hypotheses, hence the motivation for this study which proffers Bayes factor as a Bayesian alternative. Constraints were placed on effect parameters of a one-way model by assuming that the standardized random effects followed a normal distribution with mean zero and level-variance, g. Jefferys prior was placed on the mean and the error variance, while the inverse chi-squared with one degree of freedom was chosen for g. Simulated data were analysed to contrast Bayes factor with p-value, using different sizes of samples and effects. A one-way design data set from an experiment on the effect of genetic strain on fecundity of fruit fly Drosophila melanogaster was also analysed for multiple comparisons of treatment means using Bayes factors, and the posterior sample estimates using Markov chain Monte Carlo simulation were used to validate Bayes factors results.