Book

Description

Statistical inference have relied heavily on test of hypothesis and confidence intervals, particularly the p-value has been the main to for making decision about competing hypothesis or inference about mean of set of data. However, there are concerns about the use of p-value as a means of making decision in tests of hypotheses. The motivation for this dissertation are these concerns about p-value, which include that p-value is based on imaginary replicated data, its definition is not equivalent to the probability that a hypothesis is true given an observed data and that it does not give an idea of the size of an effect. This book presents an academic dissertation of the case of an alternative to p-value, the Bayes factor, particularly for the case of analysis of variance. Bayes factor was constructed for one-way analysis of variance and applied to simulations and real world datasets. The simulations involved different sample sizes and effect sizes to assess the behaviour of p-value and Bayes factor on the different case scenario. The results showed that p-values detected only large effect sizes with small sample sizes and smaller effect sizes with larger sample sizes. Bayes factors were able to detect smaller effect sizes with small sample sizes. Hence, p-value was shown to be sensitive to sample size and effect size. The Bayes factors results on the real-world data were very much in consonant with the conservative classical Duncan’s tests. The posterior sample estimates validated the Bayes factor results on the pair of equal means. From this study, the sufficiency of Bayes factor as a superior alternative to p-value in analysis of variance was justified.