ARS | Publication request: Bayesian Methods for Determining the Importance of Effects

Submitted to: Annual Meeting World Aquaculture Society
Publication Type: Proceedings
Publication Acceptance Date: December 10, 2008
Publication Date: February 15, 2009
Citation: Welker, T.L., Welker, T.L., Klesius, P.H. 2009. Bayesian Methods for Determining the Importance of Effects. In: Aquaculture America 2009, February 15-18, 2009, Seattle, Washington. p. 373.

Technical Abstract: Criticisms have plagued the frequentist null-hypothesis significance testing (NHST) procedure since the day it was created from the Fisher Significance Test and Hypothesis Test of Jerzy Neyman and Egon Pearson. Alternatives to NHST exist in frequentist statistics, but competing methods are also available in Bayesian statistics, which have important advantages over frequentist procedures. Bayesian methods, however, have been little used to determine the importance of effects, primarily due to unfamiliarity stemming from the dominance of frequentist statistical procedures during the 20th century, lack of practical information on application of the methodologies, and criticisms of the use of posterior probabilities. Recent methods designed to help bridge the Bayesian – frequentist gap have been developed and overcome the perceived subjective bias of Bayesian posterior probabilities through the use of non-informative priors. One such method integrates Bayes theorem within a frequentist-type ANOVA framework familiar to most researchers. This Bayesian approach leads to conclusions of the importance of effects based on probability and permits a reinterpretation of the usual confidence interval to determine differences between means and assertions of largeness or smallness of effect, in which the latter has no frequentist counterpart. Application examples of Bayesian methods will be presented and compared to standard frequentist techniques. Examples of a Bayesian alternative to ANOVA applied to aquaculture will be presented and compared to standard frequentist techniques.