February 15-18, 2009 Washington State Convention Center Seattle ...

BAYESIAN METHODS FOR DETERMINING THE IMPORTANCE OF EFFECTSBAYESIAN
METHODS FOR DETERMINING THE IMPORTANCE OF EFFECTS
Tom L. Welker, Tim L. Welker and Phillip H. Klesius
USDA, ARS
Aquatic Animal Health Research Unit
990 Wire Road
Auburn, AL 36832 USA
thomas.welker@ars.usda.gov
Criticisms have plagued the frequentist null-hypothesis significance testing (NHST) procedure since the time day it was fashioned
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 20 th century, lack of practical
information on application of the methodologies, and criticisms of the use of posterior probabilities. However, rRecent 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. Examples of
a Bayesian alternative to ANOVA applied to aquaculture will be presented and compared to standard frequentist techniques.
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