Novel effect size interpretation of mixed models results with a view towards sensory data

Abstract

In sensory studies, the analysis of variance is one of the most often employed statistical methods to study differences between products. However, the analysis of variance often focus just on the p-values. Therefore, it would be valuable to supplement the F-testing with some good measures of overall effect size (ES). In this thesis, a visual tool based on effect size measures is proposed to improve the F-test results interpretations of mixed model ANOVA for sensory data. The basic and straightforward idea is to interpret effects relative to the residual error and to choose the proper effect size measure. The close link between Cohen’s d, the effect size in an ANOVA framework, and the Thurstonian (Signal detection) d-prime are used to suggest the delta-tilde barplot as a better visual tool to interpret sensory and consumer data mixed model results. For multi-attribute barplots of F-statistics in balanced settings, this amounts to a simple transformation of the bar heights to get them depicting, what can be seen as approximately the average pairwise d-primes among products levels. The delta-tilde barplot becomes more important for multi-way product models, since the transformation depends on the number of observations within product levels. Then, for extensions into multi-way models, a similar transformation is suggested, in order to make valid the comparison of bar heights for factors with differences in number of levels. The methods are illustrated on a multifactorial sensory profile data set and compared to actual d-prime calculations based on Thurstonian regression modelling through the ordinal R-package. A generic implementation of the method is available on the R-package SensMixed. The use of the delta-tilde barplot can be viewed as good a and relevant additional tools for interpretation of the ANOVA table, particularly in situations with more than a single factor and with several attributes.