Binomial tests are commonly used in sensory difference and preference testing under the assumptions that choices are independent and choice probabilities do not vary from trial to trial. This paper addresses violations of the latter assumption (often referred to as overdispersion) and accounts for variation in inter‐trial choice probabilities following the Beta distribution. Such variation could arise as a result of differences in test substrate from trial to trial, differences in sensory acuity among subjects or the existence of latent preference segments. In fact, it is likely that overdispersion occurs ubiquitously in product testing. Using the Binomial model for data in which there is inter‐trial variation may lead to seriously misleading conclusions from a sensory difference or preference test. A simulation study in this paper based on product testing experience showed that when using a Binomial model for overdispersed Binomial data, Type I error may be 0.44 for a Binomial test specification corresponding to a level of 0.05. Underestimation of Type I error using the Binomial model may seriously undermine legal claims of product superiority in situations where overdispersion occurs. The Beta‐Binomial (BB) model, an extension of the Binomial distribution, was developed to fit overdispersed Binomial data. Procedures for estimating and testing the parameters as well as testing for goodness of fit are discussed. Procedures for determining sample size and for calculating estimate precision and test power based on the BB model are given. Numerical examples and simulation results are also given in the paper. The BB model should improve the validity of sensory difference and preference testing.
d' is an estimate of 6, a measure of the degree of sensory difference between two products, that can be obtained easily using tables, from the proportion of difference tests peformed correctly. Tables of 6 are available for the 2-AFC, 3-AFC, triangular and duo-trio tests. Tables for calculating the variance of d' for these tests are provided in this paper. n e y can be used for comparison of d 's, especially for those obtained from different difference tests. A simple procedure is described here for computing values for the variance of d I . Having obtained the variance, confidence intervals for d' can be obtained, tests of significance ford' can be made as well as tests of whether two or more d's are sign@cantly different. The formula and tables for the number of judgments required for the estimation of 6 are given also in this paper.
This article attempts to deliver the following message to the researchers and practitioners in the sensory field. (1) Theoretically, drivers of consumer liking is based on relative importance of explanatory variables in a linear model. The problem is complicated when the variables involve linear dependence, which is the common situation in sensory and consumer data. (2) The commonly used methodologies, e.g., conjoint analysis, preference mapping and Kano's model, have serious limitations for determination of relative importance of correlated attributes and identification of drivers of consumer liking. (3) The conventional statistics, e.g., correlation coefficient, standard regression coefficient and P values of tests for regression parameters, etc., are inadequate and invalid measures of relative importance of correlated attributes. (4) There are three state-of-the-art methods for determination of relative importance of correlated attributes. They are the Lindeman, Merenda and Gold's method, Breiman's Random Forest and Johnson's relative weight. This article also provides statistical background and almost exhaustive main references on the topic of relative importance of variables scattered in various academic journals in different fields. The information will help the sensometricians and researchers with more statistical knowledge to embrace the mainstream of the research on the topic and to pursue advanced methods for drivers of consumer liking. PRACTICAL APPLICATIONSThis article reviews some new methods for determination of relative importance of correlated explanatory variables to response variable in a regression model. The methods can be used for identification of drivers of consumer liking. The article also provides the sources of the corresponding computer packages and codes implementing the new methods. The packages and codes are freely available and easy to use. The R packages "relaimpo" for the LMG method, "randomForest" and "party" for the original and modified Breiman's Random Forest method are available at http://cran.r-project.org. The R or S-Plus code "johnson" for Johnson's relative weight is available from the online supplementary Appendix S1 of this article. Journal of Sensory Studies ISSN 0887-8250RELATIVE IMPORTANCE AND DRIVERS OF LIKING J. BI
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