A regression-based approach for testing significance of “just-about-right” variable penalties

A model-based method for relating “just-about-right” (JAR) variable responses to reference variables such as overall liking in sensory/consumer research is introduced. Overall liking is regressed against a JAR variable response after having converted the latter to a set of indicators. Coefficients resulting from ordinary least squares (OLS) regression are identical to traditional count-based penalties and are typically negative. These can be considered penalties for being “out of JAR”. Penalty weights are calculated as the products of respondent proportions at a particular JAR variable level and the corresponding regression coefficient. Significance of regression coefficients and weighted penalties is tested by two semi-parametric methods and the non-parametric percentile bootstrap. Due to a systematic skew in the distributions of penalty weights, it appears that the two semi-parametric methods, which each rely on a t-test, can undercount the number of significant penalty weights. With this in mind a distribution for the weights is proposed and used to test their significance. These parametric results are compared with the semi- and non-parametric methods and some of the assumptions underlying the proposed distribution are evaluated.