Sensory difference tests: Overdispersion and warm-up

For sensory difference tests, one way, but not the only way, of dealing with the problem of overdispersion is to use a beta-binomial analysis. Commonly, binomial statistical analyses are used for these methods and they assume that the sensitivity of the judges is uniform. However, judge sensitivity varies and this adds a problematical extra variance to the distribution. This is termed overdispersion and renders simple binomial analysis prone to Type I error. The distribution of sensitivity of the judges is described by a beta-distribution. The analysis, combining beta and binomial distributions, gives an index, gamma. This ranges from zero, for no overdispersion, to unity, for total overdispersion. A compact beta-distribution clustered around the mean of the binomial distribution, would add little extra variance and elicit minimum distortion of the binomial distribution, yielding a zero or near zero gamma value. A more scattered or even bimodal beta-distribution would have a substantial effect and yield a significant gamma value. One question that has been posed is whether some test methods are more prone to overdispersion than others. Yet, a consideration of the reasons for overdispersion would suggest that significant gamma values were more a result of obtaining a heterogenous sample of sensitive and insensitive judges by chance. To confirm this, 'less sensitive' and 'more sensitive' samples of judges performed 2-AFC and 3-AFC tests with resulting zero gamma values, indicating no overdispersion. However, when the less and more sensitive groups were combined, significant gamma values were obtained, indicating the presence of overdispersion. However, in a further experiment using 2-AFC tests, when the 'less sensitive' group had its sensitivity increased by a 'warm-up' procedure, combination with the 'more sensitive' group did not result in overdispersion.