Thurstonian scales obtained by transformation of beta distributions

According to Thurstone Case V, the quantiles of the normal standard distribution corresponding to the proportion of answers from a set of paired comparisons between several products are used to compute scales. This paper analyses two alternative approaches based on Bayesian inference by which the normal quantiles are obtained not only from the exact proportion of answers actually observed for each paired comparison but from all potentially observable proportions, continuously distributed in the range from 0 to 1 according to a beta distribution. Using the first approach a normal distribution is assumed for the obtained quantiles and so the properties of normal distributions were applied to estimate scale scores and confidence intervals. The second approach is based on a simulation process that avoids the assumption of normality. Both approaches give similar results that, for a low number of respondents, differ from those obtained by applying Thurstone Case V in its traditional way.