A method for measuring consensus within groups: An index of disagreement via conditional probability

Abstract

This paper presents a new index of disagreement (or measure of consensus) for comparison of data collected using Likert items. This new index, which assesses the level of disagreement among group members, exploits the conditional distribution of the variance for a given mean. The variance is often used as a measure of disagreement, with high variance seen as a high disagreement in a group. However, since the range of the variance is a function of the mean, this implies that for a mean close to the end points of the scale, the range of the variance is relatively small and for a mean at the center of the scale the range of the variance is larger. The index of disagreement introduced in this paper takes into account both the mean and the variance and provides a way to compare two groups that is more meaningful than just considering the variance or other measures of disagreement or consensus that only depend on the variance.