A New Index for the Comparison of Different Measurement Scales

In psychometric sciences, a common problem is the choice of a good response scale. Every scale has, by its nature, a propensity to lead a respondent to mainly positive -or negative- ratings. This paper investigates possible causes of the discordance between two ordinal scales evaluating the same goods or services. In psychometric literature, Cohen’s Kappa is one of the most important index to evaluate the strength of agreement, or disagreement, between two nominal variables, in particular in its weighted version. In this paper, a new index is proposed. A proper procedure to determine the lower and upper triangle in a non-square table is also implemented, as to generalize the index in order to compare two scales with a different number of categories. A test is set up with the aim to verify the tendency of a scale to have a different rating compared to a different one. A study with real data is conducted.