The Polychoric Ordinal Alpha, measuring the reliability of a set of polytomous ordinal items

Abstract We aim at proposing a new reliability measurement for polytomous or-dinal items. Conventionally, reliability coefficients, such as Cronbach Alpha, are calculated using the Pearson correlation matrix. We suggest a modification of the classical Cronbach Alpha for ordinal variables, by using the polychoric correlation coefficient. In particular we consider the extension of polychoric correlation coef-ficient via copula approach. It builds upon the theoretical framework of the classic polychoric correlation coefficient, but relaxes its fundamental assumption that the ordinal variables have a underlying multinormal distributions. A simulation study is conducted in order to compare the proposed index to classical reliability measures. Key words: Polychoric correlation, Copula, Cronbach Alpha 1 Cronbach Alpha for ordinal data Reliability is consistency of a set of measurements in research involving test con-struction and use. In literature several reliability measures have been proposed. The most widely used reliability coefficient in the social science is Cronbach Alpha [2]. This index is frequently applied when analyzing items on self-report instruments such as personality tests and surveys that often use rating scales with a small num-