Estimating ordinal reliability for Likert-type and ordinal item response data: A conceptual, empirical, and practical guide

Abstract

This paper provides a conceptual, empirical, and practical guide for estimating ordinal reliability coefficients for ordinal item response data (also referred to as Likert, Likert-type, ordered categorical, or rating scale item responses). Conventionally, reliability coefficients, such as Cronbach’s alpha, are calculated using a Pearson correlation matrix. Ordinal reliability coefficients, such as ordinal alpha, use the polychoric correlation matrix (Zumbo, Gadermann, & Zeisser, 2007). This paper presents (i) the theoretical-psychometric rationale for using an ordinal version of coefficient alpha for ordinal data; (ii) a summary of findings from a simulation study indicating that ordinal alpha more accurately estimates reliability than Cronbach's alpha when data come from items with few response options and/or show skewness; (iii) an empirical example from real data; and (iv) the procedure for calculating polychoric correlation matrices and ordinal alpha in the freely available software program R. We use ordinal alpha as a case study, but also provide the syntax for alternative reliability coefficients (such as beta or omega). Accessed 35,197 times on https://pareonline.net from January 17, 2012 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right.