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.

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.