On Misconceptions and the Limited Usefulness of Ordinal Alpha

Abstract

This article discusses the theoretical and practical contributions of Zumbo, Gadermann, and Zeisser’s family of ordinal reliability statistics. Implications, interpretation, recommendations, and practical applications regarding their ordinal measures, particularly ordinal alpha, are discussed. General misconceptions relating to this family of ordinal reliability statistics are highlighted, and arguments for interpreting ordinal alpha as a measure of hypothetical reliability, as opposed to observed reliability, are presented. It is concluded that ordinal alpha should not be used in routine reliability analyses and reports, and instead should be understood as hypothetical tool, similar to the Spearman–Brown prophecy formula, for theoretically increasing the number of ordinal categorical response options in future applied testing applications.