Reliability in unidimensional ordinal data: A comparison of continuous and ordinal estimators.

Abstract

This study challenges three common methodological beliefs and practices. The first question examines whether ordinal reliability estimators are more accurate than continuous estimators for unidimensional data with uncorrelated errors. Continuous estimators (e.g., coefficient alpha) can be applied to both continuous and ordinal data, while ordinal estimators (e.g., ordinal alpha and categorical omega) are specific to ordinal data. Although ordinal estimators are often argued to have conceptual advantages, comprehensive investigations into their accuracy are limited. The second question explores the relationship between skewness and kurtosis in ordinal data. Previous simulation studies have primarily examined cases where skewness and kurtosis change in the same direction, leaving gaps in understanding their independent effects. The third question addresses item response theory (IRT) models: Should the scaling constant always be fixed at the same value (e.g., 1.7)? To answer these questions, this study conducted a Monte Carlo simulation comparing four continuous estimators and eight ordinal estimators. The results indicated that most estimators achieved acceptable levels of accuracy. On average, ordinal estimators were slightly less accurate than continuous estimators, though the difference was smaller than what most users would consider practically significant (e.g., less than 0.01). However, ordinal alpha stood out as a notable exception, severely overestimating reliability across various conditions. Regarding the scaling constant in IRT models, the results indicated that its optimal value varied depending on the data type (e.g., dichotomous vs. polytomous). In some cases, values below 1.7 were optimal, while in others, values above 1.8 were optimal. (PsycInfo Database Record (c) 2025 APA, all rights reserved).