## Abstract

The population relationship between coefficient alpha and scale reliability is studied in the widely used setting of unidimensional multicomponent measuring instruments. It is demonstrated that for any set of component loadings on the common factor, regardless of the extent of their inequality, the discrepancy between alpha and reliability can be arbitrarily small in any considered population and hence practically ignorable. In addition, the set of parameter values where this discrepancy is negligible is shown to possess the same dimensionality as that of the underlying model parameter space. The article contributes to the measurement and related literature by pointing out that (a) approximate or strict loading identity is not a necessary condition for the utility of alpha as a trustworthy index of scale reliability, and (b) coefficient alpha can be a dependable reliability measure with any extent of inequality in the component loadings.

Original language | English (US) |
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Journal | Educational and Psychological Measurement |

DOIs | |

State | Accepted/In press - 2022 |

Externally published | Yes |

## Keywords

- coefficient alpha
- measurement
- multicomponent instrument
- parameter space
- population reliability to alpha discrepancy
- scale reliability
- single-factor model
- unidimensionality

## ASJC Scopus subject areas

- Education
- Developmental and Educational Psychology
- Applied Psychology
- Applied Mathematics