### Abstract

It is well known that coefficient alpha is an estimate of reliability if its underlying assumptions are met and that it is a lower-bound estimate if the assumption of essential tau equivalency is violated. Very little literature addresses the assumption of uncorrelated errors among items and the effect of violating this assumption on alpha. True score models are proposed that can account for correlated errors. These models allow random measurement errors on earlier items to affect directly or indirectly scores on later items. Coefficient alpha may yield spuriously high estimates of reliability if these true score models reflect item responding. In practice, it is important to differentiate these models from models in which the errors are correlated because 1 or more factors have been left unspecified. If the latter model is an accurate representation of item responding, the assumption of essential tau equivalency is violated and alpha is a lower-bound estimate of reliability.

Original language | English (US) |
---|---|

Pages (from-to) | 251-270 |

Number of pages | 20 |

Journal | Structural Equation Modeling |

Volume | 7 |

Issue number | 2 |

DOIs | |

State | Published - 2000 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Modeling and Simulation
- Decision Sciences(all)
- Economics, Econometrics and Finance(all)
- Sociology and Political Science

### Cite this

*Structural Equation Modeling*,

*7*(2), 251-270. https://doi.org/10.1207/S15328007SEM0702_6

**Correlated errors in true score models and their effect on coefficient alpha.** / Green, Samuel B.; Hershberger, Scott L.

Research output: Contribution to journal › Article

*Structural Equation Modeling*, vol. 7, no. 2, pp. 251-270. https://doi.org/10.1207/S15328007SEM0702_6

}

TY - JOUR

T1 - Correlated errors in true score models and their effect on coefficient alpha

AU - Green, Samuel B.

AU - Hershberger, Scott L.

PY - 2000

Y1 - 2000

N2 - It is well known that coefficient alpha is an estimate of reliability if its underlying assumptions are met and that it is a lower-bound estimate if the assumption of essential tau equivalency is violated. Very little literature addresses the assumption of uncorrelated errors among items and the effect of violating this assumption on alpha. True score models are proposed that can account for correlated errors. These models allow random measurement errors on earlier items to affect directly or indirectly scores on later items. Coefficient alpha may yield spuriously high estimates of reliability if these true score models reflect item responding. In practice, it is important to differentiate these models from models in which the errors are correlated because 1 or more factors have been left unspecified. If the latter model is an accurate representation of item responding, the assumption of essential tau equivalency is violated and alpha is a lower-bound estimate of reliability.

AB - It is well known that coefficient alpha is an estimate of reliability if its underlying assumptions are met and that it is a lower-bound estimate if the assumption of essential tau equivalency is violated. Very little literature addresses the assumption of uncorrelated errors among items and the effect of violating this assumption on alpha. True score models are proposed that can account for correlated errors. These models allow random measurement errors on earlier items to affect directly or indirectly scores on later items. Coefficient alpha may yield spuriously high estimates of reliability if these true score models reflect item responding. In practice, it is important to differentiate these models from models in which the errors are correlated because 1 or more factors have been left unspecified. If the latter model is an accurate representation of item responding, the assumption of essential tau equivalency is violated and alpha is a lower-bound estimate of reliability.

UR - http://www.scopus.com/inward/record.url?scp=0038078416&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038078416&partnerID=8YFLogxK

U2 - 10.1207/S15328007SEM0702_6

DO - 10.1207/S15328007SEM0702_6

M3 - Article

VL - 7

SP - 251

EP - 270

JO - Structural Equation Modeling

JF - Structural Equation Modeling

SN - 1070-5511

IS - 2

ER -