Internal Consistency Reliability
Internal consistency reliability is the degree to which the items of a test measure the same underlying construct, estimated from a single administration rather than from repeated testing. It is the most widely reported reliability index in language testing because it requires no second occasion and no additional rater.
Estimators
Three main estimators dominate practice. Split-half reliability divides the test into two halves and correlates them, with the Spearman–Brown prophecy formula used to project the coefficient back to the full-test length. The Kuder–Richardson formulas — KR-20 for dichotomous items of varying difficulty, KR-21 for items assumed to be of equal difficulty — were the early standard for right/wrong scoring. Cronbach's alpha generalises KR-20 to items with any scoring range and remains the default index reported in published research, despite well-known limitations: alpha assumes essential tau-equivalence, and on multidimensional tests it is neither a lower bound on reliability nor an index of unidimensionality. McDonald's omega and stratified alpha are increasingly preferred where assumptions are violated.
Interpretation
Coefficients are conventionally interpreted as the proportion of observed-score variance attributable to true-score variance under classical test theory. Values are sample-dependent: a more heterogeneous group typically yields a higher coefficient because between-person variance increases. Test length matters too — Spearman–Brown shows that doubling the items of a parallel test will substantially raise reliability up to a ceiling.
Internal-consistency estimates capture only one source of measurement error. They speak to item sampling but ignore occasion effects, rater effects, and task-sampling effects that test-retest, inter-rater, and generalizability analyses address.
References
- Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297–334.
- Bachman, L. F. (1990). Fundamental Considerations in Language Testing. Oxford University Press.
- AERA, APA, & NCME (2014). Standards for Educational and Psychological Testing. American Educational Research Association.