The Relationship Between Unstandardized and Standardized Alpha, True Reliability, and the Underlying Measurement Model
Why this work is in the frame
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Bibliographic record
Abstract
Popular computer programs print 2 versions of Cronbach's alpha: unstandardized alpha, α(Σ), based on the covariance matrix, and standardized alpha, α(R), based on the correlation matrix. Sources that accurately describe the theoretical distinction between the 2 coefficients are lacking, which can lead to the misconception that the differences between α(R) and α(Σ) are unimportant and to the temptation to report the larger coefficient. We explore the relationship between α(R) and α(Σ) and the reliability of the standardized and unstandardized composite under 3 popular measurement models; we clarify the theoretical meaning of each coefficient and conclude that researchers should choose an appropriate reliability coefficient based on theoretical considerations. We also illustrate that α(R) and α(Σ) estimate the reliability of different composite scores, and in most cases cannot be substituted for one another.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.106 | 0.072 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it