The Impact of Outliers on Cronbach’s Coefficient Alpha Estimate of Reliability: Ordinal/Rating Scale Item Responses
Bibliographic record
Abstract
In a recent Monte Carlo simulation study, Liu and Zumbo showed that outliers can severely inflate the estimates of Cronbach’s coefficient alpha for continuous item response data—visual analogue response format. Little, however, is known about the effect of outliers for ordinal item response data—also commonly referred to as Likert, Likert-type, ordered categorical, or ordinal/rating scale item responses. Building on the work of Liu and Zumbo, the authors investigated the effects of outlier contamination for binary and ordinal response scales. Their results showed that coefficient alpha estimates were severely inflated with the presence of outliers, and like the earlier findings, the effects of outliers were reduced with increasing theoretical reliability. The efficiency of coefficient alpha estimates (i.e., sample-to-sample variation) was inflated as well and affected by the number of scale points. It is worth noting that when there were no outliers, the alpha estimates were downward biased because of the ordinal scaling. However, the alpha estimates were, in general, inflated in the presence of outliers leading to positive bias.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.235 | 0.673 |
| Meta-epidemiology (narrow) | 0.001 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.004 | 0.005 |
| Science and technology studies | 0.002 | 0.005 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; the direct Gemma label and the distilled Codex classifier agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".