Being Inconsistent About Consistency: When Coefficient Alpha Does and Doesn't Matter
Bibliographic record
Abstract
One of the central tenets of classical test theory is that scales should have a high degree of internal consistency, as evidenced by Cronbach's a, the mean interitem correlation, and a strong first component. However, there are many instances in which this rule does not apply. Following Bollen and Lennox (1991), I differentiate between questionnaires such as anxiety or depression inventories, which are composed of items that are manifestations of an underlying hypothetical construct (i.e., where the items are called effect indicators) and those such as Scale 6 of the Minnesota Multiphasic Personality Inventory (Hathaway & McKinley, 1943) and ones used to tap quality of life or activities of daily living in which the items or subscales themselves define the construct (these items are called causal indicators). Questionnaires of the first sort, which are referred to as scales in this article, meet the criteria of classical test theory, whereas the second type, which are called indexes here, do not. I discuss the implications of this difference for how items are selected, the relationship among the items, and the statistics that should and should not be used in establishing the reliability of the scale or index.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.183 | 0.608 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.002 |
| Bibliometrics | 0.011 | 0.016 |
| Science and technology studies | 0.003 | 0.019 |
| Scholarly communication | 0.009 | 0.013 |
| Open science | 0.004 | 0.006 |
| Research integrity | 0.005 | 0.007 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
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; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
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".