Effectiveness of Combining Statistical Tests and Effect Sizes When Using Logistic Discriminant Function Regression to Detect Differential Item Functioning for Polytomous Items
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Bibliographic record
Abstract
The objective of this article was to find an optimal decision rule for identifying polytomous items with large or moderate amounts of differential functioning. The effectiveness of combining statistical tests with effect size measures was assessed using logistic discriminant function analysis and two effect size measures: R 2 and conditional log odds ratio in delta scale (Δ LR ). Four independent variables were manipulated: (a) different sample sizes for the reference and focal groups (1,000/500, 1,000/250, 500/250), (b) impact between reference and focal group (equal-ability distribution, i.e., no impact; or different-ability distribution, i.e., impact), (c) the percentage of differential item functioning (DIF) items in a test (0%, 12%, i.e., only the first three items of the test; 20%, i.e., the first five items of the test; 32%, i.e., the first eight items of the test), and (d) direction of DIF (one-sided and both-sided). The magnitudes of DIF were indirectly manipulated through the percentage of DIF items and DIF direction, and they were simulated to be moderate or large. The results show that the false positive rates were low when an effect size decision rule was used in combination with a statistical test, and they were very low when R 2 effect size criteria were applied. With respect to power, when a statistical test was used in conjunction with effect size criteria to determine whether an item exhibited a meaningful magnitude of DIF, we found when using the Δ LR decision rule that the percentage of meaningful DIF items was higher with greater amounts of DIF. Examining DIF by means of blended statistical tests, in other words, those incorporating both the p value and effect size measures, can be recommended as a procedure for classifying items displaying DIF.
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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 | 0.005 | 0.051 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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