On Invariance of Chi-squared Tests Under Different Probability Models
Bibliographic record
Abstract
A chi-squared test is a popular test for assessing relationship between two factors or categorical variables summarized in the form of a contingency table. In this study, we establish the invariance of a chi-squared test under three different study designs, namely, cohort, case-control and cross-sectional studies involving distinct probabilistic models. By the invariance of the chi-squared test, we refer to the fact that the form of a chi-squared test remains unchanged under different probabilistic models. The theoretical derivation of expected cell frequencies carried out in this study, under different study designs and probability models, will be exemplary and invaluable to researchers to understand as to why they can use an identical form of the chi-squared test for a contingency table resulting from case-control, cohort or cross-sectional study design for testing independence. This study is also useful in academia to demonstrate why contingency table resulting under different study designs is subject to identical form of a chi-squared test, which has not been well documented in existing literature. The examples and applications utilized in this study provide directions as to how differently formulated studies are implemented via a chi-squared test.
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How this classification was reachedexpand
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 | 0.000 | 0.000 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".