Generalized Linear Model Analyses for Treatment Group Equality when Data are Non-Normal
Bibliographic record
Abstract
One of the validity conditions of classical test statistics (e.g., Student’s t-test, the ANOVA and MANOVA F-tests) is that data be normally distributed in the populations. When this and/or other derivational assumptions do not hold the classical test statistic can be prone to too many Type I errors (i.e., falsely rejecting too often) and/or have low power (i.e., failing to reject when the null hypothesis is false) to detect treatment effects when they are present. However, alternative procedures are available for assessing equality of treatment group effects when data are non-normal. For example, researchers can use robust estimators instead of the usual least squares estimators to test that treatment effects are equivalent across groups. As well, recent advances in statistical methodology allow researchers to test for equality of treatment group effects by assuming other distributional shapes for the data. One class of such analyses is generalized linear model techniques. On the other hand, researchers can adopt sequential analyses where they first assess the normality assumption and then depending on the result determine the type of analysis that should be adopted. The purpose of the present study was to compare the above approaches for assessing equality of treatment group effects in the presence of non-normal data. Simulation results which were based on various non-normal distributions and the values of group variances and sample sizes revealed that sequential analysis coupled with a generalized linear model solution were just as prone to inflated or depressed rates of Type I error as the classical ANOVA F-test.
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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 | 0.057 | 0.242 |
| Meta-epidemiology (narrow) | 0.003 | 0.001 |
| Meta-epidemiology (broad) | 0.004 | 0.006 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.004 | 0.005 |
| Open science | 0.005 | 0.004 |
| Research integrity | 0.003 | 0.008 |
| Insufficient payload (model declined to judge) | 0.025 | 0.004 |
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".