Factorial ANOVA with unbalanced data: A fresh look at the types of sums of squares
Why this work is in the frame
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Bibliographic record
Abstract
In this paper we endeavour to provide a largely non-technical description of the issues surrounding unbalanced factorial ANOVA and review the arguments made for and against the use of Type I, Type II and Type III sums of squares. Though the issue of which is the `best' approach has been debated in the literature for decades, to date confusion remains around how the procedures differ and which is most appropriate. We ultimately recommend use of the Type II sums of squares for analysis of main effects because when no interaction is present it tests meaningful hypotheses and is the most statistically powerful alternative.
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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 | 0.008 | 0.115 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.003 | 0.001 |
| 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