From Labels to Profiles: Using Discriminant Analysis to Deepen Post Hoc ANOVA Results
Bibliographic record
Abstract
In educational research, the Analysis of Variance (ANOVA) is a cornerstone method for detecting differences among group means. Yet, post hoc test results are often reported superficially—merely identifying which groups differ without explaining how or why. This paper introduces discriminant analysis as a complementary multivariate technique that deepens the interpretation of post hoc ANOVA results by moving beyond group labels to develop rich, descriptive profiles of group characteristics. It provides a step-by-step guide for applying discriminant analysis to the homogeneous subsets identified in post hoc testing, including specific recommendations for accessible software options such as SPSS, Excel with add-ins, and the open-source R programming language. To illustrate this method, data are presented from a national study of Japanese nursing educators, in which initial ANOVA and post hoc tests revealed significant differences in teaching style across educational philosophy clusters. Applying discriminant analysis yielded detailed profiles that clarified the distinction between Teacher-Centered and Learner-Centered orientations, transforming the findings from basic group differences to actionable insights. This enhanced method bridges the gap between statistical significance and interpretability, offering clear benefits for educators, researchers, and policymakers. By integrating ANOVA, post hoc testing, and discriminant analysis, researchers can move from detecting group differences to fully describing them, enriching both methodological rigor and practical application across educational and social science research.
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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 | 0.080 | 0.223 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.002 |
| Bibliometrics | 0.009 | 0.006 |
| Science and technology studies | 0.003 | 0.004 |
| Scholarly communication | 0.009 | 0.011 |
| Open science | 0.002 | 0.007 |
| Research integrity | 0.001 | 0.007 |
| Insufficient payload (model declined to judge) | 0.006 | 0.003 |
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".