A POWER STRUGGLE: BETWEEN- VS. WITHIN-SUBJECTS DESIGNS IN DEDUCTIVE REASONING RESEARCH
Bibliographic record
Abstract
This experiment examined the relative merits of using within-and between-subjects designs to investigate deductive reasoning. Two issues were investigated: 1) the potential for expectancy and fatigue effects when using within-subjects designs, and 2) the relative power of within- vs between-subjects designs. Participants were presented with problems in a standard belief-bias paradigm in which the believability of putative conclusions varied orthogonally to their validity. The belief bias effect, as well as the effect of validity, and the interaction between beliefs and validity, were not affected by reasoners’ expectations regarding the number of problems they had to solve. The effect of beliefs and the belief by validity interaction were only marginally affected by the number of problems solved, despite adequate power to observe an effect. Thus, neither expectancy nor fatigue appear to have affected performance, suggesting that there are few drawbacks to using a within-subjects design. In contrast, however, a power analysis clearly established the desirability of using within- relative to between-subjects designs. Within-subjects designs require far fewer participants to detect effects of comparable size; this was especially true for higher-order (interaction) effects. Finally, we provide a power analysis of within- and between-subjects designs that should be of general utility to researchers planning studies using proportions as a dependent measure.
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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 | 0.011 | 0.006 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.002 |
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".