Transforming Unreplicated Factorial Designs into Replicated Structures through Factor Projection
Bibliographic record
Abstract
In factorial experiments, unreplicated design is limited by the absence of error estimation, which complicates the identification of significant effects. This often leads to reliance on the sparsity-of-effects principle, where only a few main effects and lower-order interactions are considered meaningful, while most higher-order interactions are assumed negligible. To address this challenge, this study introduces a method for projecting unreplicated factorial designs into replicated design by reducing the number of factors and increase the number of replicates. This approach utilizes factorial effect estimation, normal probability plotting, and significance testing to identify influential factors. A full factorial design involving five binary factors (A, B, C, D, and E) was analyzed in an unreplicated 2⁵ setup. The analysis indicated that factors A and E do not significantly affect the outcome, while AE interaction was minimal. However, factor B, and interactions AB, BE, and ABE shows significant effects. Based on these findings, the original 2⁵ unreplicated design was projected into a 23 factorial design involving factors A, B, and E, including AE and BE interactions, with four replicates to enable error estimation. The results demonstrate that decreasing the number of factors (k) in the design enables an increase in the number of replicates, enhancing the reliability of inference through better error estimation.
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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 | 0.016 | 0.036 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".