Correcting Two-Sample z and t Tests for Correlation: An Alternative to One-Sample Tests on Difference Scores
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Bibliographic record
Abstract
In order to circumvent the influence of correlation in paired-samples and repeated measures experimental designs, researchers typically perform a one-sample Student t test on difference scores. That procedure entails some loss of power, because it employs N – 1 degrees of freedom instead of the 2N – 2 degrees of freedom of the independent-samples t test. In the case of non-normal distributions, researchers typically substitute the Wilcoxon signed-ranks test for the one-sample t test. The present study explored an alternate strategy, using a modified two-sample t test with a correction for correlation, analogous to the “z test for correlated samples” used at one time for paired observations. For non-normal distributions, the same modified t test was performed on rank-transformed data. Simulations disclosed that this procedure protects the Type I error rate for moderate and large sample sizes, maintains power for normal distributions and several symmetric non-normal distributions, and substantially increases power for various skewed nonnormal distributions. Statistical analysis of paired-samples or repeated-measures experimental designs typically employs the one-sample Student t test on difference scores in place of the independent-samples t test. This method, widely used in the past, entails some loss of power, because the test on differences is necessarily based on N – 1 instead of 2N − 2 degrees of freedom. In the first part of the last century, data from paired-samples was often analyzed in a different way. Many introductory textbooks in that period, focusing mainly on large-sample studies for which the z-test is appropriate, presented methods of analyzing what were called correlated samples, using a modification of the familiar two-sample z test. These
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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 | 0.000 | 0.017 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| 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