A Comparison of Correlation Coefficients via a Three-Step Bootstrap Approach
Bibliographic record
Abstract
In this article we compare ten correlation coefficients using a three-step bootstrap approach (TSB). A three-step bootstrap is applied to determine the optimal repetitions, $B$, to estimate the standard error of the statistic with certain degree of accuracy. The coefficients in question are Pearson product moment ($r$), Spearman's rho ($\rho$), Kendall's tau ($\tau$) , Spearman's Footrule ($F_t$), Symmetric Footrule ($C$), the Greatest deviation ($R_g$), the Top - Down ($r_T$), Weighted Kendall's tau ($\tau_w$), Blest ($\nu$), and Symmetric Blest's coefficient ($\nu^*$). We consider a standard error criterion for our comparisons. However, since the rank correlation coefficients suffer from the tied problem that results from the bootstrap technique, we use existing modified formulas for some rank correlation coefficients, otherwise, the randomization tied-treatment is applied.
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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 | 0.036 | 0.191 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.004 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".