The Bayesian One-Sample <i>t</i>-Test Supersedes Correlation Analysis as a Test of Validity
Bibliographic record
Abstract
Abstract: Introduction: The validity of measurement, which refers to how accurately tools measure what they are intended to measure, is essential in science. Researchers rely on statistical approaches to test the validity of their measures. One such approach is correlation analysis. Even though correlation analysis can capture high nonsystematic errors between measures, it can often lead to misleading conclusions when observations are measured with systematic errors. Methods: We used Monte Carlo simulations with 10,000 iterations to generate the data in each simulation. Results: We demonstrate how correlation analysis is commonly used to test for validity and how this method can fail with systematic error. We further propose an alternative to correlation analysis – the Bayesian one-sample t-test – for cases where using a simple statistical test can be justified. We provide additional simulations as well as an application to real data, showcasing the implementation of the Bayesian one-sample t-test and how to use it to address the limitations of correlation analysis. Discussion: We suggest using the Bayesian one-sample t-test to identify both systematic and nonsystematic error and moreover to provide evidence for the null hypothesis of no differences between two measures. Conclusion: As a test of validity, the Bayesian one-sample t-test supersedes correlation analysis.
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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 | 0.019 | 0.146 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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) | 0.001 | 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 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".