A Note on Confidence Interval for the Power of the One Sample <i>t</i> Test
Why this work is in the frame
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Bibliographic record
Abstract
In introductory statistics texts, the power of the test of a one‐sample mean when the variance is known is widely discussed. However, when the variance is unknown, the power of the Student′s t ‐test is seldom mentioned. In this note, a general methodology for obtaining inference concerning a scalar parameter of interest of any exponential family model is proposed. The method is then applied to the one‐sample mean problem with unknown variance to obtain a (1 − γ )100% confidence interval for the power of the Student′s t ‐test that detects the difference ( μ − μ 0 ). The calculations require only the density and the cumulative distribution functions of the standard normal distribution. In addition, the methodology presented can also be applied to determine the required sample size when the effect size and the power of a size α test of mean are given.
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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 | 0.001 | 0.023 |
| 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