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Sample size calculation and statistical power analysis guide
Passed 24 of 24 test cases with the skill, and 23 of 24 without it.
1 fixed23 passed either way0 still failing0 broke
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A test case the skill fixed. Same model, same prompt, with and without the skill.
When conducting power calculations for binary logistic regression, what are the standard guideline values for small, medium, and large Odds Ratios (OR)?
| Checked | Without skill | With skill |
|---|---|---|
| Identifies Odds Ratio of 1.5 as a small effect size | Passed | Passed |
| Identifies Odds Ratio of 2.5 as a medium effect size | Passed | Passed |
| Identifies Odds Ratio of 4.0 as a large effect size | Missed | Passed |
The instructions your model reads when the skill loads.
Calculate appropriate sample sizes for your study using power analysis, understand effect sizes, and avoid underpowered or wastefully overpowered designs.
Every power analysis involves four interrelated quantities. Fix any three to solve for the fourth:
| Parameter | Symbol | Definition | Typical Value |
|---|---|---|---|
| Effect size | d, r, f, etc. | Magnitude of the phenomenon you expect to detect | Varies by field |
| Significance level (alpha) | alpha | Probability of Type I error (false positive) | 0.05 |
| Statistical power (1 - beta) | 1 - beta | Probability of detecting a true effect | 0.80 or 0.90 |
| Sample size | N | Number of observations needed | Solve for this |
| H0 is true (no effect) | H0 is false (effect exists) | |
|---|---|---|
| Reject H0 | Type I error (alpha) | Correct (power = 1 - beta) |
| Fail to reject H0 | Correct (1 - alpha) | Type II error (beta) |
d = (M1 - M2) / SD_pooled
| Size | Cohen's d | Interpretation |
|---|---|---|
| Small | 0.2 | Subtle, may need large N to detect |
| Medium | 0.5 | Noticeable, typical in social sciences |
| Large | 0.8 | Obvious, often visible without statistics |
test cases passed, vs 23 / 24 without
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