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Guided statistical analysis: test choice, assumption checks, effect sizes, power, APA reporting. Pick tests, verify assumptions, or format results for publication. Covers frequentist (t-test, ANOVA, chi-square, regression, correlation, survival, count, reliability) and Bayesian. Use statsmodels or pymc-bayesian-modeling to fit.
Passed 19 of 22 test cases with the skill, and 18 of 22 without it.
1 fixed18 passed either way3 still failing0 broke
Tokens, turns and time describe resource use, not a dollar price.
A test case the skill fixed. Same model, same prompt, with and without the skill.
An analyst is screening continuous survey data for extreme univariate outliers using the Interquartile Range (IQR) rule before running parametric diagnostics. What are the exact lower and upper fence formulas for identifying outliers?
| Checked | Without skill | With skill |
|---|---|---|
| State that the lower outlier threshold is calculated as Q1 minus 1.5 times IQR. | Missed | Passed |
| State that the upper outlier threshold is calculated as Q3 plus 1.5 times IQR. | Missed | Passed |
The instructions your model reads when the skill loads.
Statistical analysis is the systematic process of selecting appropriate tests, verifying assumptions, quantifying effect magnitudes, and reporting results. This knowhow guides test selection, assumption diagnostics, and APA-style reporting for frequentist and Bayesian analyses in academic research.
| Aspect | Frequentist | Bayesian |
|---|---|---|
| Core output | p-value, confidence interval | Posterior distribution, credible interval |
| Interpretation | "How likely is this data if H0 is true?" | "How likely is H1 given the data?" |
| Null support | Cannot support H0 (only fail to reject) | Can quantify evidence for H0 via Bayes Factor |
| Prior info | Not used | Incorporated via prior distributions |
| Sample size | Requires adequate power | Works with any sample size |
| Best for | Standard analyses, large samples | Small samples, prior info, complex models |
A statistically significant result (p < .05) may be trivially small in practice. Always report:
| Test | Effect Size | Small | Medium | Large |
|---|---|---|---|---|
| t-test | Cohen's d | 0.20 | 0.50 | 0.80 |
| t-test (small n) | Hedges' g | 0.20 | 0.50 | 0.80 |
| ANOVA | eta-squared partial | 0.01 | 0.06 | 0.14 |
| ANOVA | omega-squared | 0.01 | 0.06 | 0.14 |
| Correlation | r | 0.10 | 0.30 | 0.50 |
| Regression | R-squared | 0.02 | 0.13 | 0.26 |
| Regression | f-squared | 0.02 | 0.15 | 0.35 |
| Chi-square | Cramer's V | 0.07 | 0.21 | 0.35 |
| Chi-square 2x2 | phi coefficient | 0.10 | 0.30 | 0.50 |
test cases passed, vs 18 / 22 without
More skills from the same source and nearby in the registry, with their headline benchmark lift.