Effect Size Interpretation AI Prompt

Help me calculate, report, and interpret effect sizes for my study.

Study type: {{study_type}}
Statistical results: {{results}}
Field norms: {{field}} (what are typical effect sizes in this field?)

1. Why effect sizes matter more than p-values:
   - A p-value tells you whether an effect exists (given sufficient sample size)
   - An effect size tells you HOW LARGE the effect is
   - With large enough samples, trivially small effects become statistically significant
   - Effect sizes allow comparison across studies and meta-analysis
   - Always report both: the p-value for the inference decision, the effect size for the magnitude interpretation

2. Effect size families and when to use each:

   Standardized mean difference family:
   - Cohen's d: difference between two means divided by pooled standard deviation. For independent groups.
   - Glass's Δ: uses only the control group SD in the denominator. Preferred when SDs differ substantially.
   - Hedges' g: small-sample correction of Cohen's d. Use when n < 20 per group.
   - Interpretation: d = 0.2 (small), 0.5 (medium), 0.8 (large) — but these are field-agnostic; use field norms when available.

   Correlation family:
   - Pearson r: linear association between two continuous variables. r = 0.1 (small), 0.3 (medium), 0.5 (large).
   - R²: proportion of variance explained. Report alongside r.
   - Partial eta squared (η²p): proportion of variance in the outcome explained by the predictor, removing other effects. For ANOVA designs.
   - Omega squared (ω²): less biased estimator of η²p. Prefer over η²p for small samples.

   Odds ratio and relative risk:
   - Odds ratio (OR): for logistic regression and case-control studies. OR = 1 means no effect.
   - Relative risk (RR): for cohort studies with binary outcomes. More interpretable than OR.
   - Number needed to treat (NNT): 1 / absolute risk reduction. Most clinically interpretable.

3. Calculate effect sizes from my results:
   - Apply the appropriate formula to my specific results
   - Include confidence intervals around each effect size estimate

4. Contextualizing the effect size:
   - Compare to typical effect sizes in {{field}}
   - Compare to effect sizes in related prior studies
   - Translate to practical significance: what does an effect of this size mean in the real world?

Return: calculated effect sizes with CIs, interpretation against field benchmarks, and a practical significance statement.