statistical-analysis

# Statistical Analysis ## Overview 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. ## Key Concepts ### Frequentist vs Bayesian Framework | 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 | ### Statistical vs Practical Significance A statistically significant result (p < .05) may be trivially small in practice. Always report: - **Effect size**: Magnitude of the effect (Cohen's d, eta-squared, r, R-squared) - **Confidence interval**: Precision of the estimate - **Context**: Clinical/practical relevance in the domain ### Common Effect Sizes | Test | Effect Size | Small | Medium | Large | |------|-------------|-------|--------|-------| | t-test | Cohen's d | 0.20 | 0.50 | 0.80 | | t-test (...