Statistical Analysis Guide
Guide statistical analysis from hypothesis to regression modeling with rigor
What You Can Do
You can confidently navigate complex statistical analyses by working through structured workflows that match your research question and data type to the right test. The skill guides you through assumption validation, helps you interpret results accurately without common pitfalls, and walks you through regression diagnostics with full transparency about what your findings actually mean.
Features
Match your research question and data characteristics (continuous vs. categorical, paired vs. unpaired) to the appropriate statistical test
Check normality, homogeneity of variance, independence, linearity, and other preconditions before running analyses
Understand what p-values and confidence intervals actually tell you, with clear explanations of common misinterpretations
Calculate and interpret Cohen's d, Cramér's V, R², and other effect sizes to assess practical significance
Evaluate model fit, identify violations, and interpret coefficients, residuals, and multicollinearity
Structure your research question as testable hypotheses with appropriate null and alternative statements
Flag p-hacking, multiple comparison problems, and other common analytical mistakes
Apply analyses to realistic datasets with step-by-step interpretation and visualization guidance
Example Output
Example 1: Selecting a Test
Input: "I have baseline and 6-month follow-up cholesterol levels for 45 patients. Want to know if there's a significant change."
Output:
- ✓ Use: Paired t-test (same subjects, two time points)
- Check assumption: Are differences approximately normally distributed? (Q-Q plot or Shapiro-Wilk test)
- Expected output: t-statistic, degrees of freedom, p-value, 95% CI for mean difference, Cohen's d
- Interpretation: p < 0.05 suggests evidence of change; report the CI and effect size together
Example 2: Regression Diagnostics
Input: "Built a model predicting sales from marketing spend and competitor pricing. R² = 0.62. Are residuals okay?"
Output:
- ✓ Plot residuals vs. fitted values → check for homoscedasticity
- ✓ Q-Q plot of residuals → check normality
- ✓ Check VIF for each predictor → multicollinearity screening
- ✓ Report: Adjusted R², RMSE, coefficient 95% CIs, diagnostics interpretation
- Flag: If R² is moderate but residuals show patterns, consider nonlinear terms or interactions
Example 3: Interpreting Results
Input: "T-test result: t(48) = 2.31, p = 0.024. Cohen's d = 0.45. Significant?"
Output:
- ✓ Yes, statistically significant at α = 0.05 (p < 0.05)
- ✓ Effect size is small-to-medium (Cohen's d = 0.45)
- ✓ 95% CI for difference: [estimate range]
- ⚠️ Caveat: Statistical significance ≠ practical importance; evaluate effect size in your domain context
What's Included
- SKILL.md: Complete skill instructions and workflows
- Test Selection Flowchart: Decision tree for matching research questions to appropriate tests
- Assumption Checklist: Visual diagnostic checklists for each major test family
- Interpretation Guide: Plain-language reference for p-values, CIs, effect sizes, and common misinterpretations
- Regression Diagnostic Checklist: Step-by-step residual analysis and multicollinearity screening protocol
Who It's For
- Data Scientists — validate model assumptions and report results with statistical rigor
- Researchers — design hypothesis tests and interpret study results correctly
- Quality Assurance Engineers — analyze A/B tests and process improvement experiments
- Epidemiologists & Clinical Trial Analysts — conduct and interpret medical research with proper caveats
- Product Managers & Analysts — make evidence-based decisions from test results with accurate confidence intervals
Best For
- Hypothesis testing workflow design (t-tests, ANOVA, chi-square, correlation)
- Assumption validation before statistical tests
- P-value and confidence interval interpretation
- Regression model diagnostics and validation
- Effect size calculation and practical significance assessment
- Avoiding common statistical errors and misinterpretations
- Explaining statistical findings to non-technical stakeholders
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