Statistical Analysis

Overview

Statistical analysis is a systematic process for testing hypotheses and quantifying relationships. Conduct hypothesis tests (t-test, ANOVA, chi-square), regression, correlation, and Bayesian analyses with assumption checks and APA reporting. Apply this skill for academic research.

When to Use This Skill

This skill should be used when:

• Conducting statistical hypothesis tests (t-tests, ANOVA, chi-square)
• Performing regression or correlation analyses
• Running Bayesian statistical analyses
• Checking statistical assumptions and diagnostics
• Calculating effect sizes and conducting power analyses
• Reporting statistical results in APA format
• Analyzing experimental or observational data for research

---

Core Capabilities

1. Test Selection and Planning

• Choose appropriate statistical tests based on research questions and data characteristics
• Conduct a priori power analyses to determine required sample sizes
• Plan analysis strategies including multiple comparison corrections

2. Assumption Checking

• Automatically verify all relevant assumptions before running tests
• Provide diagnostic visualizations (Q-Q plots, residual plots, box plots)
• Recommend remedial actions when assumptions are violated

3. Statistical Testing

• Hypothesis testing: t-tests, ANOVA, chi-square, non-parametric alternatives
• Regression: linear, multiple, logistic, with diagnostics
• Correlations: Pearson, Spearman, with confidence intervals
• Bayesian alternatives: Bayesian t-tests, ANOVA, regression with Bayes Factors

4. Effect Sizes and Interpretation

• Calculate and interpret appropriate effect sizes for all analyses
• Provide confidence intervals for effect estimates
• Distinguish statistical from practical significance

5. Professional Reporting

• Generate APA-style statistical reports
• Create publication-ready figures and tables
• Provide complete interpretation with all required statistics

---