statistical-analysis

# 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 interval...