statistical-analysis

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Tool: SKILL.md [1/3] Description: --- name: statistical-analysis description: "Statistical analysis toolkit.

Tool: SKILL.md [2/3] Description: Scale-Location axes[1, 0].scatter(fitted, np.sqrt(np.abs(residuals / residuals.std())), alpha=0.6) axes[1, 0].set_xlabel('Fitted values') axes[1, 0].set_ylabel('√|Standardized residuals|') axes[1, 0].set_title('Scale-Location') # Residuals histogram axes[1, 1].hist(residuals, bins=20, edgecolor='black', alpha=0.7) axes[1, 1].set_xlabel('Residuals') axes[1, 1].set_ylabel('Frequency') axes[1, 1].set_title('Histogram of Residuals') plt.tight_layout() plt.show() ```

Tool: SKILL.md [3/3] Description: convergence checking and posterior predictive checks ### Key Advantages 1. **Intuitive interpretation**: "Given the data, there is a 95% probability the parameter is in this interval" 2.

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Tool: references/assumptions_and_diagnostics.md [1/2] Description: # Statistical Assumptions and Diagnostic Procedures This document provides comprehensive guidance on checking and validating statistical assumptions for various analyses.

Tool: references/assumptions_and_diagnostics.md [2/2] Description: do if violated**: - **Non-linearity**: Add polynomial terms, use GAM, or transform variables - **Heteroscedasticity**: Transform Y, use WLS, use robust SE - **Non-normal residuals**: Transform Y, use robust methods, check for outliers - **Multicollinearity**: Remove correlated predictors, use PCA, ridge regression --- ### Logistic Regression **Assumptions**: 1.

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Tool: references/bayesian_statistics.md [1/3] Description: # Bayesian Statistical Analysis This document provides guidance on conducting and interpreting Bayesian statistical analyses, which offer an alternative framework to frequentist (classical) statistics.

Tool: references/bayesian_statistics.md [2/3] Description: for skewed distributions **Python calculation**: ```python import arviz as az # Equal-tailed interval eti = np.percentile(posterior_samples, [2.5, 97.5]) # HDI hdi = az.hdi(posterior_samples, hdi_prob=0.95) ``` --- ### Posterior Distributions **Interpreting posterior distributions**: 1.

Tool: references/bayesian_statistics.md [3/3] Description: [0.38, 0.55]).

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Tool: references/effect_sizes_and_power.md [1/3] Description: # Effect Sizes and Power Analysis This document provides guidance on calculating, interpreting, and reporting effect sizes, as well as conducting power analyses for study planning.

Tool: references/effect_sizes_and_power.md [2/3] Description: - R²_AB = R² for full model with predictor - R²_A = R² for reduced model without predictor **Interpretation**: - Small: f² = 0.02 - Medium: f² = 0.15 - Large: f² = 0.35 **Python calculation**: ```python # Compare two nested models model_full = OLS(y, X_full).fit() model_reduced = OLS(y, X_reduced).fit() r2_full = model_full.rsquared r2_reduced = model_reduced.rsquared f_squared = (r2_full - r2_reduced) / (1 - r2_full) ``` --- ### Cate

Tool: references/effect_sizes_and_power.md [3/3] Description: Context matters; small effects can be meaningful 2.

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Tool: references/reporting_standards.md [1/4] Description: # Statistical Reporting Standards This document provides guidelines for reporting statistical analyses according to APA (American Psychological Association) style and general best practices for academic publications. ## General Principles 1.

Tool: references/reporting_standards.md [2/4] Description: t-test)**: > "Due to unequal variances, Welch's t-test was used.

Tool: references/reporting_standards.md [3/4] Description: = 12), U = 845, z = 3.21, p = .001, r = .32." **Wilcoxon signed-rank**: > "A Wilcoxon signed-rank test showed that scores increased significantly from pretest (Mdn = 65, IQR = 15) to posttest (Mdn = 72, IQR = 14), z = 3.89, p < .001, r = .39." **Kruskal-Wallis**: > "A Kruskal-Wallis test revealed significant differences among the three conditions, H(2) = 15.7, p < .001, η² = .09. Follow-up pairwise comparisons with Bonferroni correction

Tool: references/reporting_standards.md [4/4]

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Tool: references/test_selection_guide.md Description: # Statistical Test Selection Guide This guide provides a decision tree for selecting appropriate statistical tests based on research questions, data types, and study designs.

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Tool: scripts/assumption_checks.py [1/2] Description: """ Comprehensive statistical assumption checking utilities.

Tool: scripts/assumption_checks.py [2/2] Description: ValueError("method must be 'iqr' or 'zscore'") outlier_indices = np.where(outlier_mask)[0] outlier_values = data_clean[outlier_mask] n_outliers = len(outlier_indices) pct_outliers = (n_outliers / len(data_clean)) * 100 if plot: fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 4)) # Box plot bp = ax1.boxplot(data_clean, vert=True, patch_artist=True) bp['boxes'][0].set_facecolor('steelblue') ax1.set_ylabel('Value') ax1.set_title(f'Box Plot: {n