Add comprehensive biomedical statistical tests with visualizations

[Brijesh03032001]

@siriak @acylam @Panquesito7 Please see to this too, this is reallt awesome work. I am a machine learning researcher so I thought to add this here with the demo dataset.

🧬 Add Comprehensive Biomedical Statistical Tests with Advanced Visualizations

🚀 Overview

This PR introduces a complete suite of essential biomedical statistical tests with professional visualizations and clinical examples. All implementations are built with base R (no external dependencies) and include comprehensive educational demonstrations for biomedical research applications.

✨ Features Added

📊 Comprehensive T-Tests (t_tests_comprehensive.r)

• One-Sample T-Test: Test sample means against known values (drug efficacy studies)
• Two-Sample T-Test: Compare means between independent groups (treatment comparisons)
• Paired T-Test: Analyze before/after measurements (clinical interventions)
• Welch's T-Test: Handle unequal variances automatically
• Statistical Power Analysis: Sample size planning with effect size considerations
• Clinical Interpretations: Effect size guidelines (Cohen's d) and practical significance

🎯 Chi-Square Test Suite (chi_square_tests.r)

• Goodness of Fit Test: Compare observed vs expected distributions (blood type analysis)
• Test of Independence: Analyze relationships between categorical variables (treatment response by demographics)
• McNemar's Test: Paired categorical data analysis (before/after treatment status)
• Effect Size Measures: Cramer's V and phi coefficients
• Multiple Testing Corrections: Bonferroni and FDR adjustments
• Contingency Table Visualizations: Professional heatmaps with residual analysis

📈 Advanced Correlation Analysis (correlation_analysis.r)

• Pearson Correlation: Linear relationships with assumption checking
• Spearman Correlation: Monotonic relationships (rank-based)
• Kendall's Tau: Robust correlation resistant to outliers
• Correlation Matrices: Multi-variable analysis with significance testing
• Assumption Validation: Normality, linearity, homoscedasticity checks
• Confidence Intervals: Fisher's Z transformation for accurate CI estimation

📊 Visualization Features

🎨 Professional Statistical Plots

• Multi-panel Layouts: Comprehensive diagnostic plots for each test
• Statistical Annotations: p-values, effect sizes, confidence intervals
• Assumption Checking: Q-Q plots, residual analysis, normality tests
• Clinical Context: Before/after comparisons, dose-response curves
• Color-coded Results: Significance levels and effect size magnitudes

📋 Educational Demonstrations

Each implementation includes realistic biomedical examples:

• Drug Efficacy Studies: Blood pressure reduction analysis
• Clinical Trials: Treatment group comparisons
• Laboratory Quality Control: Measurement validation
• Epidemiological Studies: Risk factor associations
• Biomarker Analysis: Multi-variable correlations

🧪 Testing & Validation

✅ Comprehensive Test Suite

• 2,100+ lines of thoroughly tested implementations
• All functions tested with and without plotting capabilities
• Edge case handling: Missing data, small samples, assumption violations
• Error validation: Comprehensive input checking and informative messages
• Performance testing: Power analysis with Monte Carlo simulations

🔬 Real-World Applications

• Blood Type Distribution Analysis: Goodness of fit testing
• Treatment Response Studies: Independence and McNemar's tests
• Biomarker Correlations: Multi-variable relationship analysis
• Clinical Trial Design: Power analysis for sample size planning
• Quality Control: Statistical process monitoring

📁 Files Modified/Added

• biomedical/t_tests_comprehensive.r ➕ (800+ lines)
• biomedical/chi_square_tests.r ➕ (700+ lines)
• biomedical/correlation_analysis.r ➕ (600+ lines)
• DIRECTORY.md 📝 (Updated with new biomedical tests)

🎓 Educational Value

📚 Learning Features

• Step-by-step Explanations: Clear methodology descriptions
• Clinical Context: Real biomedical research scenarios
• Statistical Guidelines: Power analysis and sample size recommendations
• Best Practices: Assumption checking and result interpretation
• Effect Size Interpretation: Practical significance guidelines

📖 Documentation

• Comprehensive Comments: Detailed function documentation
• Usage Examples: Realistic biomedical data scenarios
• Statistical Theory: Background on test assumptions and applications
• Clinical Guidelines: When to use each test type

🔬 Biomedical Research Applications

🏥 Clinical Studies

• Pre/post treatment comparisons (paired t-tests)
• Treatment group efficacy (two-sample t-tests)
• Biomarker validation (correlation analysis)
• Patient characteristic associations (chi-square tests)

🧪 Laboratory Research

• Quality control analysis (goodness of fit)
• Method comparison studies (correlation analysis)
• Diagnostic test evaluation (McNemar's test)
• Reference range validation (one-sample t-tests)

📊 Public Health

• Risk factor analysis (chi-square independence)
• Population health comparisons (t-tests)
• Survey data analysis (correlation matrices)
• Intervention effectiveness (before/after studies)

🎯 Key Advantages

💪 Robust Implementation

• No External Dependencies: Pure base R implementation
• Comprehensive Error Handling: Informative error messages and warnings
• Assumption Checking: Automated validation of statistical assumptions
• Multiple Methods: Alternative approaches for different data types

📈 Professional Quality

• Publication-Ready Plots: High-quality statistical visualizations
• Clinical Relevance: Realistic biomedical examples and interpretations
• Educational Focus: Learning-oriented with detailed explanations
• Best Practices: Following statistical guidelines and conventions

🚀 Impact on Repository

🌟 Enhanced Biomedical Section

• 3x Expansion: From 2 to 5 comprehensive biomedical statistical tests
• Professional Quality: Research-grade implementations with visualizations
• Educational Resource: Complete learning materials for biomedical statistics
• Practical Applications: Real-world clinical and research examples

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Ready for Hacktoberfest! 🎃 This comprehensive biomedical statistics suite provides essential tools for medical research, clinical trials, and biomedical data analysis with professional visualizations and educational value.

[Copilot]

Pull Request Overview

This PR adds three comprehensive biomedical statistical test implementations with advanced visualizations to enhance the repository's biomedical analysis capabilities. The additions include comprehensive t-tests, chi-square tests, and correlation analysis methods.

Key Changes:

• Added three new statistical test implementations with educational demonstrations
• Implemented professional-quality visualizations for each test type
• Included power analysis and sample size calculations

Reviewed Changes

Copilot reviewed 4 out of 5 changed files in this pull request and generated 3 comments.

File	Description
biomedical/t_tests_comprehensive.r	Implements one-sample, two-sample, paired, and Welch's t-tests with visualization and power analysis
biomedical/correlation_analysis.r	Provides Pearson, Spearman, and Kendall correlation methods with assumption checking and matrix analysis
biomedical/chi_square_tests.r	Contains goodness-of-fit, independence, and McNemar's tests with effect size measures
DIRECTORY.md	Updated to include the three new biomedical statistical test files

[siriak]

Looks good, thanks!