feat: Add biomedical statistical analysis module with Wilcoxon and Mann-Whitney tests

- Implement Wilcoxon Signed-Rank Test for paired data analysis
- Implement Mann-Whitney U Test for independent group comparisons
- Add comprehensive text-based visualization utilities
- Include 5 detailed biomedical examples with real-world scenarios
- Provide extensive documentation and theory explanations
- Support effect size calculations and statistical interpretations
- Pure Python implementation with no external dependencies

Addresses common non-parametric statistical needs in biomedical research
including clinical trials, drug studies, and diagnostic biomarker analysis.

Author: Brijesh03032001

Biomedical/README.md

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+# Biomedical Statistical Analysis Module
+
+A comprehensive Python module providing implementations of non-parametric statistical tests commonly used in biomedical research, along with visualization utilities and educational examples.
+
+## 📊 Overview
+
+This module implements two fundamental non-parametric statistical tests:
+
+- **Wilcoxon Signed-Rank Test**: For analyzing paired/dependent samples
+- **Mann-Whitney U Test**: For comparing two independent groups
+
+Both tests are essential when data doesn't meet the assumptions required for parametric tests (normality, equal variances, etc.).
+
+## 🔬 Features
+
+### Core Implementations
+- **Pure Python**: No external dependencies required for core functionality
+- **Educational Focus**: Clear, well-documented algorithms for learning
+- **Biomedical Context**: Examples and documentation tailored for biomedical research
+- **Statistical Rigor**: Proper handling of ties, effect sizes, and p-value calculations
+
+### Visualization Tools
+- Text-based visualizations (no external plotting libraries required)
+- Box plot representations
+- Paired data change visualization
+- Group comparison histograms
+- Statistical summary displays
+
+### Quality Assurance
+- Comprehensive error handling and input validation
+- Type hints for better code maintainability
+- Extensive documentation and examples
+- Educational comments explaining algorithms
+
+## 📚 Theory and Applications
+
+### Wilcoxon Signed-Rank Test
+
+**When to use:**
+- Paired or dependent samples (before/after, matched pairs)
+- Data is ordinal or continuous but not normally distributed
+- Dependent variable measured at least at ordinal level
+- Differences between pairs are not normally distributed
+
+**Examples in biomedical research:**
+- Blood pressure before and after treatment
+- Pain scores pre and post medication
+- Biomarker levels before and after intervention
+- Patient quality of life scores over time
+
+**Algorithm:**
+1. Calculate differences between paired observations
+2. Remove zero differences
+3. Rank absolute differences (handle ties by averaging)
+4. Sum ranks for positive and negative differences
+5. Test statistic W = smaller of the two sums
+6. Calculate p-value using exact tables (small n) or normal approximation (large n)
+
+### Mann-Whitney U Test
+
+**When to use:**
+- Two independent groups
+- Data is ordinal or continuous but not normally distributed
+- Independent observations
+- No assumption of equal variances required
+
+**Examples in biomedical research:**
+- Treatment vs control group outcomes
+- Disease vs healthy population comparisons
+- Different drug dosage group comparisons
+- Gender differences in biomarker levels
+
+**Algorithm:**
+1. Combine both samples and rank all observations
+2. Sum ranks for each group
+3. Calculate U statistics: U₁ = R₁ - n₁(n₁+1)/2
+4. Test statistic = min(U₁, U₂)
+5. Calculate p-value using exact tables (small n) or normal approximation (large n)
+
+## 🚀 Quick Start
+
+### Basic Usage
+
+```python
+from Biomedical import wilcoxon_signed_rank_test, mann_whitney_u_test
+from Biomedical import plot_wilcoxon_results, plot_mann_whitney_results
+
+# Wilcoxon test example: Blood pressure study
+before_treatment = [145, 142, 138, 150, 155, 148, 152, 160]
+after_treatment = [140, 138, 135, 145, 148, 142, 147, 152]
+
+w_stat, p_value, stats = wilcoxon_signed_rank_test(
+    before_treatment, 
+    after_treatment, 
+    alternative="greater"  # one-sided: treatment reduces BP
+)
+
+print(f"W statistic: {w_stat}")
+print(f"p-value: {p_value:.4f}")
+print(f"Effect size: {stats['effect_size']:.3f}")
+
+# Visualize results
+plot_wilcoxon_results(
+    before_treatment, 
+    after_treatment,
+    ("Before Treatment", "After Treatment"),
+    "Blood Pressure Reduction Study"
+)
+
+# Mann-Whitney test example: Drug efficacy study
+treatment_group = [85, 88, 90, 92, 95, 98, 100]
+control_group = [78, 80, 82, 85, 87, 89, 91]
+
+u_stat, p_value, stats = mann_whitney_u_test(
+    treatment_group, 
+    control_group,
+    alternative="greater"  # treatment > control
+)
+
+print(f"U statistic: {u_stat}")
+print(f"p-value: {p_value:.4f}")
+print(f"Median difference: {stats['median_difference']:.1f}")
+
+# Visualize results
+plot_mann_whitney_results(
+    treatment_group,
+    control_group,
+    ("Treatment", "Control"),
+    "Drug Efficacy Comparison"
+)
+```
+
+## 📖 Detailed Examples
+
+### Example 1: Clinical Trial - Pain Medication
+
+```python
+# Pre and post medication pain scores (1-10 scale)
+pain_before = [8, 7, 9, 6, 8, 7, 9, 8, 7, 6]
+pain_after = [4, 3, 5, 3, 4, 3, 5, 4, 3, 2]
+
+w_stat, p_val, stats = wilcoxon_signed_rank_test(
+    pain_before, pain_after, alternative="greater"
+)
+
+print("Pain Medication Study Results:")
+print(f"Median pain reduction: {stats['median_difference']:.1f} points")
+print(f"Statistical significance: p = {p_val:.4f}")
+
+if p_val < 0.05:
+    print("✓ Medication significantly reduces pain")
+else:
+    print("✗ No significant pain reduction detected")
+```
+
+### Example 2: Biomarker Comparison Study
+
+```python
+# Biomarker levels: patients vs healthy controls
+patients = [120, 125, 130, 135, 140, 145, 150, 155]
+healthy = [100, 105, 110, 115, 118, 120, 125, 128]
+
+u_stat, p_val, stats = mann_whitney_u_test(
+    patients, healthy, alternative="greater"
+)
+
+print("Biomarker Level Comparison:")
+print(f"Patient median: {stats['median1']:.1f}")
+print(f"Healthy median: {stats['median2']:.1f}")
+print(f"Difference: {stats['median_difference']:.1f}")
+print(f"Effect size: {stats['effect_size']:.3f}")
+
+if p_val < 0.05:
+    print("✓ Significant difference between groups")
+else:
+    print("✗ No significant difference detected")
+```
+
+## 📊 Interpretation Guidelines
+
+### P-value Interpretation
+- **p < 0.001**: Very strong evidence against null hypothesis
+- **p < 0.01**: Strong evidence against null hypothesis  
+- **p < 0.05**: Moderate evidence against null hypothesis
+- **p ≥ 0.05**: Insufficient evidence to reject null hypothesis
+
+### Effect Size Interpretation (for large samples)
+- **Small effect**: r ≈ 0.1 (explains 1% of variance)
+- **Medium effect**: r ≈ 0.3 (explains 9% of variance)
+- **Large effect**: r ≈ 0.5 (explains 25% of variance)
+
+### Assumptions and Limitations
+
+**Wilcoxon Signed-Rank Test:**
+- ✓ Pairs are independent
+- ✓ Data is at least ordinal
+- ✓ Distribution of differences is approximately symmetric
+- ✗ Cannot handle tied differences well (uses average ranks)
+
+**Mann-Whitney U Test:**
+- ✓ Observations are independent
+- ✓ Data is at least ordinal
+- ✓ No assumption of equal variances
+- ✗ Assumes similar distribution shapes for location comparison
+
+## 🔧 API Reference
+
+### `wilcoxon_signed_rank_test(sample1, sample2, alternative='two-sided')`
+
+**Parameters:**
+- `sample1`: First sample (list of numbers)
+- `sample2`: Second sample (list of numbers, same length as sample1)
+- `alternative`: 'two-sided', 'greater', or 'less'
+
+**Returns:**
+- `w_statistic`: Test statistic (float)
+- `p_value`: P-value (float)
+- `stats`: Dictionary with additional statistics
+
+### `mann_whitney_u_test(group1, group2, alternative='two-sided')`
+
+**Parameters:**
+- `group1`: First group (list of numbers)
+- `group2`: Second group (list of numbers)
+- `alternative`: 'two-sided', 'greater', or 'less'
+
+**Returns:**
+- `u_statistic`: Test statistic (float)
+- `p_value`: P-value (float)
+- `stats`: Dictionary with additional statistics
+
+## 🎯 Best Practices
+
+### Study Design Considerations
+1. **Sample Size**: Consider power analysis for adequate sample size
+2. **Data Collection**: Ensure independence of observations
+3. **Multiple Comparisons**: Apply Bonferroni correction when appropriate
+4. **Effect Size**: Always report effect sizes alongside p-values
+5. **Visualization**: Use plots to understand data distribution
+
+### Code Usage Tips
+1. Always validate your data before analysis
+2. Choose appropriate alternative hypothesis
+3. Check sample size recommendations for test validity
+4. Document your analysis assumptions
+5. Provide context for statistical significance
+
+## 🤝 Contributing
+
+This module was created as part of Hacktoberfest 2024. Contributions welcome!
+
+### Areas for Enhancement
+- [ ] Additional non-parametric tests (Kruskal-Wallis, Friedman)
+- [ ] Integration with popular plotting libraries (matplotlib, seaborn)
+- [ ] Power analysis functions
+- [ ] Bootstrap confidence intervals
+- [ ] Multiple comparison corrections
+
+### Development Guidelines
+- Follow existing code style and documentation patterns
+- Include comprehensive tests for new features
+- Maintain educational focus with clear explanations
+- Ensure compatibility with existing API
+
+## 📝 License
+
+MIT License - See LICENSE file for details.
+
+## 🔗 References
+
+1. Wilcoxon, F. (1945). Individual comparisons by ranking methods. *Biometrics Bulletin*, 1(6), 80-83.
+2. Mann, H. B., & Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. *Annals of Mathematical Statistics*, 18(1), 50-60.
+3. Hollander, M., Wolfe, D. A., & Chicken, E. (2013). *Nonparametric Statistical Methods* (3rd ed.). John Wiley & Sons.
+
+## 📧 Contact
+
+Created for Hacktoberfest 2024 - Educational implementation of biomedical statistical methods.
+
+---
+
+*Happy analyzing! 🧬📈*

Biomedical/__init__.py

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+"""
+Biomedical Statistical Analysis Module
+
+This module provides implementations of statistical tests commonly used in
+biomedical research, including non-parametric tests for comparing groups
+and analyzing paired data.
+
+Available Tests:
+- Wilcoxon Signed-Rank Test: For paired data when normality assumptions
+  are violated
+- Mann-Whitney U Test: For comparing two independent groups
+  (non-parametric alternative to t-test)
+
+Features:
+- Pure Python implementations following standard algorithms
+- Comprehensive visualizations for result interpretation
+- Educational examples with biomedical contexts
+- Detailed documentation and theory explanations
+
+Author: Contributed for Hacktoberfest
+License: MIT
+"""
+
+from .mann_whitney_test import mann_whitney_u_test
+from .statistical_visualizations import (
+    plot_independent_groups,
+    plot_mann_whitney_results,
+    plot_paired_data,
+    plot_wilcoxon_results,
+)
+from .wilcoxon_test import wilcoxon_signed_rank_test
+
+__all__ = [
+    "mann_whitney_u_test",
+    "plot_independent_groups",
+    "plot_mann_whitney_results",
+    "plot_paired_data",
+    "plot_wilcoxon_results",
+    "wilcoxon_signed_rank_test",
+]
+
+__version__ = "1.0.0"