Add biomedical statistical tests: Wilcoxon and Mann-Whitney U tests

[Brijesh03032001]

🏥 Biomedical Statistical Tests for Non-parametric Analysis

This PR adds essential statistical tests commonly used in biomedical research and clinical studies.

📊 What's Added

• Wilcoxon Signed-Rank Test (Biomedical/wilcoxon_signed_rank_test.r) - For paired samples and one-sample tests
• Mann-Whitney U Test (Biomedical/mann_whitney_u_test.r) - For independent group comparisons
• Comprehensive Documentation (Biomedical/README.md) - Explaining importance for biomedical students

🔬 Features

• Complete implementations with robust error handling and input validation
• Biomedical examples with realistic dummy clinical data (892 lines of code)
• Clinical interpretations and statistical guidance for medical applications
• Educational focus specifically designed for biomedical students

📋 Examples Include

Wilcoxon Signed-Rank Test:

• Blood pressure before/after treatment analysis
• Pain scores with medication effectiveness
• Weight loss program evaluation
• Cholesterol levels vs normal reference values

Mann-Whitney U Test:

• Drug efficacy studies (treatment vs control)
• Biomarker analysis by gender differences
• Disease severity comparison by stage
• Age-related immune response analysis
• Glucose levels (pre-diabetic vs diabetic)

🎯 Why This Matters for Biomedical Research

Medical data often violates normal distribution assumptions due to:

• Skewed distributions (lab values, reaction times)
• Outliers that are medically significant
• Small sample sizes (pilot studies, rare diseases)
• Ordinal scales (pain scores, severity ratings)

These non-parametric tests are essential for:

• Clinical trial analysis
• Treatment effectiveness studies
• Biomarker research
• Quality of life assessments
• Diagnostic accuracy comparisons

✅ Testing & Quality

• ✅ Both scripts run successfully with all examples
• ✅ Produces correct statistical outputs with p-values and effect sizes
• ✅ Includes proper error handling and edge case management
• ✅ Comprehensive documentation with usage guidelines
• ✅ Follows R best practices and coding standards

📚 Educational Value

• Explains statistical theory in accessible terms
• Provides real-world biomedical applications
• Includes clinical interpretation guidelines
• Offers guidance on when to use each test
• Covers common pitfalls and considerations

[Copilot]

Pull Request Overview

Adds two non-parametric statistical test implementations in R with biomedical-focused examples and documentation.

• New Wilcoxon signed-rank test for paired/one-sample scenarios with custom print method
• New Mann-Whitney U (rank-sum) test for independent samples with custom print method and examples
• README explaining use-cases, interpretation, and example usage

Reviewed Changes

Copilot reviewed 3 out of 3 changed files in this pull request and generated 10 comments.

File	Description
Biomedical/wilcoxon_signed_rank_test.r	Adds Wilcoxon signed-rank test implementation and extensive runnable examples
Biomedical/mann_whitney_u_test.r	Adds Mann-Whitney U test implementation, tie-handling attempt, and runnable examples
Biomedical/README.md	Adds documentation and quick start usage for the new tests

[Copilot]

Per repository guidelines, please also update DIRECTORY.md to list these new algorithms in the appropriate section and ensure they are categorized consistently (e.g., statistics/mathematics).

Suggested change

	- [`mann_whitney_u_test.r`](mann_whitney_u_test.r) - Mann-Whitney U Test for independent samples
	- [`mann_whitney_u_test.r`](mann_whitney_u_test.r) - Mann-Whitney U Test for independent samples
	- [`kruskal_wallis_test.r`](kruskal_wallis_test.r) - Kruskal-Wallis Test for comparing more than two groups
	- [`friedman_test.r`](friedman_test.r) - Friedman Test for repeated measures across multiple groups

[siriak]

Please update DIRECTORY.md instead of adding this file

[siriak]

Please update DIRECTORY.md instead of adding this file