Statistical Functions - Stats Weapons

A comprehensive Python utility library for statistical analysis, hypothesis testing, outlier detection, and data exploration.

📋 Overview

Stats Weapons is a powerful statistical analysis toolkit designed to simplify complex statistical computations and hypothesis testing. It provides a unified interface for data loading, descriptive statistics, hypothesis testing (parametric and non-parametric), outlier detection, correlation analysis, and probability distribution fitting.

Author: Renery Carvalho
Last Updated: May 2, 2026
Email: reneryroniery@gmail.com

🎯 Features

Data Loading & Transformation

• extract_data() - Load data from multiple formats:
  • Spreadsheets: .csv, .xls, .xlsx, .xlsm
  • Databases: .sql, .sqlite, .sqlite3, .db
  • Other formats: .json, .parquet, .feather, .pkl, .txt, .xml, .h5, .hdf5
  • Support for SQL Server via pyodbc with authentication options
  • Automatic data type inference and basic validation

Descriptive Analysis

• basic_statistics() - Comprehensive dataset overview:
  • Statistical summaries (mean, median, std, quantiles, etc.)
  • Data type analysis
  • Missing value detection
  • Correlation matrices
  • Univariate and multivariate visualizations
  • Distribution insights

Normality Testing

• normality_tests() - Multiple normality test methodologies:
  • Shapiro-Wilk test
  • Kolmogorov-Smirnov test
  • Anderson-Darling test
  • D'Agostino-Pearson test
  • Jarque-Bera test
  • Lilliefors test
  • Visual Q-Q plots

Correlation & Association

• correlation_analysis() - Relationship detection:
  • Pearson correlation (linear relationships)
  • Spearman correlation (monotonic relationships)
  • Kendall correlation (non-parametric)
  • Visualization and p-value reporting

Outlier Detection

• outliers_detection() - Multiple outlier detection methods:
  • Z-score method
  • IQR (Interquartile Range) method
  • Isolation Forest
  • Local Outlier Factor (LOF)
  • One-Class SVM
  • DBSCAN clustering
  • Visual identification with boxplots

Probability Distributions

• probability_distributions() - Distribution fitting and analysis:
  • Test data against multiple standard distributions
  • Goodness-of-fit metrics
  • Parameter estimation
  • Visual distribution comparisons

Hypothesis Testing - Single Population

• test_population_mean() - Test population mean (t-test or z-test)
• test_population_proportion() - Test population proportion
• test_population_variance() - Test population variance (chi-square test)

Hypothesis Testing - Two Populations

• test_2independent_mean() - Compare means of two independent samples
• test_2paired_mean() - Compare means of paired samples (paired t-test)
• test_2independent_proportion() - Compare proportions of two groups
• test_2population_variance() - Compare variances of two populations (F-test)

Hypothesis Testing - Multiple Populations

• test_1way_anova() - One-way ANOVA for comparing multiple groups
  • Includes post-hoc Tukey HSD testing

Non-Parametric Tests

• independent_mannwhitneyu() - Mann-Whitney U test for independent samples
• paired_wilcoxon() - Wilcoxon signed-rank test for paired samples
• independent_chisquare_test() - Chi-square test of independence
• independent_exact_fisher() - Fisher's exact test
• dependent_mcnemar() - McNemar's test for paired categorical data

📦 Installation

Prerequisites

• Python 3.8 or higher
• pip package manager

Setup

1. Clone or download the project files

2. Navigate to the project directory:

   cd statistical_functions

3. Install dependencies:

   pip install -r requirements.txt

📚 Dependencies

Core libraries:

• pandas (3.0.3) - Data manipulation and analysis
• numpy (2.4.6) - Numerical computing
• scipy (1.17.1) - Scientific computing and statistical tests
• scikit-learn (1.9.0) - Machine learning and outlier detection
• statsmodels (0.14.6) - Advanced statistical analysis
• matplotlib (3.10.9) - Data visualization
• seaborn (0.13.2) - Statistical data visualization
• pyodbc (5.3.0) - SQL Server connectivity

🚀 Quick Start

Basic Usage

from stats_weapons import extract_data, basic_statistics, normality_tests

# Load data from CSV
df = extract_data('data.csv')

# Get comprehensive statistics
stats_summary = basic_statistics(df)

# Test for normality
normality_results = normality_tests(df, methodology='all')

Data Loading Examples

# CSV file
df = extract_data('data.csv')

# Excel file
df = extract_data('data.xlsx', sheet_name='Sheet1')

# SQLite database
df = extract_data('database.db', table_name='my_table')

# SQL Server
df = extract_data(
    'query.sql',
    server='localhost',
    database='mydb',
    table_name='my_table',
    username='user',
    password='password'
)

Hypothesis Testing Examples

# Test if population mean equals 100
results = test_population_mean(sample_data, population_mean=100)

# Compare two independent samples
results = test_2independent_mean(sample1, sample2)

# One-way ANOVA
results = test_1way_anova([group1, group2, group3])

# Mann-Whitney U test (non-parametric)
results = independent_mannwhitneyu(sample1, sample2)

Outlier Detection Examples

# Detect outliers using Z-score
outliers = outliers_detection(df, methodology='z-score')

# Using Isolation Forest
outliers = outliers_detection(df, methodology='isolation_forest')

# Using Local Outlier Factor
outliers = outliers_detection(df, methodology='lof')

📁 Project Structure

statistical_functions/
├── stats_weapons.py       # Main statistical analysis module
├── requirements.txt       # Python package dependencies
├── README.md             # This file
├── carbon1.png           # Documentation/reference image
├── carbon2.png           # Documentation/reference image
└── sts/                  # Supplementary materials directory

🔍 Key Functions Reference

Function	Purpose	Parameters
extract_data()	Load data from multiple formats	file_path, **kwargs
basic_statistics()	Comprehensive descriptive analysis	df
normality_tests()	Test for normal distribution	df, methodology, alpha
correlation_analysis()	Analyze relationships between variables	df, target, methodology
outliers_detection()	Identify outliers in data	df, methodology
probability_distributions()	Fit and test probability distributions	data
test_population_mean()	Single population mean test	sample_data, population_mean, population_std, alpha
test_2independent_mean()	Two independent samples mean test	sample1, sample2, pop_std1, pop_std2, alpha
test_1way_anova()	ANOVA for multiple groups	samples, alpha
independent_mannwhitneyu()	Non-parametric rank test	sample1, sample2, alpha
independent_chisquare_test()	Chi-square independence test	contingency_table, alpha

📊 Output Format

Most functions return a comprehensive dictionary containing:

• Test statistics and p-values
• Confidence intervals (where applicable)
• Effect sizes and assumptions checks
• Visual plots (PNG files or matplotlib figures)
• Interpretation and conclusions

⚙️ Important Notes

1. Automatic Column Dropping: The extract_data() function automatically drops the first column of loaded data. This is intentional behavior for handling index columns.

2. SQL Server Authentication: For SQL Server connections, you can use either:

   • Windows authentication (Trusted_Connection=yes)
   • Username/password authentication

3. Statistical Significance: All hypothesis tests use alpha=0.05 by default. Adjust this parameter based on your requirements.

4. Two-tailed vs One-tailed: Most tests support alternative parameter with options:

   • 'two-sided' (default)
   • 'less'
   • 'greater'

🛠️ Data Types Supported

• Numeric types: int, float, np.int64, np.float64
• String types: Categorical data for contingency tables
• Pandas objects: Series, DataFrame
• Array-like: list, np.ndarray

📝 Usage Tips

1. Data Preparation: Ensure your data is clean and properly formatted before analysis
2. Missing Values: Handle missing values before statistical testing
3. Assumptions: Always verify statistical test assumptions before interpreting results
4. Visualization: Most functions include visualization outputs for better interpretation
5. Effect Sizes: Pay attention to effect sizes, not just p-values

🐛 Error Handling

The module includes comprehensive error handling for:

• Missing files
• Unsupported file formats
• Invalid database connections
• Malformed input data
• Missing required parameters

📞 Support

For issues, questions, or contributions:

• Email: reneryroniery@gmail.com
• GitHub: Check project repository for updates

📄 License

Developed and maintained by Renery Carvalho

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Version: 1.0.0
Last Updated: May 2, 2026