Statistical Calculators Collection

A comprehensive collection of web-based statistical calculators designed for marketing research, data analysis, and educational purposes. All calculators are self-contained HTML files built with React and Tailwind CSS, with mathematically rigorous implementations using the jStat statistical library.

Live Site: https://paulneto.github.io/statistical-calculators/

Overview

This repository contains 18 different statistical calculators and reference guides, each designed to handle specific types of statistical analyses commonly used in marketing research, A/B testing, and data science. All calculators have been mathematically verified and include effect sizes, confidence intervals, and exact p-values.

Calculators

1. ANOVA Calculator

Location: anova/

Description: Performs both One-Way and Two-Way Analysis of Variance (ANOVA) tests to compare means across multiple groups.

Features:

• One-Way ANOVA for comparing 2+ groups
• Two-Way ANOVA for analyzing two factors and their interaction
• Interactive data entry for multiple groups
• F-statistic calculation with proper F-distribution (jStat)
• Eta-squared (η²) effect sizes - shows proportion of variance explained
• Exact p-values for all tests
• Significance testing at α = 0.05 and 0.01
• Detailed explanations and interpretation guides

Use Cases:

• Comparing marketing channel effectiveness
• Testing multiple campaign variations
• Analyzing factor interactions (e.g., channel × time of day)

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2. Chi-Square Calculator

Location: chi/

Description: Performs Chi-Square tests for categorical data analysis with two test types.

Features:

• Goodness of Fit test (comparing observed vs expected frequencies)
• Test of Independence (analyzing relationship between two categorical variables)
• Contingency table support
• Cramér's V effect size - shows strength of association (0-1 scale)
• Chi-square critical values for any degrees of freedom (jStat)
• Exact p-values for all tests
• Detailed contribution analysis per category/cell

Use Cases:

• Testing if data matches expected distributions
• Analyzing relationship between demographics and behavior
• Survey response analysis

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3. T-Test Calculator

Location: t-test/

Description: Comprehensive t-test calculator supporting three types of t-tests for comparing means.

Features:

• Independent Samples T-Test (comparing two separate groups)
• Paired Samples T-Test (before/after comparisons)
• One-Sample T-Test (comparing sample to known benchmark)
• Cohen's d effect size - shows magnitude of difference (small/medium/large)
• 95% confidence intervals for all test types
• T-critical values using proper t-distribution (jStat)
• Exact p-values for all tests
• Pre-loaded example datasets

Use Cases:

• A/B testing (email campaigns, landing pages)
• Before/after intervention comparisons
• Comparing against industry benchmarks

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4. Z-Test Significance Calculator

Location: z test sig/

Description: Pairwise significance testing for comparing proportions between two groups across multiple items.

Features:

• Bulk comparison of multiple percentages
• Multiple confidence levels (99%, 95%, 90%, 80%)
• Z-score calculation for each comparison
• Visual indicators for significant differences
• Support for different sample sizes per group

Use Cases:

• Survey response comparisons between segments
• Multi-item A/B test analysis
• Campaign performance across multiple metrics

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5. Correlation Calculator

Location: correlation/

Description: Calculates Pearson correlation coefficient to measure linear relationships between two variables.

Features:

• Pearson's r calculation
• Coefficient of determination (r²)
• Interactive scatter plot visualization
• Strength and direction interpretation
• Pre-loaded marketing example data

Use Cases:

• Analyzing relationship between video length and engagement
• Correlating ad spend with conversions
• Understanding relationships between metrics

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6. Mann-Whitney U Test Calculator

Location: mann-whitney/

Description: Non-parametric test for comparing two independent groups when data doesn't follow normal distribution.

Features:

• U-statistic calculation with tie correction
• Z-score for larger samples
• Exact p-values using normal approximation
• Median comparison between groups
• Multiple confidence levels
• Pre-loaded example datasets

Use Cases:

• Comparing session durations between user segments
• Analyzing engagement scores with outliers
• Small sample size comparisons
• Skewed distribution data

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7. Normal Distribution Dashboard

Location: normal distribution/

Description: Interactive visualization tool for exploring normal distributions and probability calculations.

Features:

• Interactive distribution visualization using D3.js
• Adjustable mean and standard deviation
• Probability calculations
• Visual area-under-curve highlighting
• Significance testing cheat sheet included

Use Cases:

• Understanding sampling distributions
• Probability calculations
• Educational demonstrations
• Z-score visualization

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8. Power Analysis Calculator

Location: power analysis/

Description: Calculate required sample sizes and statistical power for designing experiments.

Features:

• Sample size calculation
• Power analysis
• Effect size estimation
• Multiple test type support
• Visual power curves

Use Cases:

• A/B test planning
• Determining required sample sizes
• Understanding detection capability
• Budget planning for research studies

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9. Regression Calculator

Location: regression/

Description: Linear regression analysis with correlation and prediction capabilities.

Features:

• Simple linear regression
• Correlation analysis
• Prediction functionality
• Visual scatter plot with regression line
• R-squared and coefficients

Use Cases:

• Sales forecasting
• Predicting outcomes from variables
• Understanding variable relationships
• Trend analysis

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10. Proportion Significance Calculator

Location: proportion sig/

Description: Z-test for proportions to determine if differences in percentages are statistically significant.

Features:

• Multiple proportion comparisons
• Label and value pairing
• Confidence level selection
• Z-statistic calculation
• Marketing-focused examples

Use Cases:

• Email campaign click-through rate comparison
• Conversion rate testing
• Survey response analysis
• Engagement metric comparisons

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11. Bayesian Statistics Interactive Demo ✨ NEW

Location: bayesian/

Description: Comprehensive interactive learning tool for Bayesian inference using Beta-Binomial conjugate priors.

Features:

• 5 Interactive Demos:
  1. Basic Bayesian Inference - proportion estimation
  2. Email Campaign - conversion rate analysis
  3. A/B Testing - Bayesian comparison of treatments
  4. Customer Lifetime Value - simplified Bayesian updating
  5. Real-time Updating - sequential data incorporation
• Monte Carlo sampling for P(B > A) calculations (10,000 samples)
• 95% credible intervals using exact Beta quantiles
• Educational content on conjugate priors
• Comparison between Bayesian and frequentist approaches
• Marketing-focused examples throughout

Use Cases:

• Learning Bayesian statistics fundamentals
• A/B testing with small sample sizes
• Sequential decision-making
• Incorporating prior knowledge
• Understanding probability of superiority

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12. Stats Cheatsheet 📚

Location: cheatsheet.html

Description: Professional guide to all statistical tests with accessible language for marketing research and data analysis.

Features:

• Quick reference for 8 major statistical tests
• "What is it?" - Plain English explanations
• "When to use it" - Decision guides
• Real marketing examples for each test
• How to interpret - Results in business context
• Watch out for - Common pitfalls
• Sticky navigation for easy browsing
• Visual quick reference table

Covers:

• T-Test, ANOVA, Chi-Square, Correlation, Regression, Mann-Whitney, Proportions, Bayesian

Use Cases:

• Exam preparation
• Quick test selection reference
• Learning statistical concepts
• Understanding when to use each test

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13. Python Cheatsheet 🐍 NEW

Location: python_cheatsheet.html

Description: Copy-paste ready Python code examples for all statistical tests with complete imports and marketing-focused examples.

Features:

• 8 complete Python examples with all imports
• Copy-to-clipboard functionality for every code block
• Syntax highlighting using Prism.js
• Real marketing research examples (email campaigns, A/B tests, customer segmentation)
• Uses standard libraries: numpy, scipy, pandas, statsmodels
• Detailed comments throughout code
• Self-contained, ready-to-run examples

Covers:

• T-Test, ANOVA, Chi-Square, Correlation, Linear Regression, Mann-Whitney, Proportions, Logistic Regression

Use Cases:

• Quick Python reference
• Learning statistical programming
• Copy-paste code for analysis
• Understanding Python statistical libraries

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14. Multiple Regression Calculator ✨ NEW

Location: multiple-regression/

Description: Predict outcomes using multiple predictor variables with comprehensive coefficient analysis and multicollinearity diagnostics.

Features:

• Matrix algebra implementation (β = (X'X)⁻¹X'y)
• Multiple predictor variables support
• Full coefficient table with:
  • Coefficients and standard errors
  • t-statistics and p-values
  • Significance indicators
• VIF (Variance Inflation Factor) for multicollinearity detection
• R-squared and Adjusted R-squared
• F-statistic for overall model significance
• Regression equation display
• Pre-loaded marketing example (ad spend analysis)

Use Cases:

• Sales forecasting with multiple factors
• Marketing mix modeling
• Understanding driver contribution
• Multivariate prediction models

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15. Post-Hoc Tests Calculator ✨ NEW

Location: posthoc-tests/

Description: Pairwise comparison tests for identifying specific group differences after significant ANOVA results.

Features:

• Tukey HSD (Honestly Significant Difference) test
• Bonferroni correction for multiple comparisons
• Complete pairwise comparison table with:
  • Mean differences
  • Test statistics (q or t)
  • P-values (adjusted for Bonferroni)
  • Significance indicators
• Group summary statistics
• MSE and degrees of freedom calculations
• Pre-loaded marketing channel example

Use Cases:

• Follow-up analysis after ANOVA
• Identifying which specific groups differ
• Marketing channel performance comparisons
• Campaign variation analysis

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16. Logistic Regression Calculator ✨ NEW

Location: logistic-regression/

Description: Binary outcome prediction with odds ratios, confusion matrix, and comprehensive classification metrics.

Features:

• Newton-Raphson iterative method for maximum likelihood estimation
• Binary outcome modeling (0/1, Yes/No)
• Coefficient table with:
  • Coefficients and standard errors
  • z-statistics and p-values
  • Odds ratios with interpretations
• Confusion matrix (True Positives, False Positives, etc.)
• Classification metrics:
  • Accuracy, Precision, Recall, F1 Score
• McFadden's pseudo R-squared
• Pre-loaded customer conversion example

Use Cases:

• Customer conversion prediction
• Churn modeling
• Click-through rate prediction
• Binary classification problems

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17. Sample Size Calculator ✨ NEW

Location: sample-size/

Description: Determine required sample sizes for adequate statistical power across multiple test types.

Features:

• 4 test types supported:
  1. T-Test (two-sample means)
  2. Proportions (two-sample proportions)
  3. Correlation (Pearson's r)
  4. ANOVA (multiple groups)
• Effect size guidance (small/medium/large for each test)
• Power level specification (default: 0.80)
• Significance level specification (default: 0.05)
• Power curve visualization
• Detailed sample size recommendations

Use Cases:

• A/B test planning
• Experiment design
• Budget planning for research
• Ensuring adequate statistical power

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18. Cluster Analysis Calculator ✨ NEW

Location: cluster-analysis/

Description: K-means clustering for customer segmentation with elbow plot and comprehensive cluster analysis.

Features:

• K-means algorithm implementation (Lloyd's method)
• Multiple cluster support (2-10 clusters)
• Multi-feature analysis
• Cluster assignment table with:
  • Customer IDs
  • Cluster assignments
  • Feature values
• WCSS (Within-Cluster Sum of Squares) analysis
• Elbow plot data for optimal k selection
• Cluster centroids display
• Marketing interpretation guide
• Pre-loaded customer data example

Use Cases:

• Customer segmentation
• Market segmentation
• Behavioral grouping
• Targeting strategy development

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Technology Stack

All calculators are built with:

• HTML5 - Structure and content
• React 18 - UI components and state management (loaded via CDN)
• Tailwind CSS 2 - Styling and responsive design (loaded via CDN)
• jStat - JavaScript statistical library for distributions (F, t, Chi-square, Beta, Normal)
• D3.js - Data visualization (where applicable)
• Vanilla JavaScript - Core calculations and logic

Features

• No Installation Required: All calculators run directly in the browser
• Mathematically Rigorous: All critical values calculated using proper statistical distributions (jStat)
• Effect Sizes Included: Cohen's d, Eta-squared, Cramér's V - understand practical significance
• Confidence Intervals: 95% CIs for point estimates (T-Test, Bayesian demos)
• Exact P-Values: Continuous probability measures, not just significant/not significant
• Responsive Design: Works on desktop, tablet, and mobile devices
• Self-Contained: Each calculator is a single HTML file (requires CDN access)
• Educational: Includes interpretation guides and explanations
• Example Data: Pre-loaded datasets for testing and learning
• Copy & Paste Friendly: Easy data entry from spreadsheets
• Student-Friendly: Cheatsheet provides accessible guide for test selection

Usage

1. Open any HTML file in a modern web browser (Chrome, Firefox, Safari, Edge)
2. Enter your data or load example datasets
3. Click calculate to see results
4. Review interpretations and statistical significance

Browser Compatibility

• Chrome 90+
• Firefox 88+
• Safari 14+
• Edge 90+

Requires internet connection for CDN-loaded libraries (React, Tailwind CSS, jStat, D3.js).

File Organization

calculators/
├── index.html                          # Main dashboard
├── cheatsheet.html                     # Stats reference guide
├── python_cheatsheet.html              # Python code examples
├── anova/
│   ├── index.html
│   └── anova-calculator.html
├── chi/
│   ├── index.html
│   └── chi-square.html
├── t-test/
│   ├── index.html
│   └── ttest-calculator.html
├── z test sig/
│   ├── index.html
│   └── [additional variations]
├── correlation/
│   └── correlation-calculator.html
├── mann-whitney/
│   └── mann-whitney-html.html
├── normal distribution/
│   ├── dashboard-simulator v2.1.html
│   └── Significance_Testing_Cheat_Sheet.html
├── power analysis/
│   └── power-analysis-calculator.html
├── regression/
│   └── simple-linear-regression.html
├── proportion sig/
│   └── z proportion-calculator %.html
├── bayesian/
│   └── bayesian_interactive.html
├── multiple-regression/               # NEW
│   └── index.html
├── posthoc-tests/                     # NEW
│   └── index.html
├── logistic-regression/               # NEW
│   └── index.html
├── sample-size/                       # NEW
│   └── index.html
└── cluster-analysis/                  # NEW
    └── index.html

Common Statistical Terms

p-value: Probability that results occurred by chance. Lower values indicate stronger evidence against the null hypothesis.

Significance Level (α): Threshold for determining statistical significance (commonly 0.05 or 0.01).

Confidence Level: The probability that the true value lies within the confidence interval (commonly 95% or 99%).

Effect Size: The magnitude of difference between groups.

Statistical Power: The probability of detecting an effect when it exists.

Best Practices

1. Check Assumptions: Each test has specific assumptions (normality, sample size, etc.)
2. Consider Effect Size: Statistical significance doesn't always mean practical importance
3. Multiple Comparisons: Be cautious when running many tests simultaneously
4. Sample Size: Larger samples provide more reliable results
5. Data Quality: Ensure data is clean and properly formatted

Future Enhancements

Potential improvements for future versions:

• Offline capability with bundled libraries
• Data export functionality (CSV, JSON)
• Advanced visualizations
• Multi-language support
• Batch processing capabilities
• Integration with APIs

Contributing

This is a personal collection of calculators. If you find issues or have suggestions, please create an issue or submit a pull request.

License

This project is licensed under the MIT License - see the LICENSE file for details.

Free to use and modify for personal and commercial purposes.

Author

Paul - Statistical Calculators Collection

Acknowledgments

Built with modern web technologies to make statistical analysis accessible and user-friendly for marketing researchers, data analysts, and students.

Mathematical Verification: All calculators have been reviewed for mathematical accuracy. See internal documentation for detailed verification.

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Last Updated: January 2025