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<!DOCTYPE html>
<html lang="en">
<head>
<title>Algorithmic Fairness in R: fairml & aif360 for Bias Auditing</title>
<meta charset="utf-8">
<meta name="Description" content="Audit machine learning models for fairness using R. Learn disparate impact, calibration, and practical bias auditing with fairml and aif360.">
<meta name="Keywords" content="algorithmic fairness R, fairml, aif360 R, bias auditing, disparate impact, model fairness, fairness metrics R">
<meta name="Distribution" content="Global">
<meta name="Author" content="Selva Prabhakaran">
<meta name="Robots" content="index, follow">
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<link rel="canonical" href="https://r-statistics.co/Algorithmic-Fairness-in-R.html">
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<div id="sidebar-nav"><div class="continue-chip" data-continue-chip><span class="chip-label">Continue reading</span><a href="#" data-continue-link></a></div><div class="sidebar-tabs" role="tablist"><button class="sidebar-tab active" data-tab="posts" type="button" role="tab" onclick="var n=this.dataset.tab;document.querySelectorAll('.sidebar-tab').forEach(function(x){x.classList.toggle('active',x.dataset.tab===n)});document.querySelectorAll('.sidebar-panel').forEach(function(p){p.classList.toggle('active',p.dataset.panel===n)});try{localStorage.setItem('rstat_sidebar_tab',n)}catch(e){}">Posts</button><button class="sidebar-tab" data-tab="tools" type="button" role="tab" onclick="var n=this.dataset.tab;document.querySelectorAll('.sidebar-tab').forEach(function(x){x.classList.toggle('active',x.dataset.tab===n)});document.querySelectorAll('.sidebar-panel').forEach(function(p){p.classList.toggle('active',p.dataset.panel===n)});try{localStorage.setItem('rstat_sidebar_tab',n)}catch(e){}">Tools</button></div><div class="sidebar-panel active" data-panel="posts"><ul class="sidebar-menu list-unstyled"><li class="sidebar-section expanded"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span> Learn R<span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec0sub1" data-collapsed="false"><span class="subsec-chevron">▼</span> Getting Started</li><li data-subkey="sec0sub1"><a href="/Is-R-Worth-Learning-in-2026.html"><span class="progress-dot"></span>Is R Worth Learning?</a></li><li data-subkey="sec0sub1"><a href="/Install-R-and-RStudio-2026.html"><span class="progress-dot"></span>Install R & RStudio</a></li><li data-subkey="sec0sub1"><a href="/RStudio-IDE-Tour.html"><span class="progress-dot"></span>RStudio IDE Tour</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec0sub2" data-collapsed="false"><span class="subsec-chevron">▼</span> R Fundamentals</li><li data-subkey="sec0sub2"><a href="/R-Syntax-101.html"><span class="progress-dot"></span>R Syntax 101</a></li><li data-subkey="sec0sub2"><a href="/R-Data-Types.html"><span class="progress-dot"></span>R Data Types</a></li><li data-subkey="sec0sub2"><a href="/R-Vectors.html"><span class="progress-dot"></span>R Vectors</a></li><li data-subkey="sec0sub2"><a href="/R-Matrices.html"><span class="progress-dot"></span>R Matrices</a></li><li data-subkey="sec0sub2"><a href="/R-Factors.html"><span class="progress-dot"></span>R Factors</a></li><li data-subkey="sec0sub2"><a href="/R-Data-Frames.html"><span class="progress-dot"></span>R Data Frames</a></li><li data-subkey="sec0sub2"><a href="/R-Lists.html"><span class="progress-dot"></span>R Lists</a></li><li data-subkey="sec0sub2"><a href="/R-Control-Flow.html"><span class="progress-dot"></span>R Control Flow</a></li><li data-subkey="sec0sub2"><a href="/R-Special-Values.html"><span class="progress-dot"></span>R Special Values</a></li><li data-subkey="sec0sub2"><a href="/R-Type-Coercion.html"><span class="progress-dot"></span>R Type Coercion</a></li><li data-subkey="sec0sub2"><a href="/R-Functions.html"><span class="progress-dot"></span>Writing R Functions</a></li><li data-subkey="sec0sub2"><a href="/R-Beginner-Exercises-quiz.html"><span class="progress-dot"></span>R Fundamentals Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec0sub3" data-collapsed="false"><span class="subsec-chevron">▼</span> Working Effectively</li><li data-subkey="sec0sub3"><a href="/R-Subsetting.html"><span class="progress-dot"></span>R Subsetting</a></li><li data-subkey="sec0sub3"><a href="/Getting-Help-in-R.html"><span class="progress-dot"></span>Getting Help in R</a></li><li data-subkey="sec0sub3"><a href="/R-Project-Structure.html"><span class="progress-dot"></span>R Project Structure</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec0sub4" data-collapsed="false"><span class="subsec-chevron">▼</span> R Career & Resources</li><li data-subkey="sec0sub4"><a href="/R-vs-Python.html"><span class="progress-dot"></span>R vs Python</a></li><li data-subkey="sec0sub4"><a href="/How-to-Learn-R.html"><span class="progress-dot"></span>How to Learn R</a></li><li data-subkey="sec0sub4"><a href="/R-for-Excel-Users.html"><span class="progress-dot"></span>R for Excel Users</a></li><li data-subkey="sec0sub4"><a href="/R-Interview-Questions.html"><span class="progress-dot"></span>R Interview Questions</a></li><li data-subkey="sec0sub4"><a href="/R-Interview-Questions-quiz.html"><span class="progress-dot"></span>R Interview Readiness Quiz</a></li><li data-subkey="sec0sub4"><a href="/R-Cheat-Sheet.html"><span class="progress-dot"></span>R Cheat Sheet</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec0sub5" data-collapsed="false"><span class="subsec-chevron">▼</span> Professional R</li><li data-subkey="sec0sub5"><a href="/Data-Ethics-in-R.html"><span class="progress-dot"></span>Data Ethics</a></li><li data-subkey="sec0sub5"><a href="/Bias-in-Data-and-Models.html"><span class="progress-dot"></span>Bias in Data & Models</a></li><li data-subkey="sec0sub5"><a href="/Reproducibility-Crisis.html"><span class="progress-dot"></span>Reproducibility</a></li><li data-subkey="sec0sub5"><a href="/Data-Privacy-in-R.html"><span class="progress-dot"></span>Data Privacy</a></li><li data-subkey="sec0sub5"><a href="/Communicating-Uncertainty.html"><span class="progress-dot"></span>Communicating Uncertainty</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span> Data Wrangling<span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec1sub1" data-collapsed="false"><span class="subsec-chevron">▼</span> Import & Setup</li><li data-subkey="sec1sub1"><a href="/Importing-Data-in-R.html"><span class="progress-dot"></span>Importing Data</a></li><li data-subkey="sec1sub1"><a href="/R-Pipe-Operator.html"><span class="progress-dot"></span>Pipe Operator</a></li><li data-subkey="sec1sub1"><a href="/Tidy-Data-in-R.html"><span class="progress-dot"></span>Tidy Data</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec1sub2" data-collapsed="false"><span class="subsec-chevron">▼</span> dplyr Essentials</li><li data-subkey="sec1sub2"><a href="/dplyr-filter-select.html"><span class="progress-dot"></span>dplyr filter & select</a></li><li data-subkey="sec1sub2"><a href="/dplyr-mutate-rename.html"><span class="progress-dot"></span>dplyr mutate & rename</a></li><li data-subkey="sec1sub2"><a href="/dplyr-group-by-summarise.html"><span class="progress-dot"></span>dplyr group_by & summarise</a></li><li data-subkey="sec1sub2"><a href="/dplyr-arrange-slice.html"><span class="progress-dot"></span>dplyr arrange & slice</a></li><li data-subkey="sec1sub2"><a href="/dplyr-across.html"><span class="progress-dot"></span>dplyr across()</a></li><li data-subkey="sec1sub2"><a href="/dplyr-case-when.html"><span class="progress-dot"></span>dplyr case_when()</a></li><li data-subkey="sec1sub2"><a href="/dplyr-Exercises-in-R-quiz.html"><span class="progress-dot"></span>dplyr Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec1sub3" data-collapsed="false"><span class="subsec-chevron">▼</span> Join & Reshape</li><li data-subkey="sec1sub3"><a href="/R-Joins.html"><span class="progress-dot"></span>R Joins</a></li><li data-subkey="sec1sub3"><a href="/pivot_longer-pivot_wider-Reshape-Data-in-R.html"><span class="progress-dot"></span>pivot_longer & pivot_wider</a></li><li data-subkey="sec1sub3"><a href="/tidyr-separate-unite-Split-Combine-Columns-in-R.html"><span class="progress-dot"></span>separate() & unite()</a></li><li data-subkey="sec1sub3"><a href="/tidyr-Exercises-in-R-quiz.html"><span class="progress-dot"></span>tidyr Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec1sub4" data-collapsed="false"><span class="subsec-chevron">▼</span> Clean & Quality</li><li data-subkey="sec1sub4"><a href="/Missing-Values-in-R-Detect-Count-Remove-Impute-NA.html"><span class="progress-dot"></span>Missing Values (NA)</a></li><li data-subkey="sec1sub4"><a href="/Data-Quality-Checking-in-R.html"><span class="progress-dot"></span>Data Quality Checking</a></li><li data-subkey="sec1sub4"><a href="/janitor-Package-in-R.html"><span class="progress-dot"></span>janitor Package</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec1sub5" data-collapsed="false"><span class="subsec-chevron">▼</span> Strings & Dates</li><li data-subkey="sec1sub5"><a href="/stringr-in-R.html"><span class="progress-dot"></span>stringr</a></li><li data-subkey="sec1sub5"><a href="/R-Regex-stringr-Pattern-Matching.html"><span class="progress-dot"></span>Regex Patterns</a></li><li data-subkey="sec1sub5"><a href="/lubridate-in-R.html"><span class="progress-dot"></span>lubridate</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec1sub6" data-collapsed="false"><span class="subsec-chevron">▼</span> Scale & Connect</li><li data-subkey="sec1sub6"><a href="/DBI-in-R.html"><span class="progress-dot"></span>DBI & Databases</a></li><li data-subkey="sec1sub6"><a href="/DuckDB-in-R.html"><span class="progress-dot"></span>DuckDB & duckplyr</a></li><li data-subkey="sec1sub6"><a href="/Web-Scraping-in-R-with-rvest.html"><span class="progress-dot"></span>Web Scraping (rvest)</a></li><li data-subkey="sec1sub6"><a href="/REST-APIs-in-R-with-httr2.html"><span class="progress-dot"></span>REST APIs (httr2)</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span> Visualization<span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub1" data-collapsed="false"><span class="subsec-chevron">▼</span> ggplot2 Foundations</li><li data-subkey="sec2sub1"><a href="/ggplot2-Grammar-of-Graphics.html"><span class="progress-dot"></span>Grammar of Graphics</a></li><li data-subkey="sec2sub1"><a href="/ggplot2-Getting-Started.html"><span class="progress-dot"></span>ggplot2 Getting Started</a></li><li data-subkey="sec2sub1"><a href="/ggplot2-Aesthetics-aes-Map-Data.html"><span class="progress-dot"></span>ggplot2 Aesthetics (aes)</a></li><li data-subkey="sec2sub1"><a href="/ggplot2-Colours.html"><span class="progress-dot"></span>ggplot2 Colours</a></li><li data-subkey="sec2sub1"><a href="/ggplot2-Scales.html"><span class="progress-dot"></span>ggplot2 Scales</a></li><li data-subkey="sec2sub1"><a href="/ggplot2-Themes-in-R.html"><span class="progress-dot"></span>ggplot2 Themes</a></li><li data-subkey="sec2sub1"><a href="/ggplot2-Labels-and-Annotations.html"><span class="progress-dot"></span>Labels & Annotations</a></li><li data-subkey="sec2sub1"><a href="/ggplot2-Facets.html"><span class="progress-dot"></span>ggplot2 Facets</a></li><li data-subkey="sec2sub1"><a href="/ggplot2-Exercises-in-R-quiz.html"><span class="progress-dot"></span>ggplot2 Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub2" data-collapsed="false"><span class="subsec-chevron">▼</span> Core Charts</li><li data-subkey="sec2sub2"><a href="/ggplot2-Scatter-Plots.html"><span class="progress-dot"></span>Scatter Plots</a></li><li data-subkey="sec2sub2"><a href="/ggplot2-Line-Charts.html"><span class="progress-dot"></span>Line Charts</a></li><li data-subkey="sec2sub2"><a href="/ggplot2-Bar-Charts.html"><span class="progress-dot"></span>Bar Charts</a></li><li data-subkey="sec2sub2"><a href="/ggplot2-Distribution-Charts.html"><span class="progress-dot"></span>Distribution Charts</a></li><li data-subkey="sec2sub2"><a href="/Error-Bars-in-R.html"><span class="progress-dot"></span>Error Bars</a></li><li data-subkey="sec2sub2"><a href="/geom_smooth-in-R.html"><span class="progress-dot"></span>geom_smooth()</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub3" data-collapsed="false"><span class="subsec-chevron">▼</span> Distributions & Groups</li><li data-subkey="sec2sub3"><a href="/Violin-Plot-in-R.html"><span class="progress-dot"></span>Violin Plot</a></li><li data-subkey="sec2sub3"><a href="/Ridgeline-Plot-in-R.html"><span class="progress-dot"></span>Ridgeline Plot</a></li><li data-subkey="sec2sub3"><a href="/Lollipop-Chart-in-R.html"><span class="progress-dot"></span>Lollipop Chart</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub4" data-collapsed="false"><span class="subsec-chevron">▼</span> Relationships</li><li data-subkey="sec2sub4"><a href="/Bubble-Chart-in-R.html"><span class="progress-dot"></span>Bubble Chart</a></li><li data-subkey="sec2sub4"><a href="/Heatmap-in-R.html"><span class="progress-dot"></span>Heatmap in R</a></li><li data-subkey="sec2sub4"><a href="/Correlation-Matrix-Plot-in-R.html"><span class="progress-dot"></span>Correlation Matrix</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub5" data-collapsed="false"><span class="subsec-chevron">▼</span> Advanced Charts</li><li data-subkey="sec2sub5"><a href="/Pie-Donut-Chart-in-R.html"><span class="progress-dot"></span>Pie & Donut Chart</a></li><li data-subkey="sec2sub5"><a href="/Treemap-in-R.html"><span class="progress-dot"></span>Treemap</a></li><li data-subkey="sec2sub5"><a href="/Waffle-Chart-in-R.html"><span class="progress-dot"></span>Waffle Chart</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub6" data-collapsed="false"><span class="subsec-chevron">▼</span> Exploratory Analysis</li><li data-subkey="sec2sub6"><a href="/Exploratory-Data-Analysis-in-R.html"><span class="progress-dot"></span>EDA (7-Step Framework)</a></li><li data-subkey="sec2sub6"><a href="/Univariate-EDA-in-R.html"><span class="progress-dot"></span>Univariate EDA</a></li><li data-subkey="sec2sub6"><a href="/Bivariate-EDA-in-R.html"><span class="progress-dot"></span>Bivariate EDA</a></li><li data-subkey="sec2sub6"><a href="/Descriptive-Statistics-in-R.html"><span class="progress-dot"></span>Descriptive Statistics</a></li><li data-subkey="sec2sub6"><a href="/Correlation-Analysis-in-R.html"><span class="progress-dot"></span>Correlation Analysis</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub7" data-collapsed="false"><span class="subsec-chevron">▼</span> Interactive & Maps</li><li data-subkey="sec2sub7"><a href="/Combining-ggplot2-with-plotly.html"><span class="progress-dot"></span>ggplot2 + plotly Interactive</a></li><li data-subkey="sec2sub7"><a href="/Interactive-Maps-in-R-with-leaflet.html"><span class="progress-dot"></span>Leaflet Interactive Maps</a></li><li data-subkey="sec2sub7"><a href="/Spatial-Data-in-R-with-sf.html"><span class="progress-dot"></span>Spatial Data (sf)</a></li><li data-subkey="sec2sub7"><a href="/Choropleth-Maps-in-R.html"><span class="progress-dot"></span>Choropleth Maps (sf)</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub8" data-collapsed="false"><span class="subsec-chevron">▼</span> Customization & Reference</li><li data-subkey="sec2sub8"><a href="/ggplot2-Legends-in-R.html"><span class="progress-dot"></span>ggplot2 Legends</a></li><li data-subkey="sec2sub8"><a href="/ggplot2-Secondary-Axis.html"><span class="progress-dot"></span>Secondary Axis</a></li><li data-subkey="sec2sub8"><a href="/ggplot2-Log-Scale.html"><span class="progress-dot"></span>Log Scale</a></li><li data-subkey="sec2sub8"><a href="/patchwork-Package.html"><span class="progress-dot"></span>patchwork (Combine Plots)</a></li><li data-subkey="sec2sub8"><a href="/Publication-Quality-Figures-in-R.html"><span class="progress-dot"></span>Publication-Ready Figures</a></li><li data-subkey="sec2sub8"><a href="/ggplot2-cheatsheet.html"><span class="progress-dot"></span>ggplot2 Quickref</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span> Statistics<span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub1" data-collapsed="false"><span class="subsec-chevron">▼</span> EDA & Data Quality</li><li data-subkey="sec3sub1"><a href="/Automated-EDA-in-R.html"><span class="progress-dot"></span>Automated EDA</a></li><li data-subkey="sec3sub1"><a href="/Missing-Data-Visualization-in-R-naniar.html"><span class="progress-dot"></span>Missing Data Viz (naniar)</a></li><li data-subkey="sec3sub1"><a href="/Outlier-Detection-in-R.html"><span class="progress-dot"></span>Outlier Detection</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub2" data-collapsed="false"><span class="subsec-chevron">▼</span> Probability</li><li data-subkey="sec3sub2"><a href="/Sample-Spaces-Events-and-Probability-Axioms-in-R-With-Monte-Carlo-Proof.html"><span class="progress-dot"></span>Probability Axioms</a></li><li data-subkey="sec3sub2"><a href="/Conditional-Probability-in-R.html"><span class="progress-dot"></span>Conditional Probability</a></li><li data-subkey="sec3sub2"><a href="/Random-Variables-in-R.html"><span class="progress-dot"></span>Random Variables</a></li><li data-subkey="sec3sub2"><a href="/Binomial-and-Poisson-Distributions-in-R.html"><span class="progress-dot"></span>Binomial vs Poisson</a></li><li data-subkey="sec3sub2"><a href="/Normal-t-F-and-Chi-Squared-Distributions-in-R.html"><span class="progress-dot"></span>Normal, t, F, Chi-Squared</a></li><li data-subkey="sec3sub2"><a href="/Central-Limit-Theorem-in-R.html"><span class="progress-dot"></span>Central Limit Theorem</a></li><li data-subkey="sec3sub2"><a href="/Sampling-Distributions-in-R.html"><span class="progress-dot"></span>Sampling Distributions</a></li><li data-subkey="sec3sub2"><a href="/Law-of-Large-Numbers-vs-CLT-in-R.html"><span class="progress-dot"></span>LLN vs CLT</a></li><li data-subkey="sec3sub2"><a href="/What-Is-Probability-Simulation-First-Intuition-in-R-Before-the-Formulas.html"><span class="progress-dot"></span>Probability (Simulation-First)</a></li><li data-subkey="sec3sub2"><a href="/Expected-Value-and-Variance-in-R.html"><span class="progress-dot"></span>Expected Value and Variance</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub3" data-collapsed="false"><span class="subsec-chevron">▼</span> Inference & Estimation</li><li data-subkey="sec3sub3"><a href="/Maximum-Likelihood-Estimation-in-R.html"><span class="progress-dot"></span>Maximum Likelihood Estimation</a></li><li data-subkey="sec3sub3"><a href="/Hypothesis-Testing-in-R.html"><span class="progress-dot"></span>Hypothesis Testing</a></li><li data-subkey="sec3sub3"><a href="/Sample-Size-Planning-in-R.html"><span class="progress-dot"></span>Sample Size Planning</a></li><li data-subkey="sec3sub3"><a href="/Which-Statistical-Test-in-R.html"><span class="progress-dot"></span>Choosing the Right Test</a></li><li data-subkey="sec3sub3"><a href="/Statistical-Tests-in-R.html"><span class="progress-dot"></span>Statistical Tests</a></li><li data-subkey="sec3sub3"><a href="/Measures-of-Association-in-R.html"><span class="progress-dot"></span>Measures of Association</a></li><li data-subkey="sec3sub3"><a href="/Point-Estimation-in-R.html"><span class="progress-dot"></span>Point Estimation</a></li><li data-subkey="sec3sub3"><a href="/Confidence-Intervals-in-R.html"><span class="progress-dot"></span>Confidence Intervals</a></li><li data-subkey="sec3sub3"><a href="/Type-I-and-Type-II-Errors-in-R.html"><span class="progress-dot"></span>Type I and II Errors</a></li><li data-subkey="sec3sub3"><a href="/Statistical-Power-Analysis-in-R.html"><span class="progress-dot"></span>Power Analysis</a></li><li data-subkey="sec3sub3"><a href="/Effect-Size-in-R.html"><span class="progress-dot"></span>Effect Size</a></li><li data-subkey="sec3sub3"><a href="/t-Tests-in-R.html"><span class="progress-dot"></span>t-Tests</a></li><li data-subkey="sec3sub3"><a href="/Proportion-Tests-in-R.html"><span class="progress-dot"></span>Proportion Tests</a></li><li data-subkey="sec3sub3"><a href="/Normality-and-Variance-Tests-in-R.html"><span class="progress-dot"></span>Normality & Variance Tests</a></li><li data-subkey="sec3sub3"><a href="/Chi-Square-Tests-in-R.html"><span class="progress-dot"></span>Chi-Square Tests</a></li><li data-subkey="sec3sub3"><a href="/Wilcoxon-Mann-Whitney-and-Kruskal-Wallis-in-R.html"><span class="progress-dot"></span>Wilcoxon, Mann-Whitney & Kruskal-Wallis</a></li><li data-subkey="sec3sub3"><a href="/Multiple-Comparisons-in-R.html"><span class="progress-dot"></span>Multiple Testing Correction</a></li><li data-subkey="sec3sub3"><a href="/Hypothesis-Testing-Exercises-in-R-quiz.html"><span class="progress-dot"></span>Hypothesis Testing Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub4" data-collapsed="false"><span class="subsec-chevron">▼</span> Regression</li><li data-subkey="sec3sub4"><a href="/Linear-Regression.html"><span class="progress-dot"></span>Linear Regression</a></li><li data-subkey="sec3sub4"><a href="/Logistic-Regression-With-R.html"><span class="progress-dot"></span>Logistic Regression</a></li><li data-subkey="sec3sub4"><a href="/Variable-Selection-and-Importance-With-R.html"><span class="progress-dot"></span>Feature Selection</a></li><li data-subkey="sec3sub4"><a href="/Model-Selection-in-R.html"><span class="progress-dot"></span>Model Selection</a></li><li data-subkey="sec3sub4"><a href="/Missing-Value-Treatment-With-R.html"><span class="progress-dot"></span>Missing Value Treatment</a></li><li data-subkey="sec3sub4"><a href="/Outlier-Treatment-With-R.html"><span class="progress-dot"></span>Outlier Analysis</a></li><li data-subkey="sec3sub4"><a href="/adv-regression-models.html"><span class="progress-dot"></span>Advanced Regression Models</a></li><li data-subkey="sec3sub4"><a href="/Linear-Regression-Exercises-in-R-quiz.html"><span class="progress-dot"></span>Linear Regression Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub5" data-collapsed="false"><span class="subsec-chevron">▼</span> Reporting</li><li data-subkey="sec3sub5"><a href="/Statistical-Consulting-in-R.html"><span class="progress-dot"></span>Statistical Consulting</a></li><li data-subkey="sec3sub5"><a href="/Statistical-Report-Writing-in-R.html"><span class="progress-dot"></span>Statistical Report Writing</a></li><li data-subkey="sec3sub5"><a href="/Bootstrap-Confidence-Intervals-in-R.html"><span class="progress-dot"></span>Bootstrap Confidence Intervals</a></li><li data-subkey="sec3sub5"><a href="/Reporting-Statistics-in-R.html"><span class="progress-dot"></span>Reporting Statistics</a></li><li data-subkey="sec3sub5"><a href="/Correlation-in-R.html"><span class="progress-dot"></span>Correlation (Pearson, Spearman, Kendall)</a></li><li data-subkey="sec3sub5"><a href="/Linear-Regression-Assumptions-in-R.html"><span class="progress-dot"></span>Linear Regression Assumptions</a></li><li data-subkey="sec3sub5"><a href="/Dummy-Variables-in-R.html"><span class="progress-dot"></span>Dummy Variables in R</a></li><li data-subkey="sec3sub5"><a href="/Interaction-Effects-in-R.html"><span class="progress-dot"></span>Interaction Effects</a></li><li data-subkey="sec3sub5"><a href="/Regression-Diagnostics-in-R.html"><span class="progress-dot"></span>Regression Diagnostics</a></li><li data-subkey="sec3sub5"><a href="/Logistic-Regression-in-R.html"><span class="progress-dot"></span>Logistic Regression (glm + ROC)</a></li><li data-subkey="sec3sub5"><a href="/Variable-Selection-in-R.html"><span class="progress-dot"></span>Variable Selection</a></li><li data-subkey="sec3sub5"><a href="/Poisson-Regression-in-R.html"><span class="progress-dot"></span>Poisson Regression</a></li><li data-subkey="sec3sub5"><a href="/Ridge-and-Lasso-Regression-in-R.html"><span class="progress-dot"></span>Ridge & Lasso Regression</a></li><li data-subkey="sec3sub5"><a href="/Polynomial-and-Spline-Regression-in-R.html"><span class="progress-dot"></span>Polynomial & Splines</a></li><li data-subkey="sec3sub5"><a href="/Regression-Tables-in-R.html"><span class="progress-dot"></span>Regression Tables (3 packages)</a></li><li data-subkey="sec3sub5"><a href="/One-Way-ANOVA-in-R.html"><span class="progress-dot"></span>One-Way ANOVA</a></li><li data-subkey="sec3sub5"><a href="/Post-Hoc-Tests-After-ANOVA.html"><span class="progress-dot"></span>Post-Hoc Tests After ANOVA</a></li><li data-subkey="sec3sub5"><a href="/Two-Way-ANOVA-in-R.html"><span class="progress-dot"></span>Two-Way ANOVA</a></li><li data-subkey="sec3sub5"><a href="/Repeated-Measures-ANOVA-in-R.html"><span class="progress-dot"></span>Repeated Measures ANOVA</a></li><li data-subkey="sec3sub5"><a href="/ANCOVA-in-R.html"><span class="progress-dot"></span>ANCOVA</a></li><li data-subkey="sec3sub5"><a href="/Experimental-Design-Principles-in-R.html"><span class="progress-dot"></span>Experimental Design in R</a></li><li data-subkey="sec3sub5"><a href="/Factorial-Experiments-in-R.html"><span class="progress-dot"></span>Factorial Designs (2^k)</a></li><li data-subkey="sec3sub5"><a href="/AB-Testing-in-R.html"><span class="progress-dot"></span>A/B Testing</a></li><li data-subkey="sec3sub5"><a href="/MANOVA-in-R.html"><span class="progress-dot"></span>MANOVA</a></li><li data-subkey="sec3sub5"><a href="/Mixed-ANOVA-in-R.html"><span class="progress-dot"></span>Mixed ANOVA</a></li><li data-subkey="sec3sub5"><a href="/Multivariate-Statistics-in-R.html"><span class="progress-dot"></span>Multivariate Distances & Hotelling's T²</a></li><li data-subkey="sec3sub5"><a href="/PCA-in-R.html"><span class="progress-dot"></span>PCA with prcomp()</a></li><li data-subkey="sec3sub5"><a href="/Interpreting-PCA-Results-in-R.html"><span class="progress-dot"></span>Interpreting PCA Output</a></li><li data-subkey="sec3sub5"><a href="/Exploratory-Factor-Analysis-in-R.html"><span class="progress-dot"></span>Exploratory Factor Analysis</a></li><li data-subkey="sec3sub5"><a href="/CFA-and-Structural-Equation-Modeling-in-R.html"><span class="progress-dot"></span>SEM and CFA (lavaan)</a></li><li data-subkey="sec3sub5"><a href="/Linear-Discriminant-Analysis-in-R.html"><span class="progress-dot"></span>LDA (Linear Discriminant Analysis)</a></li><li data-subkey="sec3sub5"><a href="/Cluster-Analysis-in-R.html"><span class="progress-dot"></span>Clustering (k-Means / HC / DBSCAN)</a></li><li data-subkey="sec3sub5"><a href="/Correspondence-Analysis-in-R.html"><span class="progress-dot"></span>Correspondence Analysis</a></li><li data-subkey="sec3sub5"><a href="/t-SNE-and-UMAP-in-R.html"><span class="progress-dot"></span>t-SNE and UMAP</a></li><li data-subkey="sec3sub5"><a href="/Simple-Linear-Regression-in-R.html"><span class="progress-dot"></span>Simple Linear Regression</a></li><li data-subkey="sec3sub5"><a href="/Multiple-Regression-in-R.html"><span class="progress-dot"></span>Multiple Regression</a></li><li data-subkey="sec3sub5"><a href="/Robust-Regression-in-R.html"><span class="progress-dot"></span>Robust Regression (rlm)</a></li><li data-subkey="sec3sub5"><a href="/factoextra-and-FactoMineR.html"><span class="progress-dot"></span>factoextra (PCA + Clusters)</a></li><li data-subkey="sec3sub5"><a href="/Categorical-Data-in-R.html"><span class="progress-dot"></span>Categorical Data (Tables & Mosaic)</a></li><li data-subkey="sec3sub5"><a href="/Chi-Square-Test-of-Independence-in-R.html"><span class="progress-dot"></span>Chi-Square Test of Independence</a></li><li data-subkey="sec3sub5"><a href="/Chi-Square-Goodness-of-Fit-Test-in-R.html"><span class="progress-dot"></span>Chi-Square Goodness-of-Fit</a></li><li data-subkey="sec3sub5"><a href="/Fishers-Exact-Test-in-R.html"><span class="progress-dot"></span>Fisher's Exact Test</a></li><li data-subkey="sec3sub5"><a href="/Odds-Ratios-and-Relative-Risk-in-R.html"><span class="progress-dot"></span>Odds Ratios & Relative Risk</a></li><li data-subkey="sec3sub5"><a href="/Logistic-Regression-in-R-2.html"><span class="progress-dot"></span>Logistic Regression (Diagnostics)</a></li><li data-subkey="sec3sub5"><a href="/Poisson-and-Negative-Binomial-Regression.html"><span class="progress-dot"></span>Poisson & Negative Binomial Regression</a></li><li data-subkey="sec3sub5"><a href="/Multinomial-and-Ordinal-Logistic-Regression-in-R.html"><span class="progress-dot"></span>Multinomial & Ordinal Logistic Regression</a></li><li data-subkey="sec3sub5"><a href="/When-to-Use-Nonparametric-Tests-in-R.html"><span class="progress-dot"></span>When to Use Nonparametric Tests</a></li><li data-subkey="sec3sub5"><a href="/Wilcoxon-Signed-Rank-Test-in-R.html"><span class="progress-dot"></span>Wilcoxon Signed-Rank Test</a></li><li data-subkey="sec3sub5"><a href="/Mann-Whitney-U-Test-in-R.html"><span class="progress-dot"></span>Mann-Whitney U Test</a></li><li data-subkey="sec3sub5"><a href="/Kruskal-Wallis-Test-in-R-2.html"><span class="progress-dot"></span>Kruskal-Wallis Test</a></li><li data-subkey="sec3sub5"><a href="/Friedman-Test-in-R.html"><span class="progress-dot"></span>Friedman Test</a></li><li data-subkey="sec3sub5"><a href="/Spearman-and-Kendall-Correlation-in-R.html"><span class="progress-dot"></span>Spearman & Kendall Correlation</a></li><li data-subkey="sec3sub5"><a href="/Bootstrap-in-R.html"><span class="progress-dot"></span>Bootstrap (boot package)</a></li><li data-subkey="sec3sub5"><a href="/Quantile-Regression-in-R-2.html"><span class="progress-dot"></span>Quantile Regression</a></li><li data-subkey="sec3sub5"><a href="/Matrix-Operations-in-R.html"><span class="progress-dot"></span>Matrix Operations in R</a></li><li data-subkey="sec3sub5"><a href="/Solving-Linear-Systems-in-R.html"><span class="progress-dot"></span>Solving Linear Systems in R</a></li><li data-subkey="sec3sub5"><a href="/Eigenvalues-and-Eigenvectors-in-R.html"><span class="progress-dot"></span>Eigenvalues & Eigenvectors in R</a></li><li data-subkey="sec3sub5"><a href="/Singular-Value-Decomposition-in-R.html"><span class="progress-dot"></span>Singular Value Decomposition in R</a></li><li data-subkey="sec3sub5"><a href="/Projections-and-the-Hat-Matrix-in-R.html"><span class="progress-dot"></span>Projections & the Hat Matrix</a></li><li data-subkey="sec3sub5"><a href="/QR-Decomposition-in-R.html"><span class="progress-dot"></span>QR Decomposition in R</a></li><li data-subkey="sec3sub5"><a href="/Quadratic-Forms-in-R.html"><span class="progress-dot"></span>Quadratic Forms</a></li><li data-subkey="sec3sub5"><a href="/Matrix-Derivatives-and-the-Hessian-in-R.html"><span class="progress-dot"></span>Matrix Derivatives & Hessian</a></li><li data-subkey="sec3sub5"><a href="/Exponential-Family-Distributions-in-R.html"><span class="progress-dot"></span>Exponential Family Distributions</a></li><li data-subkey="sec3sub5"><a href="/Sufficient-Statistics-in-R.html"><span class="progress-dot"></span>Sufficient Statistics</a></li><li data-subkey="sec3sub5"><a href="/Complete-and-Ancillary-Statistics-in-R.html"><span class="progress-dot"></span>Complete & Ancillary Statistics</a></li><li data-subkey="sec3sub5"><a href="/UMVUE-in-R-2.html"><span class="progress-dot"></span>UMVUE (Rao-Blackwell & Lehmann-Scheffé)</a></li><li data-subkey="sec3sub5"><a href="/Cramer-Rao-Lower-Bound-in-R-2.html"><span class="progress-dot"></span>Cramér-Rao Lower Bound</a></li><li data-subkey="sec3sub5"><a href="/Asymptotic-Theory-in-R-2.html"><span class="progress-dot"></span>Asymptotic Theory</a></li><li data-subkey="sec3sub5"><a href="/Neyman-Pearson-Lemma-in-R-2.html"><span class="progress-dot"></span>Neyman-Pearson Lemma</a></li><li data-subkey="sec3sub5"><a href="/Likelihood-Ratio-Tests-and-Pivotal-Methods.html"><span class="progress-dot"></span>Likelihood Ratio & Pivotal Methods</a></li><li data-subkey="sec3sub5"><a href="/Decision-Theory-in-R.html"><span class="progress-dot"></span>Decision Theory</a></li><li data-subkey="sec3sub5"><a href="/Asymptotic-Relative-Efficiency-in-R.html"><span class="progress-dot"></span>Asymptotic Relative Efficiency</a></li><li data-subkey="sec3sub5"><a href="/Bayes-Theorem-in-R.html"><span class="progress-dot"></span>Bayes' Theorem</a></li><li data-subkey="sec3sub5"><a href="/Bayesian-Statistics-in-R.html"><span class="progress-dot"></span>Bayesian Statistics</a></li><li data-subkey="sec3sub5"><a href="/Conjugate-Priors-in-R.html"><span class="progress-dot"></span>Conjugate Priors</a></li><li data-subkey="sec3sub5"><a href="/Grid-Approximation-in-R.html"><span class="progress-dot"></span>Grid Approximation</a></li><li data-subkey="sec3sub5"><a href="/MCMC-in-R.html"><span class="progress-dot"></span>MCMC in R</a></li><li data-subkey="sec3sub5"><a href="/Gibbs-Sampling-in-R.html"><span class="progress-dot"></span>Gibbs Sampling</a></li><li data-subkey="sec3sub5"><a href="/Hamiltonian-Monte-Carlo-in-R.html"><span class="progress-dot"></span>Hamiltonian Monte Carlo</a></li><li data-subkey="sec3sub5"><a href="/Stan-in-R.html"><span class="progress-dot"></span>Stan</a></li><li data-subkey="sec3sub5"><a href="/brms-in-R.html"><span class="progress-dot"></span>brms</a></li><li data-subkey="sec3sub5"><a href="/Choosing-Priors-in-R.html"><span class="progress-dot"></span>Choosing Priors</a></li><li data-subkey="sec3sub5"><a href="/Prior-Predictive-Checks-in-R.html"><span class="progress-dot"></span>Prior Predictive Checks</a></li><li data-subkey="sec3sub5"><a href="/Compare-Bayesian-Models-in-R.html"><span class="progress-dot"></span>Compare Bayesian Models</a></li><li data-subkey="sec3sub5"><a href="/Posterior-Predictive-Checks-in-R.html"><span class="progress-dot"></span>Posterior Predictive Checks</a></li><li data-subkey="sec3sub5"><a href="/Bayesian-Linear-Regression-in-R.html"><span class="progress-dot"></span>Bayesian Linear Regression</a></li><li data-subkey="sec3sub5"><a href="/Bayesian-Logistic-Regression-in-R.html"><span class="progress-dot"></span>Bayesian Logistic Regression</a></li><li data-subkey="sec3sub5"><a href="/Bayesian-Hierarchical-Models-in-R.html"><span class="progress-dot"></span>Bayesian Hierarchical Models</a></li><li data-subkey="sec3sub5"><a href="/Multilevel-Models-in-R.html"><span class="progress-dot"></span>Multilevel Models</a></li><li data-subkey="sec3sub5"><a href="/Bayesian-ANOVA-in-R.html"><span class="progress-dot"></span>Bayesian ANOVA</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub6" data-collapsed="false"><span class="subsec-chevron">▼</span> Machine Learning</li><li data-subkey="sec3sub6"><a href="/Machine-Learning-Exercises-in-R-quiz.html"><span class="progress-dot"></span>Machine Learning Quiz</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span> Time Series<span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li data-subkey="sec4sub0"><a href="/Time-Series-Analysis-With-R.html"><span class="progress-dot"></span>Time Series Analysis</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Forecasting-With-R.html"><span class="progress-dot"></span>Time Series Forecasting</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Forecasting-With-R-part2.html"><span class="progress-dot"></span>More Time Series Forecasting</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Exercises-in-R-quiz.html"><span class="progress-dot"></span>Time Series Quiz</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span> Advanced R<span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec5sub1" data-collapsed="false"><span class="subsec-chevron">▼</span> Functional Programming</li><li data-subkey="sec5sub1"><a href="/Functional-Programming-in-R.html"><span class="progress-dot"></span>Functional Programming</a></li><li data-subkey="sec5sub1"><a href="/R-Functional-Programming-Exercises-quiz.html"><span class="progress-dot"></span>Functional Programming Quiz</a></li><li data-subkey="sec5sub1"><a href="/purrr-map-Variants.html"><span class="progress-dot"></span>purrr map() Variants</a></li><li data-subkey="sec5sub1"><a href="/R-Anonymous-Functions.html"><span class="progress-dot"></span>R Anonymous Functions</a></li><li data-subkey="sec5sub1"><a href="/R-Function-Factories.html"><span class="progress-dot"></span>R Function Factories</a></li><li data-subkey="sec5sub1"><a href="/R-Function-Operators.html"><span class="progress-dot"></span>R Function Operators</a></li><li data-subkey="sec5sub1"><a href="/Reduce-Filter-Map-in-R.html"><span class="progress-dot"></span>Reduce, Filter, Map</a></li><li data-subkey="sec5sub1"><a href="/Memoization-in-R.html"><span class="progress-dot"></span>Memoization in R</a></li><li data-subkey="sec5sub1"><a href="/Writing-Composable-R-Code.html"><span class="progress-dot"></span>Composable R Code</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec5sub2" data-collapsed="false"><span class="subsec-chevron">▼</span> OOP in R</li><li data-subkey="sec5sub2"><a href="/OOP-in-R.html"><span class="progress-dot"></span>OOP in R: S3/S4/R6</a></li><li data-subkey="sec5sub2"><a href="/S3-Classes-in-R.html"><span class="progress-dot"></span>S3 Classes</a></li><li data-subkey="sec5sub2"><a href="/S3-Method-Dispatch-in-R.html"><span class="progress-dot"></span>S3 Method Dispatch</a></li><li data-subkey="sec5sub2"><a href="/S4-Classes-in-R.html"><span class="progress-dot"></span>S4 Classes</a></li><li data-subkey="sec5sub2"><a href="/S4-Methods-in-R.html"><span class="progress-dot"></span>S4 Methods & Dispatch</a></li><li data-subkey="sec5sub2"><a href="/R6-Classes-in-R.html"><span class="progress-dot"></span>R6 Classes</a></li><li data-subkey="sec5sub2"><a href="/R6-Advanced.html"><span class="progress-dot"></span>R6 Advanced</a></li><li data-subkey="sec5sub2"><a href="/Operator-Overloading-in-R.html"><span class="progress-dot"></span>Operator Overloading</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec5sub3" data-collapsed="false"><span class="subsec-chevron">▼</span> How R Works</li><li data-subkey="sec5sub3"><a href="/R-Names-and-Values.html"><span class="progress-dot"></span>R Names & Values</a></li><li data-subkey="sec5sub3"><a href="/R-Assignment-Deep-Dive.html"><span class="progress-dot"></span>R Assignment Deep Dive</a></li><li data-subkey="sec5sub3"><a href="/R-Memory-lobstr.html"><span class="progress-dot"></span>R Memory & lobstr</a></li><li data-subkey="sec5sub3"><a href="/R-Environments.html"><span class="progress-dot"></span>R Environments</a></li><li data-subkey="sec5sub3"><a href="/R-Lexical-Scoping.html"><span class="progress-dot"></span>Lexical Scoping</a></li><li data-subkey="sec5sub3"><a href="/R-Closures.html"><span class="progress-dot"></span>R Closures</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec5sub4" data-collapsed="false"><span class="subsec-chevron">▼</span> Debugging & Performance</li><li data-subkey="sec5sub4"><a href="/R-Conditions-System.html"><span class="progress-dot"></span>Conditions System</a></li><li data-subkey="sec5sub4"><a href="/R-Debugging.html"><span class="progress-dot"></span>Debugging R Code</a></li><li data-subkey="sec5sub4"><a href="/R-Common-Errors.html"><span class="progress-dot"></span>50 Common R Errors</a></li><li data-subkey="sec5sub4"><a href="/Parallel-Computing-With-R.html"><span class="progress-dot"></span>Parallel Computing</a></li><li data-subkey="sec5sub4"><a href="/Strategies-To-Improve-And-Speedup-R-Code.html"><span class="progress-dot"></span>Speedup R Code</a></li><li data-subkey="sec5sub4"><a href="/Shiny-Exercises-in-R-quiz.html"><span class="progress-dot"></span>Shiny Quiz</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span> Classic Tutorials<span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li data-subkey="sec6sub0"><a href="/R-Tutorial.html"><span class="progress-dot"></span>R Tutorial (Classic)</a></li><li data-subkey="sec6sub0"><a href="/ggplot2-Tutorial-With-R.html"><span class="progress-dot"></span>ggplot2 Short Tutorial</a></li><li data-subkey="sec6sub0"><a href="/Complete-Ggplot2-Tutorial-Part1-With-R-Code.html"><span class="progress-dot"></span>ggplot2 Tutorial 1 - Intro</a></li><li data-subkey="sec6sub0"><a href="/Complete-Ggplot2-Tutorial-Part2-Customizing-Theme-With-R-Code.html"><span class="progress-dot"></span>ggplot2 Tutorial 2 - Theme</a></li><li data-subkey="sec6sub0"><a href="/Top50-Ggplot2-Visualizations-MasterList-R-Code.html"><span class="progress-dot"></span>ggplot2 Tutorial 3 - Masterlist</a></li><li data-subkey="sec6sub0"><a href="/Association-Mining-With-R.html"><span class="progress-dot"></span>Association Mining</a></li><li data-subkey="sec6sub0"><a href="/Multi-Dimensional-Scaling-With-R.html"><span class="progress-dot"></span>Multi Dimensional Scaling</a></li><li data-subkey="sec6sub0"><a href="/Optimization-With-R.html"><span class="progress-dot"></span>Optimization</a></li><li data-subkey="sec6sub0"><a href="/Information-Value-With-R.html"><span class="progress-dot"></span>InformationValue Package</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span> Practice Exercises<span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec7sub1" data-collapsed="false"><span class="subsec-chevron">▼</span> Mastery Quizzes (Certificate)</li><li data-subkey="sec7sub1"><a href="/R-Beginner-Exercises-quiz.html"><span class="progress-dot"></span>R Fundamentals Quiz</a></li><li data-subkey="sec7sub1"><a href="/dplyr-Exercises-in-R-quiz.html"><span class="progress-dot"></span>dplyr Quiz</a></li><li data-subkey="sec7sub1"><a href="/ggplot2-Exercises-in-R-quiz.html"><span class="progress-dot"></span>ggplot2 Quiz</a></li><li data-subkey="sec7sub1"><a href="/Hypothesis-Testing-Exercises-in-R-quiz.html"><span class="progress-dot"></span>Hypothesis Testing Quiz</a></li><li data-subkey="sec7sub1"><a href="/Linear-Regression-Exercises-in-R-quiz.html"><span class="progress-dot"></span>Linear Regression Quiz</a></li><li data-subkey="sec7sub1"><a href="/Machine-Learning-Exercises-in-R-quiz.html"><span class="progress-dot"></span>Machine Learning Quiz</a></li><li data-subkey="sec7sub1"><a href="/tidyr-Exercises-in-R-quiz.html"><span 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<h1>Algorithmic Fairness in R: fairml & aif360 for Bias Auditing</h1>
<p class="lead">Algorithmic fairness ensures that machine learning models don't systematically discriminate against protected groups. This guide teaches you to measure, audit, and improve fairness using R tools, because a model that's accurate on average can still be unfair to specific groups.</p>
<div class="post-byline" style="color:#6b7280;font-size:14px;margin:2px 0 18px 0;line-height:1.5;">By <strong>Selva Prabhakaran</strong> · Published May 10, 2026 · Last updated May 10, 2026</div>
<div class="engagement-header" data-difficulty="Intermediate" data-time="10"></div>
<p>A hiring model that rejects 80% of female applicants but only 30% of male applicants is unfair, even if its overall accuracy is high. A credit scoring model that gives higher rates to minorities with the same creditworthiness as non-minorities is unfair. These aren't hypothetical: they've happened in real deployments. This guide gives you the tools to catch and fix these problems.</p>
<h2>Fairness Definitions</h2>
<p>There are multiple definitions of fairness, and they can conflict with each other. Understanding them is essential for choosing the right one for your context.</p>
<table class="table table-striped">
<thead>
<tr>
<th>Definition</th>
<th>Meaning</th>
<th>Formula</th>
</tr>
</thead>
<tbody>
<tr>
<td><a class="auto-link" href="Bias-in-Data-and-Models.html" title="Bias in Data & Models: How to Detect & Reduce It in R">Demographic parity</a></td>
<td>Equal selection rates across groups</td>
<td>P(Y=1\</td>
<td>A=a) = P(Y=1\</td>
<td>A=<a class="auto-link" href="Conditional-Probability-in-R.html" title="Conditional Probability in R: P(A|B), Independence, and Bayes — With Real Examples">b)</a></td>
</tr>
<tr>
<td>Equalized odds</td>
<td>Equal TPR and FPR across groups</td>
<td>P(Yhat=1\</td>
<td>Y=y,A=a) = P(Yhat=1\</td>
<td>Y=y,A=b)</td>
</tr>
<tr>
<td>Equal opportunity</td>
<td>Equal TPR across groups</td>
<td>P(Yhat=1\</td>
<td>Y=1,A=a) = P(Yhat=1\</td>
<td>Y=1,A=b)</td>
</tr>
<tr>
<td>Calibration</td>
<td>Same meaning of scores across groups</td>
<td>P(Y=1\</td>
<td>Score=s,A=a) = P(Y=1\</td>
<td>Score=s,A=b)</td>
</tr>
<tr>
<td>Predictive parity</td>
<td>Equal precision across groups</td>
<td>P(Y=1\</td>
<td>Yhat=1,A=a) = P(Y=1\</td>
<td>Yhat=1,A=b)</td>
</tr>
<tr>
<td>Individual fairness</td>
<td>Similar individuals treated similarly</td>
<td>d(x,x') small implies d(f(x),f(x')) small</td>
</tr>
</tbody>
</table>
<h3>The Impossibility Theorem</h3>
<p>A critical result: except in trivial cases, you <strong>cannot</strong> simultaneously satisfy demographic parity, equalized odds, and calibration. You must choose which fairness criterion matters most for your application.</p>
<div class="webr-container" data-block-title="Demonstrate the fairness trade-off">
<div class="webr-code-block">
<div class="webr-header"><div class="webr-header-left"><span class="webr-header-badge">R</span><span class="webr-header-label">Demonstrate the fairness trade-off</span></div><div class="webr-header-right"><button type="button" class="webr-copy-btn" aria-label="Copy code" title="Copy code"><svg width="14" height="14" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><rect x="9" y="9" width="13" height="13" rx="2" ry="2"/><path d="M5 15H4a2 2 0 0 1-2-2V4a2 2 0 0 1 2-2h9a2 2 0 0 1 2 2v1"/></svg></button><button class="btn btn-sm btn-primary webr-run-btn" onclick="runWebR(this)">▶ Run <span class="webr-run-shortcut">Ctrl+Enter</span></button></div></div>
<div class="webr-editor" data-language="r"><span class="cl"><span class="c1"># Demonstrating the fairness trade-off</span></span>
<span class="cl"><span class="nf">set.seed</span>(<span class="m">42</span>)</span>
<span class="cl">n <span class="o"><-</span> <span class="m">1000</span></span>
<span class="cl"></span>
<span class="cl"><span class="c1"># Simulate two groups with different base rates</span></span>
<span class="cl">group <span class="o"><-</span> <span class="nf">rep</span>(<span class="nf">c</span>(<span class="s">"A"</span>,<span class="s">"B"</span>), each <span class="o">=</span> n<span class="o">/</span><span class="m">2</span>)</span>
<span class="cl">base_rate <span class="o"><-</span> <span class="nf">ifelse</span>(group <span class="o">==</span> <span class="s">"A"</span>, <span class="m">0.4</span>, <span class="m">0.2</span>) <span class="c1"># Different base rates</span></span>
<span class="cl">true_label <span class="o"><-</span> <span class="nf">rbinom</span>(n, <span class="m">1</span>, base_rate)</span>
<span class="cl"></span>
<span class="cl"><span class="c1"># A perfectly calibrated model</span></span>
<span class="cl">score <span class="o"><-</span> true_label <span class="o">+</span> <span class="nf">rnorm</span>(n, <span class="m">0</span>, <span class="m">0.3</span>)</span>
<span class="cl">predicted <span class="o"><-</span> <span class="nf">as.integer</span>(score <span class="o">></span> <span class="m">0.5</span>)</span>
<span class="cl"></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"=== Fairness Trade-off Demo ===\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"Base rates differ between groups:\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" Group A base rate:"</span>, <span class="nf">mean</span>(true_label[group <span class="o">==</span> <span class="s">"A"</span>]), <span class="s">"\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" Group B base rate:"</span>, <span class="nf">mean</span>(true_label[group <span class="o">==</span> <span class="s">"B"</span>]), <span class="s">"\n"</span>)</span>
<span class="cl"></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"\nSelection rates (demographic parity check):\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" Group A:"</span>, <span class="nf">mean</span>(predicted[group <span class="o">==</span> <span class="s">"A"</span>]), <span class="s">"\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" Group B:"</span>, <span class="nf">mean</span>(predicted[group <span class="o">==</span> <span class="s">"B"</span>]), <span class="s">"\n"</span>)</span>
<span class="cl"></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"\nTrue Positive Rates (equal opportunity check):\n"</span>)</span>
<span class="cl">tpr_a <span class="o"><-</span> <span class="nf">mean</span>(predicted[group <span class="o">==</span> <span class="s">"A"</span> <span class="o">&</span> true_label <span class="o">==</span> <span class="m">1</span>])</span>
<span class="cl">tpr_b <span class="o"><-</span> <span class="nf">mean</span>(predicted[group <span class="o">==</span> <span class="s">"B"</span> <span class="o">&</span> true_label <span class="o">==</span> <span class="m">1</span>])</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" Group A TPR:"</span>, <span class="nf">round</span>(tpr_a, <span class="m">3</span>), <span class="s">"\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" Group B TPR:"</span>, <span class="nf">round</span>(tpr_b, <span class="m">3</span>), <span class="s">"\n"</span>)</span>
<span class="cl"></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"\nEqualizing selection rates would break calibration.\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"Equalizing TPR would change selection rates.\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"You must choose which fairness criterion to prioritize.\n"</span>)</span></div>
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<pre class="webr-output"></pre>
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<div class="webr-plot-output"></div>
</div>
<h2>Measuring Disparate Impact</h2>
<p>The four-fifths rule: the selection rate for any protected group should be at least 80% of the rate for the most-selected group.</p>
<div class="webr-container" data-block-title="Measure disparate impact in hiring">
<div class="webr-code-block">
<div class="webr-header"><div class="webr-header-left"><span class="webr-header-badge">R</span><span class="webr-header-label">Measure disparate impact in hiring</span></div><div class="webr-header-right"><button type="button" class="webr-copy-btn" aria-label="Copy code" title="Copy code"><svg width="14" height="14" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><rect x="9" y="9" width="13" height="13" rx="2" ry="2"/><path d="M5 15H4a2 2 0 0 1-2-2V4a2 2 0 0 1 2-2h9a2 2 0 0 1 2 2v1"/></svg></button><button class="btn btn-sm btn-primary webr-run-btn" onclick="runWebR(this)">▶ Run <span class="webr-run-shortcut">Ctrl+Enter</span></button></div></div>
<div class="webr-editor" data-language="r"><span class="cl"><span class="c1"># Comprehensive disparate impact analysis</span></span>
<span class="cl"><span class="nf">set.seed</span>(<span class="m">42</span>)</span>
<span class="cl">n <span class="o"><-</span> <span class="m">800</span></span>
<span class="cl"></span>
<span class="cl">applicants <span class="o"><-</span> <span class="nf">data.frame</span>(</span>
<span class="cl"> gender <span class="o">=</span> <span class="nf">sample</span>(<span class="nf">c</span>(<span class="s">"Male"</span>,<span class="s">"Female"</span>), n, replace <span class="o">=</span> <span class="kc">TRUE</span>),</span>
<span class="cl"> score <span class="o">=</span> <span class="nf">rnorm</span>(n, <span class="m">70</span>, <span class="m">10</span>)</span>
<span class="cl">)</span>
<span class="cl"></span>
<span class="cl"><span class="c1"># Biased threshold: unconsciously favoring one group</span></span>
<span class="cl">applicants<span class="o">$</span>hired <span class="o"><-</span> <span class="nf">with</span>(applicants, {</span>
<span class="cl"> threshold <span class="o"><-</span> <span class="nf">ifelse</span>(gender <span class="o">==</span> <span class="s">"Male"</span>, <span class="m">65</span>, <span class="m">70</span>)</span>
<span class="cl"> <span class="nf">as.integer</span>(score <span class="o">></span> threshold)</span>
<span class="cl">})</span>
<span class="cl"></span>
<span class="cl"><span class="c1"># Disparate impact analysis</span></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"=== Disparate Impact Analysis ===\n"</span>)</span>
<span class="cl">hire_rates <span class="o"><-</span> <span class="nf">tapply</span>(applicants<span class="o">$</span>hired, applicants<span class="o">$</span>gender, mean)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"Hiring rates:\n"</span>)</span>
<span class="cl"><span class="nf">print</span>(<span class="nf">round</span>(hire_rates, <span class="m">3</span>))</span>
<span class="cl"></span>
<span class="cl">di_ratio <span class="o"><-</span> <span class="nf">min</span>(hire_rates) <span class="o">/</span> <span class="nf">max</span>(hire_rates)</span>
<span class="cl"><span class="nf">cat</span>(<span class="nf">sprintf</span>(<span class="s">"\nDisparate impact ratio: %.3f\n"</span>, di_ratio))</span>
<span class="cl"><span class="nf">cat</span>(<span class="nf">sprintf</span>(<span class="s">"Four-fifths threshold: 0.800\n"</span>))</span>
<span class="cl"><span class="nf">cat</span>(<span class="nf">sprintf</span>(<span class="s">"Result: %s\n"</span>, <span class="nf">ifelse</span>(di_ratio <span class="o">>=</span> <span class="m">0.8</span>, <span class="s">"PASS"</span>, <span class="s">"FAIL - potential bias"</span>)))</span>
<span class="cl"></span>
<span class="cl"><span class="c1"># Statistical significance</span></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"\n=== Chi-square test ===\n"</span>)</span>
<span class="cl">ct <span class="o"><-</span> <span class="nf">table</span>(applicants<span class="o">$</span>gender, applicants<span class="o">$</span>hired)</span>
<span class="cl">chi <span class="o"><-</span> <span class="nf">chisq.test</span>(ct)</span>
<span class="cl"><span class="nf">cat</span>(<span class="nf">sprintf</span>(<span class="s">"Chi-squared = %.2f, p = %.4f\n"</span>, chi<span class="o">$</span>statistic, chi<span class="o">$</span>p.value))</span></div>
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</div>
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</div>
<h2>Building a Fairness Audit Function</h2>
<div class="webr-container" data-block-title="Build a reusable fairness audit">
<div class="webr-code-block">
<div class="webr-header"><div class="webr-header-left"><span class="webr-header-badge">R</span><span class="webr-header-label">Build a reusable fairness audit</span></div><div class="webr-header-right"><button type="button" class="webr-copy-btn" aria-label="Copy code" title="Copy code"><svg width="14" height="14" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><rect x="9" y="9" width="13" height="13" rx="2" ry="2"/><path d="M5 15H4a2 2 0 0 1-2-2V4a2 2 0 0 1 2-2h9a2 2 0 0 1 2 2v1"/></svg></button><button class="btn btn-sm btn-primary webr-run-btn" onclick="runWebR(this)">▶ Run <span class="webr-run-shortcut">Ctrl+Enter</span></button></div></div>
<div class="webr-editor" data-language="r"><span class="cl"><span class="c1"># Reusable fairness audit function</span></span>
<span class="cl">fairness_audit <span class="o"><-</span> <span class="kr">function</span>(actual, predicted, group, positive_label <span class="o">=</span> <span class="m">1</span>) {</span>
<span class="cl"> groups <span class="o"><-</span> <span class="nf">unique</span>(group)</span>
<span class="cl"> results <span class="o"><-</span> <span class="nf">data.frame</span>(</span>
<span class="cl"> Group <span class="o">=</span> <span class="nf">character</span>(),</span>
<span class="cl"> N <span class="o">=</span> <span class="nf">integer</span>(),</span>
<span class="cl"> SelectionRate <span class="o">=</span> <span class="nf">numeric</span>(),</span>
<span class="cl"> TPR <span class="o">=</span> <span class="nf">numeric</span>(),</span>
<span class="cl"> FPR <span class="o">=</span> <span class="nf">numeric</span>(),</span>
<span class="cl"> Precision <span class="o">=</span> <span class="nf">numeric</span>(),</span>
<span class="cl"> stringsAsFactors <span class="o">=</span> <span class="kc">FALSE</span></span>
<span class="cl"> )</span>
<span class="cl"></span>
<span class="cl"> <span class="kr">for</span> (g <span class="kr">in</span> groups) {</span>
<span class="cl"> mask <span class="o"><-</span> group <span class="o">==</span> g</span>
<span class="cl"> a <span class="o"><-</span> actual[mask]</span>
<span class="cl"> p <span class="o"><-</span> predicted[mask]</span>
<span class="cl"></span>
<span class="cl"> tp <span class="o"><-</span> <span class="nf">sum</span>(a <span class="o">==</span> positive_label <span class="o">&</span> p <span class="o">==</span> positive_label)</span>
<span class="cl"> fp <span class="o"><-</span> <span class="nf">sum</span>(a <span class="o">!=</span> positive_label <span class="o">&</span> p <span class="o">==</span> positive_label)</span>
<span class="cl"> fn <span class="o"><-</span> <span class="nf">sum</span>(a <span class="o">==</span> positive_label <span class="o">&</span> p <span class="o">!=</span> positive_label)</span>
<span class="cl"> tn <span class="o"><-</span> <span class="nf">sum</span>(a <span class="o">!=</span> positive_label <span class="o">&</span> p <span class="o">!=</span> positive_label)</span>
<span class="cl"></span>
<span class="cl"> results <span class="o"><-</span> <span class="nf">rbind</span>(results, <span class="nf">data.frame</span>(</span>
<span class="cl"> Group <span class="o">=</span> g,</span>
<span class="cl"> N <span class="o">=</span> <span class="nf">sum</span>(mask),</span>
<span class="cl"> SelectionRate <span class="o">=</span> <span class="nf">round</span>(<span class="nf">mean</span>(p <span class="o">==</span> positive_label), <span class="m">3</span>),</span>
<span class="cl"> TPR <span class="o">=</span> <span class="nf">round</span>(<span class="nf">ifelse</span>(tp<span class="o">+</span>fn <span class="o">></span> <span class="m">0</span>, tp<span class="o">/</span>(tp<span class="o">+</span>fn), <span class="kc">NA</span>), <span class="m">3</span>),</span>
<span class="cl"> FPR <span class="o">=</span> <span class="nf">round</span>(<span class="nf">ifelse</span>(fp<span class="o">+</span>tn <span class="o">></span> <span class="m">0</span>, fp<span class="o">/</span>(fp<span class="o">+</span>tn), <span class="kc">NA</span>), <span class="m">3</span>),</span>
<span class="cl"> Precision <span class="o">=</span> <span class="nf">round</span>(<span class="nf">ifelse</span>(tp<span class="o">+</span>fp <span class="o">></span> <span class="m">0</span>, tp<span class="o">/</span>(tp<span class="o">+</span>fp), <span class="kc">NA</span>), <span class="m">3</span>),</span>
<span class="cl"> stringsAsFactors <span class="o">=</span> <span class="kc">FALSE</span></span>
<span class="cl"> ))</span>
<span class="cl"> }</span>
<span class="cl"></span>
<span class="cl"> <span class="c1"># Calculate disparities</span></span>
<span class="cl"> <span class="nf">cat</span>(<span class="s">"=== Fairness Audit Report ===\n\n"</span>)</span>
<span class="cl"> <span class="nf">print</span>(results, row.names <span class="o">=</span> <span class="kc">FALSE</span>)</span>
<span class="cl"></span>
<span class="cl"> <span class="nf">cat</span>(<span class="s">"\n--- Disparity Ratios ---\n"</span>)</span>
<span class="cl"> max_sr <span class="o"><-</span> <span class="nf">max</span>(results<span class="o">$</span>SelectionRate)</span>
<span class="cl"> <span class="kr">for</span> (i <span class="kr">in</span> <span class="m">1</span><span class="o">:</span><span class="nf">nrow</span>(results)) {</span>
<span class="cl"> ratio <span class="o"><-</span> results<span class="o">$</span>SelectionRate[i] <span class="o">/</span> max_sr</span>
<span class="cl"> status <span class="o"><-</span> <span class="nf">ifelse</span>(ratio <span class="o">>=</span> <span class="m">0.8</span>, <span class="s">"OK"</span>, <span class="s">"WARNING"</span>)</span>
<span class="cl"> <span class="nf">cat</span>(<span class="nf">sprintf</span>(<span class="s">" %s: SR ratio = %.3f [%s]\n"</span>,</span>
<span class="cl"> results<span class="o">$</span>Group[i], ratio, status))</span>
<span class="cl"> }</span>
<span class="cl"></span>
<span class="cl"> <span class="nf">cat</span>(<span class="nf">sprintf</span>(<span class="s">"\n--- Equal Opportunity (TPR) ---\n"</span>))</span>
<span class="cl"> max_tpr <span class="o"><-</span> <span class="nf">max</span>(results<span class="o">$</span>TPR, na.rm <span class="o">=</span> <span class="kc">TRUE</span>)</span>
<span class="cl"> <span class="kr">for</span> (i <span class="kr">in</span> <span class="m">1</span><span class="o">:</span><span class="nf">nrow</span>(results)) {</span>
<span class="cl"> ratio <span class="o"><-</span> results<span class="o">$</span>TPR[i] <span class="o">/</span> max_tpr</span>
<span class="cl"> <span class="nf">cat</span>(<span class="nf">sprintf</span>(<span class="s">" %s: TPR ratio = %.3f\n"</span>, results<span class="o">$</span>Group[i], ratio))</span>
<span class="cl"> }</span>
<span class="cl">}</span>
<span class="cl"></span>
<span class="cl"><span class="c1"># Test the audit function</span></span>
<span class="cl"><span class="nf">set.seed</span>(<span class="m">42</span>)</span>
<span class="cl">n <span class="o"><-</span> <span class="m">600</span></span>
<span class="cl">test_data <span class="o"><-</span> <span class="nf">data.frame</span>(</span>
<span class="cl"> group <span class="o">=</span> <span class="nf">sample</span>(<span class="nf">c</span>(<span class="s">"Young"</span>,<span class="s">"Middle"</span>,<span class="s">"Senior"</span>), n, replace <span class="o">=</span> <span class="kc">TRUE</span>, prob <span class="o">=</span> <span class="nf">c</span>(<span class="m">0.4</span>,<span class="m">0.4</span>,<span class="m">0.2</span>)),</span>
<span class="cl"> actual <span class="o">=</span> <span class="nf">rbinom</span>(n, <span class="m">1</span>, <span class="m">0.3</span>),</span>
<span class="cl"> predicted <span class="o">=</span> <span class="nf">rbinom</span>(n, <span class="m">1</span>, <span class="m">0.28</span>)</span>
<span class="cl">)</span>
<span class="cl"></span>
<span class="cl"><span class="nf">fairness_audit</span>(test_data<span class="o">$</span>actual, test_data<span class="o">$</span>predicted, test_data<span class="o">$</span>group)</span></div>
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<h2>Fairness Packages in R</h2>
<h3>fairml Package</h3>
<p>The <code>fairml</code> package implements fair regression and classification models that explicitly include fairness constraints.</p>
<div class="webr-container" data-block-title="Explore the fairml package">
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<div class="webr-editor" data-language="r"><span class="cl"><span class="c1"># fairml concepts (demonstration without package dependency)</span></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"=== fairml Package Overview ===\n\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"Key functions:\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" frrm() - Fair Ridge Regression Model\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" fgrrm() - Fair Generalized Ridge Regression\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" nclm() - Nonconvex Penalized Logistic Model\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" zlrm() - Zafar Logistic Regression Model\n\n"</span>)</span>
<span class="cl"></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"Usage pattern:\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">' library(fairml)\n'</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">' model <- frrm(y ~ x1 + x2, data = df,\n'</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">' sensitive = df$protected_attr,\n'</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">' unfairness = 0.05) # Max allowed unfairness\n\n'</span>)</span>
<span class="cl"></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"The unfairness parameter (0 to 1) controls the trade-off:\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" 0.00 = Perfectly fair (may sacrifice accuracy)\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" 0.05 = 5% unfairness tolerance (good balance)\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" 1.00 = No fairness constraint (standard model)\n"</span>)</span></div>
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<h3>aif360 (AI Fairness 360)</h3>
<div class="webr-container" data-block-title="Survey the AIF360 toolkit">
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<div class="webr-header"><div class="webr-header-left"><span class="webr-header-badge">R</span><span class="webr-header-label">Survey the AIF360 toolkit</span></div><div class="webr-header-right"><button type="button" class="webr-copy-btn" aria-label="Copy code" title="Copy code"><svg width="14" height="14" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><rect x="9" y="9" width="13" height="13" rx="2" ry="2"/><path d="M5 15H4a2 2 0 0 1-2-2V4a2 2 0 0 1 2-2h9a2 2 0 0 1 2 2v1"/></svg></button><button class="btn btn-sm btn-primary webr-run-btn" onclick="runWebR(this)">▶ Run <span class="webr-run-shortcut">Ctrl+Enter</span></button></div></div>
<div class="webr-editor" data-language="r"><span class="cl"><span class="nf">cat</span>(<span class="s">"=== AIF360 for R ===\n\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"IBM's AI Fairness 360 toolkit (Python-based, R interface available):\n\n"</span>)</span>
<span class="cl"></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"Bias metrics:\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" - Statistical parity difference\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" - Disparate impact ratio\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" - Equal opportunity difference\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" - Average odds difference\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" - Theil index\n\n"</span>)</span>
<span class="cl"></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"Bias mitigation algorithms:\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" Pre-processing: Reweighting, Optimized Preprocessing\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" In-processing: Adversarial Debiasing, Prejudice Remover\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" Post-processing: Equalized Odds, Calibrated Equalized Odds\n\n"</span>)</span>
<span class="cl"></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"R usage via reticulate:\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">' library(reticulate)\n'</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">' aif <- import("aif360.datasets")\n'</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">' metrics <- import("aif360.metrics")\n'</span>)</span></div>
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<h2>Practical Audit Workflow</h2>
<table class="table table-striped">
<thead>
<tr>
<th>Step</th>
<th>Action</th>
<th>Tool</th>
</tr>
</thead>
<tbody>
<tr>
<td>1. Define protected attributes</td>
<td>List sensitive variables</td>
<td>Domain knowledge</td>
</tr>
<tr>
<td>2. Choose fairness metric</td>
<td>Match to application context</td>
<td>See definitions table above</td>
</tr>
<tr>
<td>3. Measure baseline</td>
<td>Calculate metrics on current model</td>
<td><code>fairness_audit()</code> function</td>
</tr>
<tr>
<td>4. Set threshold</td>
<td>Define acceptable disparity level</td>
<td>Four-fifths rule or domain-specific</td>
</tr>
<tr>
<td>5. Mitigate if needed</td>
<td>Apply debiasing technique</td>
<td>fairml, reweighting, threshold tuning</td>
</tr>
<tr>
<td>6. Re-measure</td>
<td>Verify improvement</td>
<td>Same audit function</td>
</tr>
<tr>
<td>7. Document</td>
<td>Record decisions and trade-offs</td>
<td>Analysis report</td>
</tr>
</tbody>
</table>
<div class="webr-container" data-block-title="Tune thresholds for fairness">
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<div class="webr-editor" data-language="r"><span class="cl"><span class="c1"># Step 5 example: threshold tuning for fairness</span></span>
<span class="cl"><span class="nf">set.seed</span>(<span class="m">42</span>)</span>
<span class="cl">n <span class="o"><-</span> <span class="m">500</span></span>
<span class="cl"></span>
<span class="cl">df <span class="o"><-</span> <span class="nf">data.frame</span>(</span>
<span class="cl"> group <span class="o">=</span> <span class="nf">rep</span>(<span class="nf">c</span>(<span class="s">"A"</span>,<span class="s">"B"</span>), each <span class="o">=</span> n<span class="o">/</span><span class="m">2</span>),</span>
<span class="cl"> score <span class="o">=</span> <span class="nf">c</span>(<span class="nf">rnorm</span>(n<span class="o">/</span><span class="m">2</span>, <span class="m">0.6</span>, <span class="m">0.2</span>), <span class="nf">rnorm</span>(n<span class="o">/</span><span class="m">2</span>, <span class="m">0.5</span>, <span class="m">0.2</span>)),</span>
<span class="cl"> actual <span class="o">=</span> <span class="nf">c</span>(<span class="nf">rbinom</span>(n<span class="o">/</span><span class="m">2</span>, <span class="m">1</span>, <span class="m">0.6</span>), <span class="nf">rbinom</span>(n<span class="o">/</span><span class="m">2</span>, <span class="m">1</span>, <span class="m">0.4</span>))</span>
<span class="cl">)</span>
<span class="cl"></span>
<span class="cl"><span class="c1"># Single threshold: may create disparate impact</span></span>
<span class="cl">single_threshold <span class="o"><-</span> <span class="m">0.5</span></span>
<span class="cl">df<span class="o">$</span>pred_single <span class="o"><-</span> <span class="nf">as.integer</span>(df<span class="o">$</span>score <span class="o">></span> single_threshold)</span>
<span class="cl"></span>
<span class="cl"><span class="c1"># Group-specific thresholds: equalize selection rates</span></span>
<span class="cl">target_rate <span class="o"><-</span> <span class="nf">mean</span>(df<span class="o">$</span>actual)</span>
<span class="cl">thresh_a <span class="o"><-</span> <span class="nf">quantile</span>(df<span class="o">$</span>score[df<span class="o">$</span>group <span class="o">==</span> <span class="s">"A"</span>], <span class="m">1</span> <span class="o">-</span> target_rate)</span>
<span class="cl">thresh_b <span class="o"><-</span> <span class="nf">quantile</span>(df<span class="o">$</span>score[df<span class="o">$</span>group <span class="o">==</span> <span class="s">"B"</span>], <span class="m">1</span> <span class="o">-</span> target_rate)</span>
<span class="cl">df<span class="o">$</span>pred_adjusted <span class="o"><-</span> <span class="nf">ifelse</span>(df<span class="o">$</span>group <span class="o">==</span> <span class="s">"A"</span>,</span>
<span class="cl"> <span class="nf">as.integer</span>(df<span class="o">$</span>score <span class="o">></span> thresh_a),</span>
<span class="cl"> <span class="nf">as.integer</span>(df<span class="o">$</span>score <span class="o">></span> thresh_b))</span>
<span class="cl"></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"=== Threshold Tuning ===\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"Single threshold (0.5):\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" Group A rate:"</span>, <span class="nf">mean</span>(df<span class="o">$</span>pred_single[df<span class="o">$</span>group <span class="o">==</span> <span class="s">"A"</span>]), <span class="s">"\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" Group B rate:"</span>, <span class="nf">mean</span>(df<span class="o">$</span>pred_single[df<span class="o">$</span>group <span class="o">==</span> <span class="s">"B"</span>]), <span class="s">"\n"</span>)</span>
<span class="cl"></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"\nAdjusted thresholds:\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" Group A threshold:"</span>, <span class="nf">round</span>(thresh_a, <span class="m">3</span>), <span class="s">"-> rate:"</span>,</span>
<span class="cl"> <span class="nf">mean</span>(df<span class="o">$</span>pred_adjusted[df<span class="o">$</span>group <span class="o">==</span> <span class="s">"A"</span>]), <span class="s">"\n"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">" Group B threshold:"</span>, <span class="nf">round</span>(thresh_b, <span class="m">3</span>), <span class="s">"-> rate:"</span>,</span>
<span class="cl"> <span class="nf">mean</span>(df<span class="o">$</span>pred_adjusted[df<span class="o">$</span>group <span class="o">==</span> <span class="s">"B"</span>]), <span class="s">"\n"</span>)</span></div>
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<h2>Summary</h2>
<table class="table table-striped">
<thead>
<tr>
<th>Fairness Criterion</th>
<th>Best For</th>
<th>Trade-off</th>
</tr>
</thead>
<tbody>
<tr>
<td>Demographic parity</td>
<td>Employment, lending</td>
<td>May select less qualified from one group</td>
</tr>
<tr>
<td>Equalized odds</td>
<td>Criminal justice, medical</td>
<td>Harder to achieve with different base rates</td>
</tr>
<tr>
<td>Equal opportunity</td>
<td>Scholarship, hiring</td>
<td>Only equalizes true positive rate</td>
</tr>
<tr>
<td>Calibration</td>
<td>Risk assessment, insurance</td>
<td>Doesn't guarantee equal rates</td>
</tr>
<tr>
<td>Individual fairness</td>
<td>Any</td>
<td>Hard to define similarity metric</td>
</tr>
</tbody>
</table>
<h2>FAQ</h2>
<p><strong>Which fairness metric should I use?</strong> It depends on context. For hiring: demographic parity or disparate impact. For criminal risk: equalized odds (equal TPR and FPR). For medical diagnostics: equal opportunity (equal sensitivity). Discuss with stakeholders and domain experts, this is not a purely technical decision.</p>
<p><strong>Can I just remove the protected attribute from the model?</strong> No. This is "fairness through unawareness" and it doesn't work because other features (zip code, name patterns, school attended) can serve as proxies. You need to test outcomes by protected group regardless.</p>
<p><strong>Is there a legal requirement for algorithmic fairness?</strong> Increasingly, yes. The EU AI Act classifies hiring and credit models as "high-risk" requiring bias audits. US agencies (EEOC, CFPB) use disparate impact analysis. Several US states have enacted algorithmic accountability laws. The legal landscape is evolving rapidly.</p>
<h2>Continue Learning</h2>
<ul>
<li><a href="Data-Ethics-in-R.html">Data Ethics in R</a>, The broader ethical framework</li>
<li><a href="Bias-in-Data-and-Models.html">Bias in Data & Models</a>, Detecting bias at the data level</li>
<li><a href="Synthetic-Data-in-R.html">Synthetic Data in R</a>, Generate unbiased synthetic datasets</li>
</ul>
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