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<!DOCTYPE html>
<html lang="en">
<head>
<title>A/B Testing Exercises in R: 18 Real-World Practice Problems</title>
<meta charset="utf-8">
<meta name="Description" content="Solve 18 A/B testing exercises in R covering sample size, prop.test, Welch t-test, peeking, Bonferroni, dropout inflation, and end-to-end analysis.">
<meta name="Keywords" content="a/b testing exercises R, a/b test sample size, pwr.2p.test exercises, prop.test a/b, peeking problem R, minimum detectable effect, ab test dropout, novelty effect R">
<meta name="Distribution" content="Global">
<meta name="Author" content="Selva Prabhakaran">
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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 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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 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(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 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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 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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 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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 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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 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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 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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 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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 expanded"><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" 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<h1>A/B Testing Exercises in R: 18 Real-World Practice Problems</h1>
<p class="lead">These 18 A/B testing exercises in R cover the end-to-end experiment workflow: sizing tests with <code>pwr</code>, analysing proportions with <code>prop.test()</code>, comparing skewed continuous metrics, quantifying the <a class="auto-link" href="AB-Testing-in-R.html" title="A/B Testing in R: Plan Your Sample Size, Analyse Correctly, and Know When to Stop">peeking problem</a>, correcting for multiple metrics, and writing a stakeholder-ready summary. Each problem hides a full runnable solution; try it yourself first.</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 17, 2026 · Last updated May 17, 2026</div>
<div class="engagement-header" data-difficulty="Mixed" data-time="45" data-exercises="18" data-xp="270"></div>
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<div class="webr-editor" data-language="r"><span class="cl"><span class="nf">library</span>(pwr)</span>
<span class="cl"><span class="nf">library</span>(dplyr)</span>
<span class="cl"><span class="nf">library</span>(tidyr)</span>
<span class="cl"><span class="nf">library</span>(broom)</span>
<span class="cl"><span class="nf">library</span>(ggplot2)</span></div>
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<h2>Section 1. Sample size and power planning (4 problems)</h2>
<section class="exercise" data-exercise-id="AB-Testing-Exercises-in-R-ex-1-1" data-grade-mode="output-compare" data-difficulty="beginner">
<h3 class="exercise-title">Exercise 1.1: Compute per-arm sample size for a two-proportion test</h3>
<p class="exercise-task"><strong>Task:</strong> A growth team at a B2C app wants to test a new checkout flow against the current one. Baseline conversion is 4%, the PM wants to detect an absolute lift to 5% with 80% power at a 5% <a class="auto-link" href="Hypothesis-Testing-in-R.html" title="Hypothesis Testing in R: Understand the Framework, Not Just the p-Value">significance level</a>. Use <code>pwr.2p.test()</code> with <code>ES.h()</code> to compute the per-arm sample size and save the full result object to <code>ex_1_1</code>.</p>
<div class="exercise-expected">
<p><strong>Expected result:</strong></p>
<pre><code>#> Difference of proportion power calculation for binomial distribution (arcsine transformation)
#>
#> h = 0.04832
#> n = 3364.181
#> sig.level = 0.05
#> power = 0.8
#> alternative = two.sided
#>
#> NOTE: same sample sizes</code></pre>
</div>
<p><strong>Difficulty:</strong> Beginner</p>
<div class="exercise-hints" hidden><p>Power, significance, <a class="auto-link" href="Effect-Size-in-R.html" title="Effect Size in R: The Number p-Values Never Tell You (Cohen's d, η², and r)">effect size</a>, and sample size form one locked system: fix any three and the fourth is determined.</p><p>Convert the two proportions into <a class="auto-link" href="One-Sample-Proportion-z-Test-in-R.html" title="One-Sample Proportion z-Test in R: Large Sample Inference">Cohen's h</a> with <code>ES.h(p1 = 0.05, p2 = 0.04)</code>, pass it as <code>h</code> along with <code>sig.level</code> and <code>power</code>, and leave the sample-size argument out.</p></div>
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<span class="cl">ex_1_1</span></div>
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<div class="webr-editor" data-language="r"><span class="cl">ex_1_1 <span class="o"><-</span> <span class="nf">pwr.2p.test</span>(</span>
<span class="cl"> h <span class="o">=</span> <span class="nf">ES.h</span>(p1 <span class="o">=</span> <span class="m">0.05</span>, p2 <span class="o">=</span> <span class="m">0.04</span>),</span>
<span class="cl"> sig.level <span class="o">=</span> <span class="m">0.05</span>,</span>
<span class="cl"> power <span class="o">=</span> <span class="m">0.80</span></span>
<span class="cl">)</span>
<span class="cl">ex_1_1</span>
<span class="cl"><span class="c1">#> Difference of proportion power calculation for binomial distribution (arcsine transformation)</span></span>
<span class="cl"><span class="c1">#></span></span>
<span class="cl"><span class="c1">#> h = 0.04832381</span></span>
<span class="cl"><span class="c1">#> n = 3364.181</span></span>
<span class="cl"><span class="c1">#> sig.level = 0.05</span></span>
<span class="cl"><span class="c1">#> power = 0.8</span></span>
<span class="cl"><span class="c1">#> alternative = two.sided</span></span>
<span class="cl"><span class="c1">#></span></span>
<span class="cl"><span class="c1">#> NOTE: same sample sizes</span></span></div>
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<p class="exercise-explanation"><strong>Explanation:</strong> <code>ES.h()</code> converts two proportions into Cohen's h, an arcsine-transformed effect size that stabilises variance across the 0-1 range. Plugging h into <code>pwr.2p.test()</code> lets you solve for any one missing piece (<code>n</code>, <code>power</code>, <code>sig.level</code>, or <code>h</code>); pass three and leave the fourth as <code>NULL</code>. A common mistake is plugging the raw difference <code>p1 - p2 = 0.01</code> instead of <code>h</code>: that conflates effect size with proportion units and undersizes the test by roughly 20% at low baselines.</p>
</details>
</section>
<section class="exercise" data-exercise-id="AB-Testing-Exercises-in-R-ex-1-2" data-grade-mode="output-compare" data-difficulty="beginner">
<h3 class="exercise-title">Exercise 1.2: Sample size for a continuous metric with pwr.t.test</h3>
<p class="exercise-task"><strong>Task:</strong> A finance team wants to detect a $4 lift on average order value (current AOV = $48, sd $32) at 80% power and 5% alpha using a two-sample <a class="auto-link" href="t-Test-Exercises-in-R.html" title="t-Test Exercises in R: 12 One, Two & Paired Sample Problems, Solved Step-by-Step">Welch t-test</a>. Use <code>pwr.t.test()</code> to compute the per-arm sample size and save the result object to <code>ex_1_2</code>.</p>
<div class="exercise-expected">
<p><strong>Expected result:</strong></p>
<pre><code>#> Two-sample t test power calculation
#>
#> n = 1004.214
#> d = 0.125
#> sig.level = 0.05
#> power = 0.8
#> alternative = two.sided
#>
#> NOTE: n is number in *each* group</code></pre>
</div>
<p><strong>Difficulty:</strong> Beginner</p>
<div class="exercise-hints" hidden><p>A continuous-metric effect size is the mean difference rescaled into standard-deviation units.</p><p>Give <code>pwr.t.test()</code> a <code>d</code> of <code>4 / 32</code>, set <code>sig.level</code> and <code>power</code>, and pass <code>type = "two.sample"</code>.</p></div>
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<div class="webr-editor" data-language="r"><span class="cl">ex_1_2 <span class="o"><-</span> <span class="nf">pwr.t.test</span>(</span>
<span class="cl"> d <span class="o">=</span> <span class="m">4</span> <span class="o">/</span> <span class="m">32</span>,</span>
<span class="cl"> sig.level <span class="o">=</span> <span class="m">0.05</span>,</span>
<span class="cl"> power <span class="o">=</span> <span class="m">0.80</span>,</span>
<span class="cl"> type <span class="o">=</span> <span class="s">"two.sample"</span>,</span>
<span class="cl"> alternative <span class="o">=</span> <span class="s">"two.sided"</span></span>
<span class="cl">)</span>
<span class="cl">ex_1_2</span>
<span class="cl"><span class="c1">#> Two-sample t test power calculation</span></span>
<span class="cl"><span class="c1">#></span></span>
<span class="cl"><span class="c1">#> n = 1004.214</span></span>
<span class="cl"><span class="c1">#> d = 0.125</span></span>
<span class="cl"><span class="c1">#> sig.level = 0.05</span></span>
<span class="cl"><span class="c1">#> power = 0.8</span></span>
<span class="cl"><span class="c1">#> alternative = two.sided</span></span>
<span class="cl"><span class="c1">#></span></span>
<span class="cl"><span class="c1">#> NOTE: n is number in *each* group</span></span></div>
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<p class="exercise-explanation"><strong>Explanation:</strong> Cohen's d for two samples is <code>(mu1 - mu2) / sd_pooled</code>; here it collapses to <code>4 / 32 = 0.125</code>, a "small" effect. The <code>type = "two.sample"</code> argument is critical: dropping it defaults to a one-sample test, which dramatically undersizes the experiment. For unequal sds use <code>pwr.t2n.test()</code> with the more conservative pooled sd, or simulate power directly since <code>pwr.t.test()</code> assumes equal variances under the hood.</p>
</details>
</section>
<section class="exercise" data-exercise-id="AB-Testing-Exercises-in-R-ex-1-3" data-grade-mode="output-compare" data-difficulty="intermediate">
<h3 class="exercise-title">Exercise 1.3: Solve for the minimum detectable effect under a fixed sample budget</h3>
<p class="exercise-task"><strong>Task:</strong> Engineering capped the experiment at 5,000 users per arm. With baseline conversion 4%, alpha 0.05, and 80% power, compute the minimum detectable Cohen's h, then back-translate it into an absolute lift (proportion units) and a relative lift (percent). Save a named numeric vector <code>ex_1_3</code> with elements <code>h</code>, <code>mde_abs</code>, and <code>mde_rel</code>.</p>
<div class="exercise-expected">
<p><strong>Expected result:</strong></p>
<pre><code>#> h mde_abs mde_rel
#> 0.0560422 0.0117042 29.2604499</code></pre>
</div>
<p><strong>Difficulty:</strong> Intermediate</p>
<div class="exercise-hints" hidden><p>With sample size fixed, the unknown flips to effect size, which you then translate back into proportion units.</p><p>Call <code>pwr.2p.test()</code> with <code>n</code>, <code>sig.level</code>, and <code>power</code> set, read <code>$h</code>, and invert the arcsine transform with <code>sin(asin(sqrt(0.04)) + h/2)^2</code>.</p></div>
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<span class="cl">ex_1_3</span></div>
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<div class="webr-editor" data-language="r"><span class="cl">h_mde <span class="o"><-</span> <span class="nf">pwr.2p.test</span>(n <span class="o">=</span> <span class="m">5000</span>, sig.level <span class="o">=</span> <span class="m">0.05</span>, power <span class="o">=</span> <span class="m">0.80</span>)<span class="o">$</span>h</span>
<span class="cl">p1 <span class="o"><-</span> (<span class="nf">sin</span>(<span class="nf">asin</span>(<span class="nf">sqrt</span>(<span class="m">0.04</span>)) <span class="o">+</span> h_mde <span class="o">/</span> <span class="m">2</span>))<span class="o">^</span><span class="m">2</span></span>
<span class="cl">mde_abs <span class="o"><-</span> p1 <span class="o">-</span> <span class="m">0.04</span></span>
<span class="cl">mde_rel <span class="o"><-</span> <span class="m">100</span> <span class="o">*</span> mde_abs <span class="o">/</span> <span class="m">0.04</span></span>
<span class="cl"></span>
<span class="cl">ex_1_3 <span class="o"><-</span> <span class="nf">c</span>(h <span class="o">=</span> h_mde, mde_abs <span class="o">=</span> mde_abs, mde_rel <span class="o">=</span> mde_rel)</span>
<span class="cl">ex_1_3</span>
<span class="cl"><span class="c1">#> h mde_abs mde_rel</span></span>
<span class="cl"><span class="c1">#> 0.0560422 0.0117042 29.2604499</span></span></div>
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<p class="exercise-explanation"><strong>Explanation:</strong> With a sample cap, the meaningful question flips from "how many users?" to "how big a lift must we believe in?". The h returned by <code>pwr.2p.test()</code> is in arcsine units; inverting <code>2*asin(sqrt(p))</code> back to a proportion gives the detectable treatment rate. At 4% baseline with 5,000 per arm, you can only see lifts of ~29% relative or larger; smaller lifts will look like noise. This is the right diagnostic to run before launching, not after a flat result.</p>
</details>
</section>
<section class="exercise" data-exercise-id="AB-Testing-Exercises-in-R-ex-1-4" data-grade-mode="output-compare" data-difficulty="intermediate">
<h3 class="exercise-title">Exercise 1.4: Build a power curve over a grid of sample sizes</h3>
<p class="exercise-task"><strong>Task:</strong> A marketing analyst wants to show stakeholders how power grows with sample size. Compute the achieved power for <code>n = seq(2000, 20000, by = 2000)</code> per arm, assuming baseline 5%, target 6%, and alpha 0.05, using <code>pwr.2p.test()</code>. Save a tibble <code>ex_1_4</code> with columns <code>n</code> and <code>power</code>.</p>
<div class="exercise-expected">
<p><strong>Expected result:</strong></p>
<pre><code>#> # A tibble: 10 x 2
#> n power
#> <dbl> <dbl>
#> 1 2000 0.278
#> 2 4000 0.495
#> 3 6000 0.666
#> 4 8000 0.787
#> 5 10000 0.869
#> 6 12000 0.921
#> 7 14000 0.954
#> 8 16000 0.974
#> 9 18000 0.985
#> 10 20000 0.992</code></pre>
</div>
<p><strong>Difficulty:</strong> Intermediate</p>
<div class="exercise-hints" hidden><p>Achieved power is what you compute when sample size is the input rather than the quantity being solved for.</p><p>Iterate over the n grid with <code>sapply()</code>, calling <code>pwr.2p.test(h = ..., n = nn, sig.level = 0.05)$power</code> for each, and collect the results into a tibble with <code>mutate()</code>.</p></div>
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<div class="webr-editor" data-language="r"><span class="cl">h_target <span class="o"><-</span> <span class="nf">ES.h</span>(p1 <span class="o">=</span> <span class="m">0.06</span>, p2 <span class="o">=</span> <span class="m">0.05</span>)</span>
<span class="cl"></span>
<span class="cl">ex_1_4 <span class="o"><-</span> <span class="nf">tibble</span>(n <span class="o">=</span> <span class="nf">seq</span>(<span class="m">2000</span>, <span class="m">20000</span>, by <span class="o">=</span> <span class="m">2000</span>)) <span class="o">|></span></span>
<span class="cl"> <span class="nf">mutate</span>(power <span class="o">=</span> <span class="nf">sapply</span>(n, <span class="kr">function</span>(nn) {</span>
<span class="cl"> <span class="nf">pwr.2p.test</span>(h <span class="o">=</span> h_target, n <span class="o">=</span> nn, sig.level <span class="o">=</span> <span class="m">0.05</span>)<span class="o">$</span>power</span>
<span class="cl"> }))</span>
<span class="cl">ex_1_4</span>
<span class="cl"><span class="c1">#> # A tibble: 10 x 2</span></span>
<span class="cl"><span class="c1">#> n power</span></span>
<span class="cl"><span class="c1">#> <dbl> <dbl></span></span>
<span class="cl"><span class="c1">#> 1 2000 0.278</span></span>
<span class="cl"><span class="c1">#> 2 4000 0.495</span></span>
<span class="cl"><span class="c1">#> 3 6000 0.666</span></span>
<span class="cl"><span class="c1">#> 4 8000 0.787</span></span>
<span class="cl"><span class="c1">#> 5 10000 0.869</span></span>
<span class="cl"><span class="c1">#> # 5 more rows hidden</span></span></div>
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<p class="exercise-explanation"><strong>Explanation:</strong> Power curves communicate experiment cost far more effectively than a single "need 14,000 users" number. The curve is concave: doubling n from 2,000 to 4,000 buys you 22 power points; doubling again from 10,000 to 20,000 only buys 12. Plot this with <code>geom_line()</code> and add a horizontal line at 0.8 so stakeholders can read off the inflection point. <code>sapply()</code> over the n grid is fine here; for many parameter combinations, <code>purrr::map_dfr()</code> over an <code>expand_grid()</code> is cleaner.</p>
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</section>
<h2>Section 2. Two-proportion analysis (3 problems)</h2>
<section class="exercise" data-exercise-id="AB-Testing-Exercises-in-R-ex-2-1" data-grade-mode="output-compare" data-difficulty="beginner">
<h3 class="exercise-title">Exercise 2.1: Run a vanilla prop.test on observed A/B results</h3>
<p class="exercise-task"><strong>Task:</strong> The experimentation team wrapped a checkout test with 412 conversions in 9,800 control users and 478 conversions in 9,750 treatment users. Use <code>prop.test()</code> to compare the two conversion rates and save the htest object to <code>ex_2_1</code>.</p>
<div class="exercise-expected">
<p><strong>Expected result:</strong></p>
<pre><code>#> 2-sample test for equality of proportions with continuity correction
#>
#> data: c(412, 478) out of c(9800, 9750)
#> X-squared = 5.4213, df = 1, p-value = 0.01992
#> alternative hypothesis: two.sided
#> 95 percent confidence interval:
#> -0.012843 -0.001127
#> sample estimates:
#> prop 1 prop 2
#> 0.04204082 0.04902564</code></pre>
</div>
<p><strong>Difficulty:</strong> Beginner</p>
<div class="exercise-hints" hidden><p>Comparing two conversion rates means comparing two success counts against their two totals.</p><p>Pass the conversions as <code>x = c(412, 478)</code> and the totals as <code>n = c(9800, 9750)</code> to <code>prop.test()</code>.</p></div>
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<div class="webr-editor" data-language="r"><span class="cl">ex_2_1 <span class="o"><-</span> <span class="nf">prop.test</span>(</span>
<span class="cl"> x <span class="o">=</span> <span class="nf">c</span>(<span class="m">412</span>, <span class="m">478</span>),</span>
<span class="cl"> n <span class="o">=</span> <span class="nf">c</span>(<span class="m">9800</span>, <span class="m">9750</span>)</span>
<span class="cl">)</span>
<span class="cl">ex_2_1</span>
<span class="cl"><span class="c1">#> 2-sample test for equality of proportions with continuity correction</span></span>
<span class="cl"><span class="c1">#></span></span>
<span class="cl"><span class="c1">#> data: c(412, 478) out of c(9800, 9750)</span></span>
<span class="cl"><span class="c1">#> X-squared = 5.4213, df = 1, p-value = 0.01992</span></span>
<span class="cl"><span class="c1">#> alternative hypothesis: two.sided</span></span>
<span class="cl"><span class="c1">#> 95 percent confidence interval:</span></span>
<span class="cl"><span class="c1">#> -0.012843 -0.001127</span></span>
<span class="cl"><span class="c1">#> sample estimates:</span></span>
<span class="cl"><span class="c1">#> prop 1 prop 2</span></span>
<span class="cl"><span class="c1">#> 0.04204082 0.04902564</span></span></div>
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<p class="exercise-explanation"><strong>Explanation:</strong> <code>prop.test()</code> is the workhorse two-sample comparison: pass conversions as <code>x</code> and totals as <code>n</code>, both length-2. By default it applies Yates' continuity correction, which inflates the chi-square statistic slightly and is conservative at small counts; pass <code>correct = FALSE</code> for the uncorrected z-test that most modern A/B platforms report. The CI here is for <code>prop 1 - prop 2</code>, so a wholly negative interval means treatment beats control; flip your sign convention only if your stakeholder reports lift as <code>treatment - control</code>.</p>
</details>
</section>
<section class="exercise" data-exercise-id="AB-Testing-Exercises-in-R-ex-2-2" data-grade-mode="self-check" data-difficulty="intermediate">
<h3 class="exercise-title">Exercise 2.2: Tidy the prop.test result with broom</h3>
<p class="exercise-task"><strong>Task:</strong> Take the same A/B data from Exercise 2.1 (412/9800 vs 478/9750) and run <code>broom::tidy()</code> on the <code>prop.test()</code> output to produce a one-row tibble. Save the tibble to <code>ex_2_2</code> and confirm it contains both proportion estimates plus the CI for the difference.</p>
<div class="exercise-expected">
<p><strong>Expected result:</strong></p>
<pre><code>#> # A tibble: 1 x 9
#> estimate1 estimate2 statistic p.value parameter conf.low conf.high method alternative
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr> <chr>
#> 1 0.0420 0.0490 5.42 0.0199 1 -0.0128 -0.00113 2-sample test for equality of proportions with c... two.sided</code></pre>
</div>
<p><strong>Difficulty:</strong> Intermediate</p>
<div class="exercise-hints" hidden><p>An htest object prints nicely but is awkward to stack across many tests, so convert it into a single data row.</p><p>Pipe the <code>prop.test()</code> result into <code>broom::tidy()</code> to get a one-row tibble.</p></div>
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<div class="webr-editor" data-language="r"><span class="cl">ex_2_2 <span class="o"><-</span> <span class="nf">prop.test</span>(<span class="nf">c</span>(<span class="m">412</span>, <span class="m">478</span>), <span class="nf">c</span>(<span class="m">9800</span>, <span class="m">9750</span>)) <span class="o">|></span></span>
<span class="cl"> broom<span class="o">::</span><span class="nf">tidy</span>()</span>
<span class="cl">ex_2_2</span>
<span class="cl"><span class="c1">#> # A tibble: 1 x 9</span></span>
<span class="cl"><span class="c1">#> estimate1 estimate2 statistic p.value parameter conf.low conf.high method alternative</span></span>
<span class="cl"><span class="c1">#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <chr> <chr></span></span>
<span class="cl"><span class="c1">#> 1 0.0420 0.0490 5.42 0.0199 1 -0.0128 -0.00113 2-sample test for equality of proportions with c... two.sided</span></span></div>
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<p class="exercise-explanation"><strong>Explanation:</strong> Wrapping <code>prop.test()</code> in <code>broom::tidy()</code> is what turns a printable htest into a row you can bind across dozens of tests. Use this inside <code>purrr::map_dfr()</code> when you sweep over many metric/segment combinations; you get a single tibble where each row is one A/B comparison, ready for <code>arrange(p.value)</code> or <code>mutate(p_adj = p.adjust(p.value, "BH"))</code>. <code>glance()</code> is an alternative for some htest classes but <code>tidy()</code> is the right choice for prop.test because it surfaces both estimates and the CI in one row.</p>
</details>
</section>
<section class="exercise" data-exercise-id="AB-Testing-Exercises-in-R-ex-2-3" data-grade-mode="output-compare" data-difficulty="intermediate">
<h3 class="exercise-title">Exercise 2.3: Chi-square test on a 2x2 churn contingency table</h3>
<p class="exercise-task"><strong>Task:</strong> A retention team prepared a <a class="auto-link" href="Fishers-Exact-Test-in-R.html" title="Fisher's Exact Test in R: 2×2 Tables, Odds Ratios & Small Samples">2x2 contingency table</a> comparing 30-day churn between control and treatment arms. Control: 1,180 churned, 2,820 retained out of 4,000. Treatment: 1,080 churned, 2,920 retained out of 4,000. Build the matrix with row names "control" and "treatment", column names "churned" and "retained", run <code>chisq.test()</code>, and save the result to <code>ex_2_3</code>.</p>
<div class="exercise-expected">
<p><strong>Expected result:</strong></p>
<pre><code>#> Pearson's Chi-squared test with Yates' continuity correction
#>
#> data: m
#> X-squared = 6.0593, df = 1, p-value = 0.01383</code></pre>
</div>
<p><strong>Difficulty:</strong> Intermediate</p>
<div class="exercise-hints" hidden><p>A contingency table tests whether the row classification and column classification are independent of each other.</p><p>Pass the matrix <code>m</code> directly to <code>chisq.test()</code>.</p></div>
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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">Your turn</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">m <span class="o"><-</span> <span class="nf">matrix</span>(</span>
<span class="cl"> <span class="nf">c</span>(<span class="m">1180</span>, <span class="m">2820</span>, <span class="m">1080</span>, <span class="m">2920</span>),</span>
<span class="cl"> nrow <span class="o">=</span> <span class="m">2</span>, byrow <span class="o">=</span> <span class="kc">TRUE</span>,</span>
<span class="cl"> dimnames <span class="o">=</span> <span class="nf">list</span>(</span>
<span class="cl"> variant <span class="o">=</span> <span class="nf">c</span>(<span class="s">"control"</span>, <span class="s">"treatment"</span>),</span>
<span class="cl"> churn <span class="o">=</span> <span class="nf">c</span>(<span class="s">"churned"</span>, <span class="s">"retained"</span>)</span>
<span class="cl"> )</span>
<span class="cl">)</span>
<span class="cl">ex_2_3 <span class="o"><-</span> <span class="c1"># your code here</span></span>
<span class="cl">ex_2_3</span></div>
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<details class="exercise-solution">
<summary>Click to reveal solution</summary>
<div class="webr-container" data-block-title="Solution">
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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">Solution</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">m <span class="o"><-</span> <span class="nf">matrix</span>(</span>
<span class="cl"> <span class="nf">c</span>(<span class="m">1180</span>, <span class="m">2820</span>, <span class="m">1080</span>, <span class="m">2920</span>),</span>
<span class="cl"> nrow <span class="o">=</span> <span class="m">2</span>, byrow <span class="o">=</span> <span class="kc">TRUE</span>,</span>
<span class="cl"> dimnames <span class="o">=</span> <span class="nf">list</span>(</span>
<span class="cl"> variant <span class="o">=</span> <span class="nf">c</span>(<span class="s">"control"</span>, <span class="s">"treatment"</span>),</span>
<span class="cl"> churn <span class="o">=</span> <span class="nf">c</span>(<span class="s">"churned"</span>, <span class="s">"retained"</span>)</span>
<span class="cl"> )</span>
<span class="cl">)</span>
<span class="cl">ex_2_3 <span class="o"><-</span> <span class="nf">chisq.test</span>(m)</span>