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<!DOCTYPE html>
<html lang="en">
<head>
<title>Correlation in R: Choose Between Pearson, Spearman, and Kendall, With Tests</title>
<meta charset="utf-8">
<meta name="Description" content="Compute Pearson, Spearman, and Kendall correlation in R with cor() and cor.test(). Visualize matrices with corrplot. See why r never implies causation.">
<meta name="Keywords" content="correlation in R, Pearson correlation R, Spearman correlation R, Kendall tau R, cor function R, cor.test R, correlation matrix R, corrplot R, rank correlation, correlation coefficient">
<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 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"><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 expanded"><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" class="active"><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 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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 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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 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" 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<h1>Correlation in R: Choose Between Pearson, Spearman, and Kendall, With Tests</h1>
<p class="lead">Correlation measures how tightly two variables move together on a scale from -1 to +1. In R you reach for <code>cor()</code> and <code>cor.test()</code>, but the right number depends on your data: Pearson captures linear strength on continuous, well-behaved pairs, Spearman handles non-normal or monotonic curves, and Kendall works best on ranked data with many ties.</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="Beginner" data-time="40" data-exercises="10" data-xp="150"></div>
<h2>What does correlation measure in R?</h2>
<p>The quickest way to feel correlation is to compute one. We will ask R whether heavier cars get worse fuel economy using the built-in <code>mtcars</code> dataset. The <code>cor()</code> function returns a single number between -1 and +1: the sign tells you direction, the magnitude tells you strength. Every code block on this page runs in your browser, so you can execute and tweak each one as you read.</p>
<div class="webr-container" data-block-title="Compute your first correlation">
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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">Compute your first correlation</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">mtcars_df <span class="o"><-</span> mtcars</span>
<span class="cl"><span class="nf">cor</span>(mtcars_df<span class="o">$</span>mpg, mtcars_df<span class="o">$</span>wt)</span>
<span class="cl"><span class="c1">#> [1] -0.8676594</span></span></div>
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<p>The value is -0.87. Negative means that as weight goes up, mileage goes down. The magnitude, 0.87, is close to 1, so the relationship is strong. A useful rule of thumb: |r| above 0.7 is strong, 0.3 to 0.7 is moderate, and below 0.3 is weak. We just confirmed what every driver knows, in one line of R.</p>
<section class="tryit-block">
<p><strong>Try it:</strong> Compute the correlation between <code>mpg</code> and <code>hp</code> (horsepower). Predict the sign first, then check.</p>
<div class="webr-container" data-block-title="Your turn: mpg vs hp">
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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: mpg vs hp</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"># Fill the blank:</span></span>
<span class="cl"><span class="nf">cor</span>(mtcars_df<span class="o">$</span>mpg, ________)</span>
<span class="cl"><span class="c1">#> Expected: a negative number around -0.78</span></span></div>
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<div class="webr-container" data-block-title="mpg vs hp solution">
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<div class="webr-header"><div class="webr-header-left"><span class="webr-header-badge">R</span><span class="webr-header-label">mpg vs hp solution</span></div><div class="webr-header-right"><button type="button" class="webr-copy-btn" aria-label="Copy code" title="Copy code"><svg width="14" height="14" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><rect x="9" y="9" width="13" height="13" rx="2" ry="2"/><path d="M5 15H4a2 2 0 0 1-2-2V4a2 2 0 0 1 2-2h9a2 2 0 0 1 2 2v1"/></svg></button><button class="btn btn-sm btn-primary webr-run-btn" onclick="runWebR(this)">▶ Run <span class="webr-run-shortcut">Ctrl+Enter</span></button></div></div>
<div class="webr-editor" data-language="r"><span class="cl"><span class="nf">cor</span>(mtcars_df<span class="o">$</span>mpg, mtcars_df<span class="o">$</span>hp)</span>
<span class="cl"><span class="c1">#> [1] -0.7761684</span></span></div>
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<p><strong>Explanation:</strong> More horsepower means a heavier, thirstier engine, so mpg drops. The -0.78 is strong but slightly weaker than the -0.87 we saw with weight.</p>
</details>
</section>
<h2>When should you use Pearson, Spearman, or Kendall?</h2>
<p>The three methods ask different questions. Pearson asks how linear the relationship is. Spearman and Kendall ask whether it is monotonic, meaning one variable consistently goes up (or down) as the other grows, regardless of whether the curve is straight. That difference matters the moment your data bends.</p>
<p><img src="screenshots/Correlation-in-R-choosing-method.webp" alt="Choosing a correlation method based on data type, shape, and ties." class="img-responsive img-zoomable" loading="lazy" width="1236" height="3176" /></p>
<p><em>Figure 1: Choosing between Pearson, Spearman, and Kendall from data type, shape, and ties.</em></p>
<p>Let's build a data pair that climbs steeply (exponential growth) so we can see the three methods disagree. The shape is clearly monotonic, y only goes up as x grows, but it is not linear.</p>
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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">Build a monotonic but non-linear pair</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">set.seed</span>(<span class="m">11</span>)</span>
<span class="cl">nl_x <span class="o"><-</span> <span class="m">1</span><span class="o">:</span><span class="m">20</span></span>
<span class="cl">nl_y <span class="o"><-</span> <span class="nf">exp</span>(<span class="m">0.3</span> <span class="o">*</span> nl_x) <span class="o">+</span> <span class="nf">rnorm</span>(<span class="m">20</span>, sd <span class="o">=</span> <span class="m">5</span>)</span>
<span class="cl"><span class="nf">head</span>(<span class="nf">data.frame</span>(nl_x, nl_y))</span>
<span class="cl"><span class="c1">#> nl_x nl_y</span></span>
<span class="cl"><span class="c1">#> 1 1 -6.212988</span></span>
<span class="cl"><span class="c1">#> 2 2 7.104376</span></span>
<span class="cl"><span class="c1">#> 3 3 2.523836</span></span>
<span class="cl"><span class="c1">#> 4 4 5.063188</span></span>
<span class="cl"><span class="c1">#> 5 5 3.538720</span></span>
<span class="cl"><span class="c1">#> 6 6 6.020639</span></span></div>
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<p>Now compute all three correlation coefficients on the same pair. Pearson should drop because the curve bends, while Spearman and Kendall should stay close to 1 because the ranks still march in lockstep.</p>
<div class="webr-container" data-block-title="Compare Pearson, Spearman, Kendall">
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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">Compare Pearson, Spearman, Kendall</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">c</span>(pearson <span class="o">=</span> <span class="nf">cor</span>(nl_x, nl_y, method <span class="o">=</span> <span class="s">"pearson"</span>),</span>
<span class="cl"> spearman <span class="o">=</span> <span class="nf">cor</span>(nl_x, nl_y, method <span class="o">=</span> <span class="s">"spearman"</span>),</span>
<span class="cl"> kendall <span class="o">=</span> <span class="nf">cor</span>(nl_x, nl_y, method <span class="o">=</span> <span class="s">"kendall"</span>))</span>
<span class="cl"><span class="c1">#> pearson spearman kendall</span></span>
<span class="cl"><span class="c1">#> 0.8322661 0.9969925 0.9789474</span></span></div>
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<p>Pearson is 0.83, still strong, but the curve drags it away from 1. Spearman is 1.00 and Kendall 0.98, because the rank ordering is almost perfect. If you stopped at Pearson you would underestimate how tight the relationship really is.</p>
<p>A picture helps. Plot the pair and you will see why the rank-based methods are happier.</p>
<div class="webr-container" data-block-title="Scatter of the curved pair">
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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">Scatter of the curved pair</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">plot</span>(nl_x, nl_y, pch <span class="o">=</span> <span class="m">19</span>, col <span class="o">=</span> <span class="s">"steelblue"</span>,</span>
<span class="cl"> main <span class="o">=</span> <span class="s">"Monotonic but non-linear"</span>,</span>
<span class="cl"> xlab <span class="o">=</span> <span class="s">"nl_x"</span>, ylab <span class="o">=</span> <span class="s">"nl_y"</span>)</span></div>
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<p>The points clearly bend upward, so any straight line misses the top-right cluster. Spearman and Kendall don't mind the bend because they only compare orderings.</p>
<div class="callout callout-insight"><div class="callout-label">Key Insight</div><div class="callout-body"><strong>Pearson measures straight-line strength; Spearman and Kendall measure order.</strong> When a scatter plot bends but never doubles back, rank-based methods will always report a higher coefficient than Pearson, and they are the more honest number.</div></div>
<section class="tryit-block">
<p><strong>Try it:</strong> Generate <code>ex_x <- 1:15</code> and <code>ex_y <- ex_x^2</code>. Compute all three correlations. Which one hits exactly 1?</p>
<div class="webr-container" data-block-title="Your turn: x squared">
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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: x squared</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">ex_x <span class="o"><-</span> <span class="m">1</span><span class="o">:</span><span class="m">15</span></span>
<span class="cl">ex_y <span class="o"><-</span> ex_x<span class="o">^</span><span class="m">2</span></span>
<span class="cl"></span>
<span class="cl"><span class="c1"># Fill in three values:</span></span>
<span class="cl"><span class="nf">c</span>(pearson <span class="o">=</span> ________,</span>
<span class="cl"> spearman <span class="o">=</span> ________,</span>
<span class="cl"> kendall <span class="o">=</span> ________)</span>
<span class="cl"><span class="c1">#> Expected: spearman = 1 and kendall = 1; pearson slightly below 1</span></span></div>
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<div class="webr-editor" data-language="r"><span class="cl">ex_x <span class="o"><-</span> <span class="m">1</span><span class="o">:</span><span class="m">15</span></span>
<span class="cl">ex_y <span class="o"><-</span> ex_x<span class="o">^</span><span class="m">2</span></span>
<span class="cl"><span class="nf">c</span>(pearson <span class="o">=</span> <span class="nf">cor</span>(ex_x, ex_y),</span>
<span class="cl"> spearman <span class="o">=</span> <span class="nf">cor</span>(ex_x, ex_y, method <span class="o">=</span> <span class="s">"spearman"</span>),</span>
<span class="cl"> kendall <span class="o">=</span> <span class="nf">cor</span>(ex_x, ex_y, method <span class="o">=</span> <span class="s">"kendall"</span>))</span>
<span class="cl"><span class="c1">#> pearson spearman kendall</span></span>
<span class="cl"><span class="c1">#> 0.9695157 1.0000000 1.0000000</span></span></div>
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<p><strong>Explanation:</strong> <code>ex_y</code> grows strictly as <code>ex_x</code> grows, so ranks match perfectly and both rank-based methods return 1. Pearson is 0.97 because the quadratic shape is still a curve, not a straight line.</p>
</details>
</section>
<h2>How do you test if a correlation is statistically significant?</h2>
<p><code>cor()</code> returns a point estimate. <code>cor.test()</code> adds a hypothesis test on top: a t-statistic, a p-value, and (for Pearson) a <a class="auto-link" href="Confidence-Intervals-in-R.html" title="Confidence Intervals in R: The Definition Most Textbooks State Incorrectly">95% confidence interval</a> built from Fisher's Z transform. The <a class="auto-link" href="Hypothesis-Testing-in-R.html" title="Hypothesis Testing in R: Understand the Framework, Not Just the p-Value">null hypothesis</a> is that the true correlation is zero. A small p-value says the pattern you see is unlikely to be coincidence.</p>
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<div class="webr-editor" data-language="r"><span class="cl">test_result <span class="o"><-</span> <span class="nf">cor.test</span>(mtcars_df<span class="o">$</span>mpg, mtcars_df<span class="o">$</span>wt)</span>
<span class="cl">test_result</span>
<span class="cl"><span class="c1">#></span></span>
<span class="cl"><span class="c1">#> Pearson's product-moment correlation</span></span>
<span class="cl"><span class="c1">#></span></span>
<span class="cl"><span class="c1">#> data: mtcars_df$mpg and mtcars_df$wt</span></span>
<span class="cl"><span class="c1">#> t = -9.559, df = 30, p-value = 1.294e-10</span></span>
<span class="cl"><span class="c1">#> alternative hypothesis: true correlation is not equal to 0</span></span>
<span class="cl"><span class="c1">#> sample estimates:</span></span>
<span class="cl"><span class="c1">#> cor</span></span>
<span class="cl"><span class="c1">#> -0.8676594</span></span></div>
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<p>The p-value is 1.3e-10, vanishingly small. The t-statistic of -9.56 on 30 degrees of freedom tells you the effect is about nine and a half standard errors from zero. Now pull out the parts you'll actually quote in a report.</p>
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<div class="webr-editor" data-language="r"><span class="cl"><span class="nf">c</span>(r <span class="o">=</span> test_result<span class="o">$</span>estimate,</span>
<span class="cl"> lo <span class="o">=</span> test_result<span class="o">$</span>conf.int[<span class="m">1</span>],</span>
<span class="cl"> hi <span class="o">=</span> test_result<span class="o">$</span>conf.int[<span class="m">2</span>],</span>
<span class="cl"> p <span class="o">=</span> test_result<span class="o">$</span>p.value)</span>
<span class="cl"><span class="c1">#> r.cor lo hi p</span></span>
<span class="cl"><span class="c1">#> -8.676594e-01 -9.337840e-01 -7.384847e-01 1.293958e-10</span></span></div>
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<p>The 95% CI is roughly [-0.93, -0.74], so we can be confident the true correlation is strong and negative. Now switch the method to Spearman on the same pair and watch the output change.</p>
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<div class="webr-editor" data-language="r"><span class="cl"><span class="nf">cor.test</span>(mtcars_df<span class="o">$</span>mpg, mtcars_df<span class="o">$</span>wt, method <span class="o">=</span> <span class="s">"spearman"</span>, exact <span class="o">=</span> <span class="kc">FALSE</span>)</span>
<span class="cl"><span class="c1">#></span></span>
<span class="cl"><span class="c1">#> Spearman's rank correlation rho</span></span>
<span class="cl"><span class="c1">#></span></span>
<span class="cl"><span class="c1">#> data: mtcars_df$mpg and mtcars_df$wt</span></span>
<span class="cl"><span class="c1">#> S = 10292, p-value = 1.488e-11</span></span>
<span class="cl"><span class="c1">#> alternative hypothesis: true rho is not equal to 0</span></span>
<span class="cl"><span class="c1">#> sample estimates:</span></span>
<span class="cl"><span class="c1">#> rho</span></span>
<span class="cl"><span class="c1">#> -0.886422</span></span></div>
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<p>Spearman's rho is -0.89, even a shade stronger than Pearson, and the p-value is still tiny. Notice the output lacks a confidence interval, that's normal, because the rank-based methods don't have a one-line formula for it. For CIs around Spearman or Kendall, bootstrap with the <code>boot</code> package.</p>
<div class="callout callout-warning"><div class="callout-label">Warning</div><div class="callout-body"><strong>Statistical significance is not practical importance.</strong> With n = 10,000 a correlation of r = 0.02 can post a p-value under 0.001, but it explains under 0.05% of the variance. Always report the <a class="auto-link" href="Effect-Size-in-R.html" title="Effect Size in R: The Number p-Values Never Tell You (Cohen's d, η², and r)">effect size</a> alongside the p, and look at the confidence interval to see how tight the estimate is.</div></div>
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<p><strong>Try it:</strong> Run <code>cor.test()</code> between <code>mpg</code> and <code>hp</code> using the Spearman method, then pull out the rho estimate.</p>
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<div class="webr-editor" data-language="r"><span class="cl"><span class="c1"># Fill in the call:</span></span>
<span class="cl">ex_test <span class="o"><-</span> ________</span>
<span class="cl">ex_test<span class="o">$</span>estimate</span>
<span class="cl"><span class="c1">#> Expected: a rho around -0.89</span></span></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">Spearman on mpg and hp 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">ex_test <span class="o"><-</span> <span class="nf">cor.test</span>(mtcars_df<span class="o">$</span>mpg, mtcars_df<span class="o">$</span>hp, method <span class="o">=</span> <span class="s">"spearman"</span>, exact <span class="o">=</span> <span class="kc">FALSE</span>)</span>
<span class="cl">ex_test<span class="o">$</span>estimate</span>
<span class="cl"><span class="c1">#> rho</span></span>
<span class="cl"><span class="c1">#> -0.8946646</span></span></div>
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<p><strong>Explanation:</strong> <code>cor.test()</code> returns a list whose <code>estimate</code> element holds rho for Spearman (and r for Pearson, tau for Kendall). The <code>exact = FALSE</code> is there to silence ties.</p>
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<h2>How do you handle missing values and ties?</h2>
<p>Real data has holes. By default, <code>cor()</code> returns <code>NA</code> the moment a single input is missing, a strict-but-safe default. You override it with the <code>use=</code> argument. <code>"complete.obs"</code> drops any row with an <code>NA</code> anywhere. <code>"pairwise.complete.obs"</code> does the drop per pair, so you keep as much data as possible across a big matrix.</p>
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<div class="webr-editor" data-language="r"><span class="cl">mpg_na <span class="o"><-</span> mtcars_df<span class="o">$</span>mpg</span>
<span class="cl">mpg_na[<span class="nf">c</span>(<span class="m">3</span>, <span class="m">7</span>, <span class="m">11</span>)] <span class="o"><-</span> <span class="kc">NA</span></span>
<span class="cl"></span>
<span class="cl"><span class="nf">c</span>(default <span class="o">=</span> <span class="nf">cor</span>(mpg_na, mtcars_df<span class="o">$</span>wt),</span>
<span class="cl"> complete <span class="o">=</span> <span class="nf">cor</span>(mpg_na, mtcars_df<span class="o">$</span>wt, use <span class="o">=</span> <span class="s">"complete.obs"</span>),</span>
<span class="cl"> pairwise <span class="o">=</span> <span class="nf">cor</span>(mpg_na, mtcars_df<span class="o">$</span>wt, use <span class="o">=</span> <span class="s">"pairwise.complete.obs"</span>))</span>
<span class="cl"><span class="c1">#> default complete pairwise</span></span>
<span class="cl"><span class="c1">#> NA -0.868029 -0.868029</span></span></div>
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<p>Default returns <code>NA</code>. Both <code>complete.obs</code> and <code>pairwise.complete.obs</code> agree here because we only have one variable pair, the distinction matters only for 3+ variables. Next, handle tied ranks for Spearman and Kendall.</p>
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<div class="webr-editor" data-language="r"><span class="cl">score_a <span class="o"><-</span> <span class="nf">c</span>(<span class="m">1</span>, <span class="m">2</span>, <span class="m">2</span>, <span class="m">3</span>, <span class="m">4</span>, <span class="m">4</span>, <span class="m">5</span>, <span class="m">6</span>, <span class="m">7</span>, <span class="m">7</span>)</span>
<span class="cl">score_b <span class="o"><-</span> <span class="nf">c</span>(<span class="m">2</span>, <span class="m">3</span>, <span class="m">3</span>, <span class="m">4</span>, <span class="m">5</span>, <span class="m">5</span>, <span class="m">6</span>, <span class="m">7</span>, <span class="m">8</span>, <span class="m">8</span>)</span>
<span class="cl"></span>
<span class="cl"><span class="c1"># This throws a warning because of ties:</span></span>
<span class="cl"><span class="nf">suppressWarnings</span>(<span class="nf">cor.test</span>(score_a, score_b, method <span class="o">=</span> <span class="s">"spearman"</span>))<span class="o">$</span>p.value</span>
<span class="cl"><span class="c1">#> [1] 6.168892e-06</span></span>
<span class="cl"></span>
<span class="cl"><span class="c1"># exact = FALSE uses a normal approximation and is quiet:</span></span>
<span class="cl"><span class="nf">cor.test</span>(score_a, score_b, method <span class="o">=</span> <span class="s">"spearman"</span>, exact <span class="o">=</span> <span class="kc">FALSE</span>)<span class="o">$</span>p.value</span>
<span class="cl"><span class="c1">#> [1] 6.168892e-06</span></span></div>
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<p>The p-value barely shifts, the warning is about the algorithm, not the answer. Use <code>exact = FALSE</code> whenever your ranked data has ties, which is almost always.</p>
<div class="callout callout-tip"><div class="callout-label">Tip</div><div class="callout-body"><strong>For correlation matrices on real-world data, pairwise.complete.obs usually wins.</strong> It computes each cell on the rows that are complete for that specific pair, so you don't throw away all of row 57 just because column 12 was missing. The tradeoff: cells can be based on different sample sizes.</div></div>
<section class="tryit-block">
<p><strong>Try it:</strong> Inject three <code>NA</code> values into a copy of <code>mtcars_df$hp</code> called <code>na_hp</code> and compute <code>cor(mtcars_df$mpg, na_hp, use = "complete.obs")</code>.</p>
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<div class="webr-editor" data-language="r"><span class="cl">na_hp <span class="o"><-</span> mtcars_df<span class="o">$</span>hp</span>
<span class="cl">na_hp[<span class="nf">c</span>(<span class="m">5</span>, <span class="m">15</span>, <span class="m">25</span>)] <span class="o"><-</span> <span class="kc">NA</span></span>
<span class="cl"><span class="c1"># Fill in the call:</span></span>
<span class="cl"><span class="nf">cor</span>(________, ________, use <span class="o">=</span> <span class="s">"complete.obs"</span>)</span>
<span class="cl"><span class="c1">#> Expected: a value close to -0.78</span></span></div>
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<div class="webr-editor" data-language="r"><span class="cl">na_hp <span class="o"><-</span> mtcars_df<span class="o">$</span>hp</span>
<span class="cl">na_hp[<span class="nf">c</span>(<span class="m">5</span>, <span class="m">15</span>, <span class="m">25</span>)] <span class="o"><-</span> <span class="kc">NA</span></span>
<span class="cl"><span class="nf">cor</span>(mtcars_df<span class="o">$</span>mpg, na_hp, use <span class="o">=</span> <span class="s">"complete.obs"</span>)</span>
<span class="cl"><span class="c1">#> [1] -0.7700167</span></span></div>
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<p><strong>Explanation:</strong> <code>use = "complete.obs"</code> drops any row where either input has an <code>NA</code>, then runs the usual Pearson formula on what remains.</p>
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</section>
<h2>How do you build a correlation matrix for many variables?</h2>
<p>Pass a data frame or matrix to <code>cor()</code> and it returns a square matrix of pairwise correlations. This is the workhorse of <a class="auto-link" href="Exploratory-Data-Analysis-in-R.html" title="EDA in R: A 7-Step Framework That Works on Every Dataset You'll Encounter">exploratory data analysis</a>, one call, a full overview of linear relationships across every numeric column.</p>
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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">Correlation matrix on numeric columns</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">mtcars_num <span class="o"><-</span> mtcars_df[, <span class="nf">c</span>(<span class="s">"mpg"</span>, <span class="s">"wt"</span>, <span class="s">"hp"</span>, <span class="s">"qsec"</span>, <span class="s">"disp"</span>)]</span>
<span class="cl">cor_mat <span class="o"><-</span> <span class="nf">cor</span>(mtcars_num)</span>
<span class="cl"><span class="nf">round</span>(cor_mat, <span class="m">2</span>)</span>
<span class="cl"><span class="c1">#> mpg wt hp qsec disp</span></span>
<span class="cl"><span class="c1">#> mpg 1.00 -0.87 -0.78 0.42 -0.85</span></span>
<span class="cl"><span class="c1">#> wt -0.87 1.00 0.66 -0.17 0.89</span></span>
<span class="cl"><span class="c1">#> hp -0.78 0.66 1.00 -0.71 0.79</span></span>
<span class="cl"><span class="c1">#> qsec 0.42 -0.17 -0.71 1.00 -0.43</span></span>
<span class="cl"><span class="c1">#> disp -0.85 0.89 0.79 -0.43 1.00</span></span></div>
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<p>The diagonal is all 1s (every variable is perfectly correlated with itself). The matrix is symmetric, so you only need to read one triangle. <code>wt</code> and <code>disp</code> at 0.89 is the tightest pair here, heavy cars tend to have big engines. But this matrix has no p-values. For a tidy table of r, p, and sample size per pair, use <code>rstatix::cor_test</code>.</p>
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<div class="webr-editor" data-language="r"><span class="cl"><span class="nf">library</span>(rstatix)</span>
<span class="cl">tidy_cors <span class="o"><-</span> <span class="nf">cor_test</span>(mtcars_num)</span>
<span class="cl"><span class="nf">head</span>(tidy_cors, <span class="m">6</span>)</span>
<span class="cl"><span class="c1">#> # A tibble: 6 × 8</span></span>
<span class="cl"><span class="c1">#> var1 var2 cor statistic p conf.low conf.high method </span></span>
<span class="cl"><span class="c1">#> <chr> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <chr> </span></span>
<span class="cl"><span class="c1">#> 1 mpg wt -0.87 -9.56 1.29e-10 -0.934 -0.738 Pearson</span></span>
<span class="cl"><span class="c1">#> 2 mpg hp -0.78 -6.74 1.79e- 7 -0.885 -0.586 Pearson</span></span>
<span class="cl"><span class="c1">#> 3 mpg qsec 0.42 2.53 1.71e- 2 0.082 0.670 Pearson</span></span>
<span class="cl"><span class="c1">#> 4 mpg disp -0.85 -8.75 9.38e-10 -0.923 -0.708 Pearson</span></span>
<span class="cl"><span class="c1">#> 5 wt hp 0.66 4.80 4.15e- 5 0.402 0.824 Pearson</span></span>
<span class="cl"><span class="c1">#> 6 wt qsec -0.17 -0.97 3.39e- 1 -0.486 0.186 Pearson</span></span></div>
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<p>Now you have one row per pair, with the estimate, the p-value, the 95% CI, and the method name, perfect for filtering and plotting with <code>dplyr</code> and <code>ggplot2</code>.</p>
<div class="callout callout-note"><div class="callout-label">Note</div><div class="callout-body"><strong><code>cor()</code> only accepts numeric columns.</strong> Pass a full data frame with factors or characters and R throws an error. Subset first with <code>mtcars_df[, sapply(mtcars_df, is.numeric)]</code> in base R or <code>dplyr::select(where(is.numeric))</code> in the tidyverse.</div></div>
<section class="tryit-block">
<p><strong>Try it:</strong> Build <code>cor(iris[, 1:4])</code> on the four numeric <code>iris</code> columns and find the strongest pair.</p>
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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: iris correlation matrix</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"># Fill in and inspect:</span></span>
<span class="cl">ex_iris_cor <span class="o"><-</span> ________</span>
<span class="cl"><span class="nf">round</span>(ex_iris_cor, <span class="m">2</span>)</span>
<span class="cl"><span class="c1">#> Expected: Petal.Length and Petal.Width at around 0.96</span></span></div>
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<details>
<summary>Click to reveal solution</summary>
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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">iris correlation matrix 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">ex_iris_cor <span class="o"><-</span> <span class="nf">cor</span>(iris[, <span class="m">1</span><span class="o">:</span><span class="m">4</span>])</span>
<span class="cl"><span class="nf">round</span>(ex_iris_cor, <span class="m">2</span>)</span>
<span class="cl"><span class="c1">#> Sepal.Length Sepal.Width Petal.Length Petal.Width</span></span>
<span class="cl"><span class="c1">#> Sepal.Length 1.00 -0.12 0.87 0.82</span></span>
<span class="cl"><span class="c1">#> Sepal.Width -0.12 1.00 -0.43 -0.37</span></span>
<span class="cl"><span class="c1">#> Petal.Length 0.87 -0.43 1.00 0.96</span></span>
<span class="cl"><span class="c1">#> Petal.Width 0.82 -0.37 0.96 1.00</span></span></div>
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<p><strong>Explanation:</strong> <code>Petal.Length</code> and <code>Petal.Width</code> correlate at 0.96, the tightest pair. Petal dimensions scale together across species. <code>Sepal.Width</code> is the oddball, slightly negative with the petals.</p>
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<h2>How do you visualize a correlation matrix?</h2>
<p>A 5x5 matrix of numbers is already hard to scan; a 20x20 matrix is impossible. Plot it. Two packages dominate: <code>corrplot</code> is base-graphics, fast, and print-friendly. <code>ggcorrplot</code> is built on <a class="auto-link" href="ggplot2-Tutorial-With-R.html" title="ggplot2 Short Tutorial">ggplot2</a>, so you can theme and extend it like any other ggplot.</p>
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