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<!DOCTYPE html>
<html lang="en">
<head>
<title>Correlation in R: Pearson vs Spearman vs Kendall, Compute, Test, and Visualise</title>
<meta charset="utf-8">
<meta name="Description" content="Choose the right correlation for your data in R. Pearson for linear, Spearman for ranked, Kendall for small samples, with significance tests and corrplot.">
<meta name="Keywords" content="correlation in R, Pearson correlation R, Spearman correlation R, Kendall tau R, cor.test R, correlation matrix R, corrplot, correlation coefficient, cor function R, correlation significance test">
<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 expanded"><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" class="active"><span class="progress-dot"></span>Correlation Analysis</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub7" data-collapsed="false"><span class="subsec-chevron">▼</span> Interactive & Maps</li><li data-subkey="sec2sub7"><a href="/Combining-ggplot2-with-plotly.html"><span class="progress-dot"></span>ggplot2 + plotly Interactive</a></li><li data-subkey="sec2sub7"><a href="/Interactive-Maps-in-R-with-leaflet.html"><span class="progress-dot"></span>Leaflet Interactive Maps</a></li><li data-subkey="sec2sub7"><a href="/Spatial-Data-in-R-with-sf.html"><span class="progress-dot"></span>Spatial Data (sf)</a></li><li data-subkey="sec2sub7"><a href="/Choropleth-Maps-in-R.html"><span class="progress-dot"></span>Choropleth Maps (sf)</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec2sub8" data-collapsed="false"><span class="subsec-chevron">▼</span> Customization & Reference</li><li data-subkey="sec2sub8"><a href="/ggplot2-Legends-in-R.html"><span class="progress-dot"></span>ggplot2 Legends</a></li><li data-subkey="sec2sub8"><a href="/ggplot2-Secondary-Axis.html"><span class="progress-dot"></span>Secondary Axis</a></li><li data-subkey="sec2sub8"><a href="/ggplot2-Log-Scale.html"><span class="progress-dot"></span>Log Scale</a></li><li data-subkey="sec2sub8"><a href="/patchwork-Package.html"><span class="progress-dot"></span>patchwork (Combine Plots)</a></li><li data-subkey="sec2sub8"><a href="/Publication-Quality-Figures-in-R.html"><span class="progress-dot"></span>Publication-Ready Figures</a></li><li data-subkey="sec2sub8"><a href="/ggplot2-cheatsheet.html"><span class="progress-dot"></span>ggplot2 Quickref</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span> Statistics<span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub1" data-collapsed="false"><span class="subsec-chevron">▼</span> EDA & Data Quality</li><li data-subkey="sec3sub1"><a href="/Automated-EDA-in-R.html"><span class="progress-dot"></span>Automated EDA</a></li><li data-subkey="sec3sub1"><a href="/Missing-Data-Visualization-in-R-naniar.html"><span class="progress-dot"></span>Missing Data Viz (naniar)</a></li><li data-subkey="sec3sub1"><a href="/Outlier-Detection-in-R.html"><span class="progress-dot"></span>Outlier Detection</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub2" data-collapsed="false"><span class="subsec-chevron">▼</span> Probability</li><li data-subkey="sec3sub2"><a href="/Sample-Spaces-Events-and-Probability-Axioms-in-R-With-Monte-Carlo-Proof.html"><span class="progress-dot"></span>Probability Axioms</a></li><li data-subkey="sec3sub2"><a href="/Conditional-Probability-in-R.html"><span class="progress-dot"></span>Conditional Probability</a></li><li data-subkey="sec3sub2"><a href="/Random-Variables-in-R.html"><span class="progress-dot"></span>Random Variables</a></li><li data-subkey="sec3sub2"><a href="/Binomial-and-Poisson-Distributions-in-R.html"><span class="progress-dot"></span>Binomial vs Poisson</a></li><li data-subkey="sec3sub2"><a href="/Normal-t-F-and-Chi-Squared-Distributions-in-R.html"><span class="progress-dot"></span>Normal, t, F, Chi-Squared</a></li><li data-subkey="sec3sub2"><a href="/Central-Limit-Theorem-in-R.html"><span class="progress-dot"></span>Central Limit Theorem</a></li><li data-subkey="sec3sub2"><a href="/Sampling-Distributions-in-R.html"><span class="progress-dot"></span>Sampling Distributions</a></li><li data-subkey="sec3sub2"><a href="/Law-of-Large-Numbers-vs-CLT-in-R.html"><span class="progress-dot"></span>LLN vs CLT</a></li><li data-subkey="sec3sub2"><a href="/What-Is-Probability-Simulation-First-Intuition-in-R-Before-the-Formulas.html"><span class="progress-dot"></span>Probability (Simulation-First)</a></li><li data-subkey="sec3sub2"><a href="/Expected-Value-and-Variance-in-R.html"><span class="progress-dot"></span>Expected Value and Variance</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub3" data-collapsed="false"><span class="subsec-chevron">▼</span> Inference & Estimation</li><li data-subkey="sec3sub3"><a href="/Maximum-Likelihood-Estimation-in-R.html"><span class="progress-dot"></span>Maximum Likelihood Estimation</a></li><li data-subkey="sec3sub3"><a href="/Hypothesis-Testing-in-R.html"><span class="progress-dot"></span>Hypothesis Testing</a></li><li data-subkey="sec3sub3"><a href="/Sample-Size-Planning-in-R.html"><span class="progress-dot"></span>Sample Size Planning</a></li><li data-subkey="sec3sub3"><a href="/Which-Statistical-Test-in-R.html"><span class="progress-dot"></span>Choosing the Right Test</a></li><li data-subkey="sec3sub3"><a href="/Statistical-Tests-in-R.html"><span class="progress-dot"></span>Statistical Tests</a></li><li data-subkey="sec3sub3"><a href="/Measures-of-Association-in-R.html"><span class="progress-dot"></span>Measures of Association</a></li><li data-subkey="sec3sub3"><a href="/Point-Estimation-in-R.html"><span class="progress-dot"></span>Point Estimation</a></li><li data-subkey="sec3sub3"><a href="/Confidence-Intervals-in-R.html"><span class="progress-dot"></span>Confidence Intervals</a></li><li data-subkey="sec3sub3"><a href="/Type-I-and-Type-II-Errors-in-R.html"><span class="progress-dot"></span>Type I and II Errors</a></li><li data-subkey="sec3sub3"><a href="/Statistical-Power-Analysis-in-R.html"><span class="progress-dot"></span>Power Analysis</a></li><li data-subkey="sec3sub3"><a href="/Effect-Size-in-R.html"><span class="progress-dot"></span>Effect Size</a></li><li data-subkey="sec3sub3"><a href="/t-Tests-in-R.html"><span class="progress-dot"></span>t-Tests</a></li><li data-subkey="sec3sub3"><a href="/Proportion-Tests-in-R.html"><span class="progress-dot"></span>Proportion Tests</a></li><li data-subkey="sec3sub3"><a href="/Normality-and-Variance-Tests-in-R.html"><span class="progress-dot"></span>Normality & Variance Tests</a></li><li data-subkey="sec3sub3"><a href="/Chi-Square-Tests-in-R.html"><span class="progress-dot"></span>Chi-Square Tests</a></li><li data-subkey="sec3sub3"><a href="/Wilcoxon-Mann-Whitney-and-Kruskal-Wallis-in-R.html"><span class="progress-dot"></span>Wilcoxon, Mann-Whitney & Kruskal-Wallis</a></li><li data-subkey="sec3sub3"><a href="/Multiple-Comparisons-in-R.html"><span class="progress-dot"></span>Multiple Testing Correction</a></li><li data-subkey="sec3sub3"><a href="/Hypothesis-Testing-Exercises-in-R-quiz.html"><span class="progress-dot"></span>Hypothesis Testing Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub4" data-collapsed="false"><span class="subsec-chevron">▼</span> Regression</li><li data-subkey="sec3sub4"><a href="/Linear-Regression.html"><span class="progress-dot"></span>Linear Regression</a></li><li data-subkey="sec3sub4"><a href="/Logistic-Regression-With-R.html"><span class="progress-dot"></span>Logistic Regression</a></li><li data-subkey="sec3sub4"><a href="/Variable-Selection-and-Importance-With-R.html"><span class="progress-dot"></span>Feature Selection</a></li><li data-subkey="sec3sub4"><a href="/Model-Selection-in-R.html"><span class="progress-dot"></span>Model Selection</a></li><li data-subkey="sec3sub4"><a href="/Missing-Value-Treatment-With-R.html"><span class="progress-dot"></span>Missing Value Treatment</a></li><li data-subkey="sec3sub4"><a href="/Outlier-Treatment-With-R.html"><span class="progress-dot"></span>Outlier Analysis</a></li><li data-subkey="sec3sub4"><a href="/adv-regression-models.html"><span class="progress-dot"></span>Advanced Regression Models</a></li><li data-subkey="sec3sub4"><a href="/Linear-Regression-Exercises-in-R-quiz.html"><span class="progress-dot"></span>Linear Regression Quiz</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub5" data-collapsed="false"><span class="subsec-chevron">▼</span> Reporting</li><li data-subkey="sec3sub5"><a href="/Statistical-Consulting-in-R.html"><span class="progress-dot"></span>Statistical Consulting</a></li><li data-subkey="sec3sub5"><a href="/Statistical-Report-Writing-in-R.html"><span class="progress-dot"></span>Statistical Report Writing</a></li><li data-subkey="sec3sub5"><a href="/Bootstrap-Confidence-Intervals-in-R.html"><span class="progress-dot"></span>Bootstrap Confidence Intervals</a></li><li data-subkey="sec3sub5"><a href="/Reporting-Statistics-in-R.html"><span class="progress-dot"></span>Reporting Statistics</a></li><li data-subkey="sec3sub5"><a href="/Correlation-in-R.html"><span class="progress-dot"></span>Correlation (Pearson, Spearman, Kendall)</a></li><li data-subkey="sec3sub5"><a href="/Linear-Regression-Assumptions-in-R.html"><span class="progress-dot"></span>Linear Regression Assumptions</a></li><li data-subkey="sec3sub5"><a href="/Dummy-Variables-in-R.html"><span class="progress-dot"></span>Dummy Variables in R</a></li><li data-subkey="sec3sub5"><a href="/Interaction-Effects-in-R.html"><span class="progress-dot"></span>Interaction Effects</a></li><li data-subkey="sec3sub5"><a href="/Regression-Diagnostics-in-R.html"><span class="progress-dot"></span>Regression Diagnostics</a></li><li data-subkey="sec3sub5"><a href="/Logistic-Regression-in-R.html"><span class="progress-dot"></span>Logistic Regression (glm + ROC)</a></li><li data-subkey="sec3sub5"><a href="/Variable-Selection-in-R.html"><span class="progress-dot"></span>Variable Selection</a></li><li data-subkey="sec3sub5"><a href="/Poisson-Regression-in-R.html"><span class="progress-dot"></span>Poisson Regression</a></li><li data-subkey="sec3sub5"><a href="/Ridge-and-Lasso-Regression-in-R.html"><span class="progress-dot"></span>Ridge & Lasso Regression</a></li><li data-subkey="sec3sub5"><a href="/Polynomial-and-Spline-Regression-in-R.html"><span class="progress-dot"></span>Polynomial & Splines</a></li><li data-subkey="sec3sub5"><a href="/Regression-Tables-in-R.html"><span class="progress-dot"></span>Regression Tables (3 packages)</a></li><li data-subkey="sec3sub5"><a href="/One-Way-ANOVA-in-R.html"><span class="progress-dot"></span>One-Way ANOVA</a></li><li data-subkey="sec3sub5"><a href="/Post-Hoc-Tests-After-ANOVA.html"><span class="progress-dot"></span>Post-Hoc Tests After ANOVA</a></li><li data-subkey="sec3sub5"><a href="/Two-Way-ANOVA-in-R.html"><span class="progress-dot"></span>Two-Way ANOVA</a></li><li data-subkey="sec3sub5"><a href="/Repeated-Measures-ANOVA-in-R.html"><span class="progress-dot"></span>Repeated Measures ANOVA</a></li><li data-subkey="sec3sub5"><a href="/ANCOVA-in-R.html"><span class="progress-dot"></span>ANCOVA</a></li><li data-subkey="sec3sub5"><a href="/Experimental-Design-Principles-in-R.html"><span class="progress-dot"></span>Experimental Design in R</a></li><li data-subkey="sec3sub5"><a href="/Factorial-Experiments-in-R.html"><span class="progress-dot"></span>Factorial Designs (2^k)</a></li><li data-subkey="sec3sub5"><a href="/AB-Testing-in-R.html"><span class="progress-dot"></span>A/B Testing</a></li><li data-subkey="sec3sub5"><a href="/MANOVA-in-R.html"><span class="progress-dot"></span>MANOVA</a></li><li data-subkey="sec3sub5"><a href="/Mixed-ANOVA-in-R.html"><span class="progress-dot"></span>Mixed ANOVA</a></li><li data-subkey="sec3sub5"><a href="/Multivariate-Statistics-in-R.html"><span class="progress-dot"></span>Multivariate Distances & Hotelling's T²</a></li><li data-subkey="sec3sub5"><a href="/PCA-in-R.html"><span class="progress-dot"></span>PCA with prcomp()</a></li><li data-subkey="sec3sub5"><a href="/Interpreting-PCA-Results-in-R.html"><span class="progress-dot"></span>Interpreting PCA Output</a></li><li data-subkey="sec3sub5"><a href="/Exploratory-Factor-Analysis-in-R.html"><span class="progress-dot"></span>Exploratory Factor Analysis</a></li><li 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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 class="progress-dot"></span>Kruskal-Wallis Test</a></li><li data-subkey="sec3sub5"><a href="/Friedman-Test-in-R.html"><span class="progress-dot"></span>Friedman Test</a></li><li data-subkey="sec3sub5"><a href="/Spearman-and-Kendall-Correlation-in-R.html"><span class="progress-dot"></span>Spearman & Kendall Correlation</a></li><li data-subkey="sec3sub5"><a href="/Bootstrap-in-R.html"><span class="progress-dot"></span>Bootstrap (boot package)</a></li><li data-subkey="sec3sub5"><a href="/Quantile-Regression-in-R-2.html"><span class="progress-dot"></span>Quantile Regression</a></li><li data-subkey="sec3sub5"><a href="/Matrix-Operations-in-R.html"><span class="progress-dot"></span>Matrix Operations in R</a></li><li data-subkey="sec3sub5"><a href="/Solving-Linear-Systems-in-R.html"><span class="progress-dot"></span>Solving Linear Systems in R</a></li><li data-subkey="sec3sub5"><a href="/Eigenvalues-and-Eigenvectors-in-R.html"><span class="progress-dot"></span>Eigenvalues & Eigenvectors in R</a></li><li data-subkey="sec3sub5"><a href="/Singular-Value-Decomposition-in-R.html"><span class="progress-dot"></span>Singular Value Decomposition in R</a></li><li data-subkey="sec3sub5"><a href="/Projections-and-the-Hat-Matrix-in-R.html"><span class="progress-dot"></span>Projections & the Hat Matrix</a></li><li data-subkey="sec3sub5"><a href="/QR-Decomposition-in-R.html"><span class="progress-dot"></span>QR Decomposition in R</a></li><li data-subkey="sec3sub5"><a href="/Quadratic-Forms-in-R.html"><span class="progress-dot"></span>Quadratic Forms</a></li><li data-subkey="sec3sub5"><a href="/Matrix-Derivatives-and-the-Hessian-in-R.html"><span class="progress-dot"></span>Matrix Derivatives & Hessian</a></li><li data-subkey="sec3sub5"><a href="/Exponential-Family-Distributions-in-R.html"><span class="progress-dot"></span>Exponential Family Distributions</a></li><li data-subkey="sec3sub5"><a href="/Sufficient-Statistics-in-R.html"><span class="progress-dot"></span>Sufficient Statistics</a></li><li data-subkey="sec3sub5"><a href="/Complete-and-Ancillary-Statistics-in-R.html"><span class="progress-dot"></span>Complete & Ancillary Statistics</a></li><li data-subkey="sec3sub5"><a href="/UMVUE-in-R-2.html"><span class="progress-dot"></span>UMVUE (Rao-Blackwell & Lehmann-Scheffé)</a></li><li data-subkey="sec3sub5"><a href="/Cramer-Rao-Lower-Bound-in-R-2.html"><span class="progress-dot"></span>Cramér-Rao Lower Bound</a></li><li data-subkey="sec3sub5"><a href="/Asymptotic-Theory-in-R-2.html"><span class="progress-dot"></span>Asymptotic Theory</a></li><li data-subkey="sec3sub5"><a href="/Neyman-Pearson-Lemma-in-R-2.html"><span class="progress-dot"></span>Neyman-Pearson Lemma</a></li><li data-subkey="sec3sub5"><a href="/Likelihood-Ratio-Tests-and-Pivotal-Methods.html"><span class="progress-dot"></span>Likelihood Ratio & Pivotal Methods</a></li><li data-subkey="sec3sub5"><a href="/Decision-Theory-in-R.html"><span class="progress-dot"></span>Decision Theory</a></li><li data-subkey="sec3sub5"><a href="/Asymptotic-Relative-Efficiency-in-R.html"><span class="progress-dot"></span>Asymptotic Relative Efficiency</a></li><li data-subkey="sec3sub5"><a href="/Bayes-Theorem-in-R.html"><span class="progress-dot"></span>Bayes' Theorem</a></li><li data-subkey="sec3sub5"><a href="/Bayesian-Statistics-in-R.html"><span class="progress-dot"></span>Bayesian Statistics</a></li><li data-subkey="sec3sub5"><a href="/Conjugate-Priors-in-R.html"><span class="progress-dot"></span>Conjugate Priors</a></li><li data-subkey="sec3sub5"><a href="/Grid-Approximation-in-R.html"><span class="progress-dot"></span>Grid Approximation</a></li><li data-subkey="sec3sub5"><a href="/MCMC-in-R.html"><span class="progress-dot"></span>MCMC in R</a></li><li data-subkey="sec3sub5"><a href="/Gibbs-Sampling-in-R.html"><span class="progress-dot"></span>Gibbs Sampling</a></li><li data-subkey="sec3sub5"><a href="/Hamiltonian-Monte-Carlo-in-R.html"><span class="progress-dot"></span>Hamiltonian Monte Carlo</a></li><li data-subkey="sec3sub5"><a href="/Stan-in-R.html"><span class="progress-dot"></span>Stan</a></li><li data-subkey="sec3sub5"><a href="/brms-in-R.html"><span class="progress-dot"></span>brms</a></li><li data-subkey="sec3sub5"><a href="/Choosing-Priors-in-R.html"><span class="progress-dot"></span>Choosing Priors</a></li><li data-subkey="sec3sub5"><a href="/Prior-Predictive-Checks-in-R.html"><span class="progress-dot"></span>Prior Predictive Checks</a></li><li data-subkey="sec3sub5"><a href="/Compare-Bayesian-Models-in-R.html"><span class="progress-dot"></span>Compare Bayesian Models</a></li><li data-subkey="sec3sub5"><a href="/Posterior-Predictive-Checks-in-R.html"><span class="progress-dot"></span>Posterior Predictive Checks</a></li><li data-subkey="sec3sub5"><a href="/Bayesian-Linear-Regression-in-R.html"><span class="progress-dot"></span>Bayesian Linear Regression</a></li><li data-subkey="sec3sub5"><a href="/Bayesian-Logistic-Regression-in-R.html"><span class="progress-dot"></span>Bayesian Logistic Regression</a></li><li data-subkey="sec3sub5"><a href="/Bayesian-Hierarchical-Models-in-R.html"><span class="progress-dot"></span>Bayesian Hierarchical Models</a></li><li data-subkey="sec3sub5"><a href="/Multilevel-Models-in-R.html"><span class="progress-dot"></span>Multilevel Models</a></li><li data-subkey="sec3sub5"><a href="/Bayesian-ANOVA-in-R.html"><span class="progress-dot"></span>Bayesian ANOVA</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec3sub6" data-collapsed="false"><span class="subsec-chevron">▼</span> Machine Learning</li><li data-subkey="sec3sub6"><a href="/Machine-Learning-Exercises-in-R-quiz.html"><span class="progress-dot"></span>Machine Learning Quiz</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span> Time Series<span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li data-subkey="sec4sub0"><a href="/Time-Series-Analysis-With-R.html"><span class="progress-dot"></span>Time Series Analysis</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Forecasting-With-R.html"><span class="progress-dot"></span>Time Series Forecasting</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Forecasting-With-R-part2.html"><span class="progress-dot"></span>More Time Series Forecasting</a></li><li data-subkey="sec4sub0"><a href="/Time-Series-Exercises-in-R-quiz.html"><span class="progress-dot"></span>Time Series Quiz</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span> Advanced R<span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec5sub1" data-collapsed="false"><span class="subsec-chevron">▼</span> Functional Programming</li><li data-subkey="sec5sub1"><a href="/Functional-Programming-in-R.html"><span class="progress-dot"></span>Functional Programming</a></li><li data-subkey="sec5sub1"><a href="/R-Functional-Programming-Exercises-quiz.html"><span class="progress-dot"></span>Functional Programming Quiz</a></li><li data-subkey="sec5sub1"><a href="/purrr-map-Variants.html"><span class="progress-dot"></span>purrr map() Variants</a></li><li data-subkey="sec5sub1"><a href="/R-Anonymous-Functions.html"><span class="progress-dot"></span>R Anonymous Functions</a></li><li data-subkey="sec5sub1"><a href="/R-Function-Factories.html"><span class="progress-dot"></span>R Function Factories</a></li><li data-subkey="sec5sub1"><a href="/R-Function-Operators.html"><span class="progress-dot"></span>R Function Operators</a></li><li data-subkey="sec5sub1"><a href="/Reduce-Filter-Map-in-R.html"><span class="progress-dot"></span>Reduce, Filter, Map</a></li><li data-subkey="sec5sub1"><a href="/Memoization-in-R.html"><span class="progress-dot"></span>Memoization in R</a></li><li data-subkey="sec5sub1"><a href="/Writing-Composable-R-Code.html"><span class="progress-dot"></span>Composable R Code</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec5sub2" data-collapsed="false"><span class="subsec-chevron">▼</span> OOP in R</li><li data-subkey="sec5sub2"><a href="/OOP-in-R.html"><span class="progress-dot"></span>OOP in R: S3/S4/R6</a></li><li data-subkey="sec5sub2"><a href="/S3-Classes-in-R.html"><span class="progress-dot"></span>S3 Classes</a></li><li data-subkey="sec5sub2"><a href="/S3-Method-Dispatch-in-R.html"><span class="progress-dot"></span>S3 Method Dispatch</a></li><li data-subkey="sec5sub2"><a href="/S4-Classes-in-R.html"><span class="progress-dot"></span>S4 Classes</a></li><li data-subkey="sec5sub2"><a href="/S4-Methods-in-R.html"><span class="progress-dot"></span>S4 Methods & Dispatch</a></li><li data-subkey="sec5sub2"><a href="/R6-Classes-in-R.html"><span class="progress-dot"></span>R6 Classes</a></li><li data-subkey="sec5sub2"><a href="/R6-Advanced.html"><span class="progress-dot"></span>R6 Advanced</a></li><li data-subkey="sec5sub2"><a href="/Operator-Overloading-in-R.html"><span class="progress-dot"></span>Operator Overloading</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec5sub3" data-collapsed="false"><span class="subsec-chevron">▼</span> How R Works</li><li data-subkey="sec5sub3"><a href="/R-Names-and-Values.html"><span class="progress-dot"></span>R Names & Values</a></li><li data-subkey="sec5sub3"><a href="/R-Assignment-Deep-Dive.html"><span class="progress-dot"></span>R Assignment Deep Dive</a></li><li data-subkey="sec5sub3"><a href="/R-Memory-lobstr.html"><span class="progress-dot"></span>R Memory & lobstr</a></li><li data-subkey="sec5sub3"><a href="/R-Environments.html"><span class="progress-dot"></span>R Environments</a></li><li data-subkey="sec5sub3"><a href="/R-Lexical-Scoping.html"><span class="progress-dot"></span>Lexical Scoping</a></li><li data-subkey="sec5sub3"><a href="/R-Closures.html"><span class="progress-dot"></span>R Closures</a></li><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec5sub4" data-collapsed="false"><span class="subsec-chevron">▼</span> Debugging & Performance</li><li data-subkey="sec5sub4"><a href="/R-Conditions-System.html"><span class="progress-dot"></span>Conditions System</a></li><li data-subkey="sec5sub4"><a href="/R-Debugging.html"><span class="progress-dot"></span>Debugging R Code</a></li><li data-subkey="sec5sub4"><a href="/R-Common-Errors.html"><span class="progress-dot"></span>50 Common R Errors</a></li><li data-subkey="sec5sub4"><a href="/Parallel-Computing-With-R.html"><span class="progress-dot"></span>Parallel Computing</a></li><li data-subkey="sec5sub4"><a href="/Strategies-To-Improve-And-Speedup-R-Code.html"><span class="progress-dot"></span>Speedup R Code</a></li><li data-subkey="sec5sub4"><a href="/Shiny-Exercises-in-R-quiz.html"><span class="progress-dot"></span>Shiny Quiz</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span> Classic Tutorials<span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li data-subkey="sec6sub0"><a href="/R-Tutorial.html"><span class="progress-dot"></span>R Tutorial (Classic)</a></li><li data-subkey="sec6sub0"><a href="/ggplot2-Tutorial-With-R.html"><span class="progress-dot"></span>ggplot2 Short Tutorial</a></li><li data-subkey="sec6sub0"><a href="/Complete-Ggplot2-Tutorial-Part1-With-R-Code.html"><span class="progress-dot"></span>ggplot2 Tutorial 1 - Intro</a></li><li data-subkey="sec6sub0"><a href="/Complete-Ggplot2-Tutorial-Part2-Customizing-Theme-With-R-Code.html"><span class="progress-dot"></span>ggplot2 Tutorial 2 - Theme</a></li><li data-subkey="sec6sub0"><a href="/Top50-Ggplot2-Visualizations-MasterList-R-Code.html"><span class="progress-dot"></span>ggplot2 Tutorial 3 - Masterlist</a></li><li data-subkey="sec6sub0"><a href="/Association-Mining-With-R.html"><span class="progress-dot"></span>Association Mining</a></li><li data-subkey="sec6sub0"><a href="/Multi-Dimensional-Scaling-With-R.html"><span class="progress-dot"></span>Multi Dimensional Scaling</a></li><li data-subkey="sec6sub0"><a href="/Optimization-With-R.html"><span class="progress-dot"></span>Optimization</a></li><li data-subkey="sec6sub0"><a href="/Information-Value-With-R.html"><span class="progress-dot"></span>InformationValue Package</a></li></ul></li><li class="sidebar-section"><div class="sidebar-section-header"><span class="sidebar-chevron">▸</span> Practice Exercises<span class="section-meta" data-section-meta></span></div><ul class="sidebar-section-items list-unstyled"><li class="sidebar-divider sidebar-subsection-toggle" data-subkey="sec7sub1" data-collapsed="false"><span class="subsec-chevron">▼</span> Mastery Quizzes (Certificate)</li><li data-subkey="sec7sub1"><a href="/R-Beginner-Exercises-quiz.html"><span class="progress-dot"></span>R Fundamentals Quiz</a></li><li data-subkey="sec7sub1"><a href="/dplyr-Exercises-in-R-quiz.html"><span class="progress-dot"></span>dplyr Quiz</a></li><li data-subkey="sec7sub1"><a href="/ggplot2-Exercises-in-R-quiz.html"><span class="progress-dot"></span>ggplot2 Quiz</a></li><li data-subkey="sec7sub1"><a href="/Hypothesis-Testing-Exercises-in-R-quiz.html"><span class="progress-dot"></span>Hypothesis Testing Quiz</a></li><li data-subkey="sec7sub1"><a href="/Linear-Regression-Exercises-in-R-quiz.html"><span class="progress-dot"></span>Linear Regression Quiz</a></li><li data-subkey="sec7sub1"><a href="/Machine-Learning-Exercises-in-R-quiz.html"><span class="progress-dot"></span>Machine Learning Quiz</a></li><li data-subkey="sec7sub1"><a href="/tidyr-Exercises-in-R-quiz.html"><span 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<h1>Correlation in R: Pearson vs Spearman vs Kendall, Compute, Test, and Visualise</h1>
<p class="lead">Correlation measures the strength and direction of the relationship between two variables, a number between −1 and +1. R gives you three methods: Pearson for linear relationships, Spearman for monotonic (ranked) data, and Kendall's tau for small or tied samples.</p>
<div class="post-byline" style="color:#6b7280;font-size:14px;margin:2px 0 18px 0;line-height:1.5;">By <strong>Selva Prabhakaran</strong> · Published May 10, 2026 · Last updated May 10, 2026</div>
<div class="engagement-header" data-difficulty="Intermediate" data-time="40" data-exercises="10" data-xp="150"></div>
<h2>How do you compute a correlation in R?</h2>
<p>How strong is the link between a car's weight and its fuel economy? That's the question correlation answers, it gives you a single number that captures both the direction and strength of a relationship. Let's compute one right now with <code>cor()</code> and see the result.</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">Weight versus fuel economy 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"><span class="c1"># Correlation between weight and fuel economy</span></span>
<span class="cl">r_value <span class="o"><-</span> <span class="nf">cor</span>(mtcars<span class="o">$</span>wt, mtcars<span class="o">$</span>mpg)</span>
<span class="cl">r_value</span>
<span class="cl"><span class="c1">#> [1] -0.8676594</span></span></div>
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<p>The result is −0.87, which tells you two things. The negative sign means heavier cars get <em>worse</em> fuel economy (mpg goes down as weight goes up). The magnitude, close to 1, tells you this is a strong relationship. In other words, weight is one of the best predictors of fuel economy in this dataset.</p>
<p>By default, <code>cor()</code> computes <a class="auto-link" href="How-to-do-Pearson-Correlation-Test-in-R.html" title="Pearson Correlation Test in R: cor.test() Guide">Pearson correlation</a>. You can switch to the other two methods by passing the <code>method</code> argument. Let's see all three on the same data.</p>
<div class="webr-container" data-block-title="Compare pearson spearman and 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 and 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="c1"># Compare all three methods</span></span>
<span class="cl">pearson_r <span class="o"><-</span> <span class="nf">cor</span>(mtcars<span class="o">$</span>wt, mtcars<span class="o">$</span>mpg, method <span class="o">=</span> <span class="s">"pearson"</span>)</span>
<span class="cl">spearman_r <span class="o"><-</span> <span class="nf">cor</span>(mtcars<span class="o">$</span>wt, mtcars<span class="o">$</span>mpg, method <span class="o">=</span> <span class="s">"spearman"</span>)</span>
<span class="cl">kendall_r <span class="o"><-</span> <span class="nf">cor</span>(mtcars<span class="o">$</span>wt, mtcars<span class="o">$</span>mpg, method <span class="o">=</span> <span class="s">"kendall"</span>)</span>
<span class="cl"></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"Pearson: "</span>, <span class="nf">round</span>(pearson_r, <span class="m">3</span>),</span>
<span class="cl"> <span class="s">"\nSpearman:"</span>, <span class="nf">round</span>(spearman_r, <span class="m">3</span>),</span>
<span class="cl"> <span class="s">"\nKendall: "</span>, <span class="nf">round</span>(kendall_r, <span class="m">3</span>))</span>
<span class="cl"><span class="c1">#> Pearson: -0.868</span></span>
<span class="cl"><span class="c1">#> Spearman: -0.886</span></span>
<span class="cl"><span class="c1">#> Kendall: -0.734</span></span></div>
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<p>All three agree on the direction (negative) and general strength (strong). Pearson and Spearman are close because the relationship is roughly linear. Kendall's value is smaller, that's expected and normal. We'll explain why in the Kendall section below.</p>
<p>Here's a quick reference for interpreting the magnitude of any <a class="auto-link" href="Correlation-in-R.html" title="Correlation in R: Choose Between Pearson, Spearman, and Kendall, With Tests">correlation coefficient</a>.</p>
<p><img src="screenshots/Correlation-Analysis-in-R-strength-scale.webp" alt="Correlation strength scale" class="img-responsive img-zoomable" loading="lazy" width="2248" height="368" /></p>
<p><em>Figure 1: Interpreting correlation strength: from perfect negative to perfect positive.</em></p>
<p>These thresholds come from Cohen's (1988) conventions for behavioural sciences. In some fields, physics, finance, genomics, the standards differ. Use them as a starting point, not a rigid rule.</p>
<div class="callout callout-insight"><div class="callout-label">Key Insight</div><div class="callout-body"><strong>A correlation of 0 does not mean "no relationship."</strong> It means no <em>linear</em> relationship. A perfect U-shaped curve gives a Pearson correlation of zero. Always plot your data before concluding there's nothing going on.</div></div>
<section class="tryit-block">
<p><strong>Try it:</strong> Compute the correlation between <code>mtcars$hp</code> (horsepower) and <code>mtcars$qsec</code> (quarter-mile time). Before running the code, predict: will it be positive or negative?</p>
<div class="webr-container" data-block-title="Exercise: correlate horsepower and quarter mile">
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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">Exercise: correlate horsepower and quarter mile</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"># Try it: correlate hp and qsec</span></span>
<span class="cl">ex_r <span class="o"><-</span> <span class="nf">cor</span>(mtcars<span class="o">$</span>hp, mtcars<span class="o">$</span>qsec)</span>
<span class="cl">ex_r</span>
<span class="cl"><span class="c1">#> Expected: a negative value (more power = faster = lower qsec)</span></span></div>
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<details>
<summary>Click to reveal solution</summary>
<div class="webr-container" data-block-title="Horsepower and quarter mile 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">Horsepower and quarter mile 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_r <span class="o"><-</span> <span class="nf">cor</span>(mtcars<span class="o">$</span>hp, mtcars<span class="o">$</span>qsec)</span>
<span class="cl">ex_r</span>
<span class="cl"><span class="c1">#> [1] -0.7082234</span></span></div>
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<p><strong>Explanation:</strong> The correlation is −0.71 (strong negative). More horsepower means a <em>lower</em> quarter-mile time, the car accelerates faster.</p>
</details>
</section>
<h2>What is Pearson correlation and when should you use it?</h2>
<p>Pearson correlation measures how closely two variables follow a <em>straight-line</em> relationship. Think of it as asking: "If I draw the best-fitting line through these points, how tightly do the points cluster around it?"</p>
<p>The formula captures this intuition. For two variables $x$ and $y$ with $n$ observations:</p>
<p>$$r = \frac{\sum_{i=1}^{n}(x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=1}^{n}(x_i - \bar{x})^2 \cdot \sum_{i=1}^{n}(y_i - \bar{y})^2}}$$</p>
<p>Where:</p>
<ul>
<li>$r$ = Pearson correlation coefficient (ranges from −1 to +1)</li>
<li>$x_i, y_i$ = individual observations</li>
<li>$\bar{x}, \bar{y}$ = means of each variable</li>
<li>The numerator measures how much $x$ and $y$ move together</li>
<li>The denominator standardises the result to the −1 to +1 scale</li>
</ul>
<p><em>If you're not interested in the math, skip ahead, the practical code above is all you need.</em></p>
<p>Pearson works well when three assumptions hold: (1) both variables are continuous, (2) the relationship is linear, and (3) both variables are approximately normally distributed. Let's check these visually and statistically.</p>
<div class="webr-container" data-block-title="Scatter plot with linear fit">
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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 plot with linear fit</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"># Scatter plot: is the relationship linear?</span></span>
<span class="cl"><span class="nf">plot</span>(mtcars<span class="o">$</span>wt, mtcars<span class="o">$</span>mpg,</span>
<span class="cl"> xlab <span class="o">=</span> <span class="s">"Weight (1000 lbs)"</span>, ylab <span class="o">=</span> <span class="s">"Miles per Gallon"</span>,</span>
<span class="cl"> main <span class="o">=</span> <span class="s">"Weight vs Fuel Economy"</span>,</span>
<span class="cl"> pch <span class="o">=</span> <span class="m">19</span>, col <span class="o">=</span> <span class="s">"steelblue"</span>)</span>
<span class="cl"><span class="nf">abline</span>(<span class="nf">lm</span>(mpg <span class="o">~</span> wt, data <span class="o">=</span> mtcars), col <span class="o">=</span> <span class="s">"red"</span>, lwd <span class="o">=</span> <span class="m">2</span>)</span></div>
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<p>The scatter plot shows points clustering around a straight line, good evidence that Pearson is appropriate here. The red line is the linear fit, and the points stick close to it.</p>
<p>Now let's check normality with the <a class="auto-link" href="Normality-and-Variance-Tests-in-R.html" title="Test Normality and Equal Variance in R: What the Tests Can and Can't Tell You">Shapiro-Wilk test</a>. A p-value above 0.05 means we can't reject normality.</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">Shapiro wilk normality check</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"># Normality check</span></span>
<span class="cl"><span class="nf">shapiro.test</span>(mtcars<span class="o">$</span>wt)</span>
<span class="cl"><span class="c1">#> Shapiro-Wilk normality test</span></span>
<span class="cl"><span class="c1">#> data: mtcars$wt</span></span>
<span class="cl"><span class="c1">#> W = 0.94326, p-value = 0.09265</span></span>
<span class="cl"></span>
<span class="cl"><span class="nf">shapiro.test</span>(mtcars<span class="o">$</span>mpg)</span>
<span class="cl"><span class="c1">#> Shapiro-Wilk normality test</span></span>
<span class="cl"><span class="c1">#> data: mtcars$mpg</span></span>
<span class="cl"><span class="c1">#> W = 0.94756, p-value = 0.1229</span></span></div>
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<p>Both p-values are above 0.05, so we can't reject normality for either variable. Combined with the linear scatter plot, Pearson is a solid choice here.</p>
<div class="callout callout-warning"><div class="callout-label">Warning</div><div class="callout-body"><strong>Pearson is sensitive to outliers.</strong> A single extreme point can inflate or deflate the coefficient dramatically. Always visualise your data with a scatter plot before trusting a Pearson value.</div></div>
<section class="tryit-block">
<p><strong>Try it:</strong> Check whether <code>airquality$Ozone</code> and <code>airquality$Temp</code> pass the normality assumption. Use <code>shapiro.test()</code> on each. Remember to handle <a class="auto-link" href="Missing-Value-Treatment-With-R.html" title="Missing Value Treatment">missing values</a> with <code>na.rm = TRUE</code> when subsetting.</p>
<div class="webr-container" data-block-title="Exercise: normality check for airquality">
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<div class="webr-editor" data-language="r"><span class="cl"><span class="c1"># Try it: normality check for airquality</span></span>
<span class="cl"><span class="c1"># Hint: airquality has NAs, filter them out first</span></span>
<span class="cl">ex_ozone <span class="o"><-</span> <span class="nf">na.omit</span>(airquality<span class="o">$</span>Ozone)</span>
<span class="cl"><span class="nf">shapiro.test</span>(ex_ozone)</span>
<span class="cl"><span class="c1">#> Expected: p-value < 0.05 (Ozone is right-skewed, fails normality)</span></span></div>
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<summary>Click to reveal solution</summary>
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<div class="webr-editor" data-language="r"><span class="cl">ex_ozone <span class="o"><-</span> <span class="nf">na.omit</span>(airquality<span class="o">$</span>Ozone)</span>
<span class="cl">ex_temp <span class="o"><-</span> <span class="nf">na.omit</span>(airquality<span class="o">$</span>Temp)</span>
<span class="cl"></span>
<span class="cl"><span class="nf">shapiro.test</span>(ex_ozone)</span>
<span class="cl"><span class="c1">#> Shapiro-Wilk normality test</span></span>
<span class="cl"><span class="c1">#> data: ex_ozone</span></span>
<span class="cl"><span class="c1">#> W = 0.87868, p-value = 2.793e-08</span></span>
<span class="cl"></span>
<span class="cl"><span class="nf">shapiro.test</span>(ex_temp)</span>
<span class="cl"><span class="c1">#> Shapiro-Wilk normality test</span></span>
<span class="cl"><span class="c1">#> data: ex_temp</span></span>
<span class="cl"><span class="c1">#> W = 0.98537, p-value = 0.2329</span></span></div>
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<p><strong>Explanation:</strong> Ozone fails normality (p < 0.001) because it's right-skewed. Temperature passes (p = 0.23). Since one variable violates the normality assumption, Spearman would be more appropriate for this pair.</p>
</details>
</section>
<h2>When should you use Spearman's rank correlation?</h2>
<p>Spearman's <a class="auto-link" href="Spearman-and-Kendall-Correlation-in-R.html" title="Spearman & Kendall Correlation in R: Rank-Based Association Measures">rank correlation</a> works by converting your raw data to ranks, then computing Pearson correlation on those ranks. This simple trick makes it robust to outliers, skewed distributions, and non-linear monotonic relationships.</p>
<p>A monotonic relationship means "as one variable goes up, the other consistently goes up (or consistently goes down)", but the change doesn't have to follow a straight line. An exponential curve is monotonic but not linear. Spearman catches these; Pearson doesn't.</p>
<p>Let's see the difference with a concrete example. We'll create data that follows an exponential curve, clearly monotonic, but not linear.</p>
<div class="webr-container" data-block-title="Exponential growth pearson versus spearman">
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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">Exponential growth pearson versus spearman</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"># Monotonic but non-linear: exponential growth</span></span>
<span class="cl"><span class="nf">set.seed</span>(<span class="m">21</span>)</span>
<span class="cl">x_exp <span class="o"><-</span> <span class="m">1</span><span class="o">:</span><span class="m">30</span></span>
<span class="cl">y_exp <span class="o"><-</span> <span class="nf">exp</span>(x_exp <span class="o">/</span> <span class="m">10</span>) <span class="o">+</span> <span class="nf">rnorm</span>(<span class="m">30</span>, sd <span class="o">=</span> <span class="m">0.3</span>)</span>
<span class="cl"></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"Pearson: "</span>, <span class="nf">round</span>(<span class="nf">cor</span>(x_exp, y_exp, method <span class="o">=</span> <span class="s">"pearson"</span>), <span class="m">3</span>),</span>
<span class="cl"> <span class="s">"\nSpearman:"</span>, <span class="nf">round</span>(<span class="nf">cor</span>(x_exp, y_exp, method <span class="o">=</span> <span class="s">"spearman"</span>), <span class="m">3</span>))</span>
<span class="cl"><span class="c1">#> Pearson: 0.889</span></span>
<span class="cl"><span class="c1">#> Spearman: 0.993</span></span></div>
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<p>Spearman (0.993) is much closer to 1 than Pearson (0.889) because the relationship is perfectly monotonic, every increase in <code>x</code> produces an increase in <code>y</code>, even though the curve bends upward. Pearson underestimates the strength because it's looking for a straight line that isn't there.</p>
<p>Spearman also works naturally with ordinal data (ranks, survey ratings, Likert scales) where the raw numbers are just labels for order.</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">Ordinal ratings and satisfaction</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"># Ordinal data: customer satisfaction vs product rating</span></span>
<span class="cl"><span class="nf">set.seed</span>(<span class="m">33</span>)</span>
<span class="cl">ratings <span class="o"><-</span> <span class="nf">sample</span>(<span class="m">1</span><span class="o">:</span><span class="m">5</span>, <span class="m">20</span>, replace <span class="o">=</span> <span class="kc">TRUE</span>)</span>
<span class="cl">satisfaction <span class="o"><-</span> ratings <span class="o">+</span> <span class="nf">sample</span>(<span class="nf">c</span>(<span class="m">-1</span>, <span class="m">0</span>, <span class="m">0</span>, <span class="m">1</span>), <span class="m">20</span>, replace <span class="o">=</span> <span class="kc">TRUE</span>)</span>
<span class="cl">satisfaction <span class="o"><-</span> <span class="nf">pmin</span>(<span class="nf">pmax</span>(satisfaction, <span class="m">1</span>), <span class="m">5</span>) <span class="c1"># clamp to 1-5</span></span>
<span class="cl"></span>
<span class="cl"><span class="nf">cor</span>(ratings, satisfaction, method <span class="o">=</span> <span class="s">"spearman"</span>)</span>
<span class="cl"><span class="c1">#> [1] 0.7013561</span></span></div>
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<p>A <a class="auto-link" href="When-to-Use-Nonparametric-Tests-in-R.html" title="When to Use Nonparametric Tests in R: Decision Guide with Flowchart">Spearman correlation</a> of 0.70 on ordinal data tells us that higher product ratings are strongly associated with higher customer satisfaction scores. Pearson would give a similar number here, but Spearman is the theoretically correct choice because the data is ordinal, not truly continuous.</p>
<div class="callout callout-tip"><div class="callout-label">Tip</div><div class="callout-body"><strong>When in doubt between Pearson and Spearman, compute both.</strong> If they agree, the relationship is likely linear. If Spearman is notably higher, the relationship is monotonic but not linear, Spearman is the better summary.</div></div>
<section class="tryit-block">
<p><strong>Try it:</strong> The <code>iris</code> dataset has numeric measurements. Compute both Pearson and Spearman correlation between <code>Sepal.Length</code> and <code>Petal.Length</code>. Which one is stronger?</p>
<div class="webr-container" data-block-title="Exercise: pearson versus spearman on iris">
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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">Exercise: pearson versus spearman on iris</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"># Try it: Pearson vs Spearman on iris</span></span>
<span class="cl">ex_pearson <span class="o"><-</span> <span class="nf">cor</span>(iris<span class="o">$</span>Sepal.Length, iris<span class="o">$</span>Petal.Length, method <span class="o">=</span> <span class="s">"pearson"</span>)</span>
<span class="cl">ex_spearman <span class="o"><-</span> <span class="nf">cor</span>(iris<span class="o">$</span>Sepal.Length, iris<span class="o">$</span>Petal.Length, method <span class="o">=</span> <span class="s">"spearman"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"Pearson:"</span>, ex_pearson, <span class="s">"\nSpearman:"</span>, ex_spearman)</span>
<span class="cl"><span class="c1">#> Expected: both strong positive, Spearman slightly higher</span></span></div>
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<div class="webr-container" data-block-title="Iris pearson spearman solution">
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<div class="webr-header"><div class="webr-header-left"><span class="webr-header-badge">R</span><span class="webr-header-label">Iris pearson spearman solution</span></div><div class="webr-header-right"><button type="button" class="webr-copy-btn" aria-label="Copy code" title="Copy code"><svg width="14" height="14" viewBox="0 0 24 24" fill="none" stroke="currentColor" stroke-width="2" stroke-linecap="round" stroke-linejoin="round" aria-hidden="true"><rect x="9" y="9" width="13" height="13" rx="2" ry="2"/><path d="M5 15H4a2 2 0 0 1-2-2V4a2 2 0 0 1 2-2h9a2 2 0 0 1 2 2v1"/></svg></button><button class="btn btn-sm btn-primary webr-run-btn" onclick="runWebR(this)">▶ Run <span class="webr-run-shortcut">Ctrl+Enter</span></button></div></div>
<div class="webr-editor" data-language="r"><span class="cl">ex_pearson <span class="o"><-</span> <span class="nf">cor</span>(iris<span class="o">$</span>Sepal.Length, iris<span class="o">$</span>Petal.Length, method <span class="o">=</span> <span class="s">"pearson"</span>)</span>
<span class="cl">ex_spearman <span class="o"><-</span> <span class="nf">cor</span>(iris<span class="o">$</span>Sepal.Length, iris<span class="o">$</span>Petal.Length, method <span class="o">=</span> <span class="s">"spearman"</span>)</span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"Pearson: "</span>, <span class="nf">round</span>(ex_pearson, <span class="m">4</span>),</span>
<span class="cl"> <span class="s">"\nSpearman:"</span>, <span class="nf">round</span>(ex_spearman, <span class="m">4</span>))</span>
<span class="cl"><span class="c1">#> Pearson: 0.8718</span></span>
<span class="cl"><span class="c1">#> Spearman: 0.8819</span></span></div>
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<p><strong>Explanation:</strong> Both are strong (~0.87-0.88). Spearman is slightly higher, suggesting a mild non-linearity driven by the three species forming clusters along the relationship.</p>
</details>
</section>
<h2>When is Kendall's tau the better choice?</h2>
<p>Kendall's tau takes a fundamentally different approach. Instead of working with the actual values or even their ranks, it looks at every possible <em>pair</em> of observations and asks: "Do these two points agree on the direction?"</p>
<p>For a pair of points $(x_1, y_1)$ and $(x_2, y_2)$:</p>
<ul>
<li><strong>Concordant:</strong> both variables move in the same direction ($x_1 < x_2$ and $y_1 < y_2$, or both greater)</li>
<li><strong>Discordant:</strong> the variables move in opposite directions</li>
</ul>
<p>$$\tau = \frac{\text{concordant pairs} - \text{<a class="auto-link" href="McNemars-Test-in-R.html" title="McNemar's Test in R: Paired Categorical Data & Matched Case-Control">discordant pairs</a>}}{\text{total pairs}}$$</p>
<p>Where:</p>
<ul>
<li>$\tau$ = Kendall's tau</li>
<li>Total pairs = $\frac{n(n-1)}{2}$</li>
</ul>
<p>This pair-counting approach gives Kendall two practical advantages. First, it's more reliable than Spearman with <strong>small samples</strong> (n < 30), because each pair provides an independent piece of evidence. Second, it handles <strong>tied values</strong> more gracefully, important with ordinal or discrete data.</p>
<div class="webr-container" data-block-title="Small sample all three methods">
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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">Small sample all three methods</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"># Small sample: compare all three</span></span>
<span class="cl"><span class="nf">set.seed</span>(<span class="m">55</span>)</span>
<span class="cl">small_x <span class="o"><-</span> <span class="nf">c</span>(<span class="m">2</span>, <span class="m">5</span>, <span class="m">3</span>, <span class="m">8</span>, <span class="m">7</span>, <span class="m">1</span>, <span class="m">9</span>, <span class="m">4</span>, <span class="m">6</span>, <span class="m">10</span>)</span>
<span class="cl">small_y <span class="o"><-</span> <span class="nf">c</span>(<span class="m">3</span>, <span class="m">6</span>, <span class="m">2</span>, <span class="m">9</span>, <span class="m">8</span>, <span class="m">1</span>, <span class="m">10</span>, <span class="m">5</span>, <span class="m">4</span>, <span class="m">7</span>)</span>
<span class="cl"></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"Pearson: "</span>, <span class="nf">round</span>(<span class="nf">cor</span>(small_x, small_y, method <span class="o">=</span> <span class="s">"pearson"</span>), <span class="m">3</span>),</span>
<span class="cl"> <span class="s">"\nSpearman:"</span>, <span class="nf">round</span>(<span class="nf">cor</span>(small_x, small_y, method <span class="o">=</span> <span class="s">"spearman"</span>), <span class="m">3</span>),</span>
<span class="cl"> <span class="s">"\nKendall: "</span>, <span class="nf">round</span>(<span class="nf">cor</span>(small_x, small_y, method <span class="o">=</span> <span class="s">"kendall"</span>), <span class="m">3</span>))</span>
<span class="cl"><span class="c1">#> Pearson: 0.939</span></span>
<span class="cl"><span class="c1">#> Spearman: 0.927</span></span>
<span class="cl"><span class="c1">#> Kendall: 0.822</span></span></div>
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<p>Notice that Kendall's tau (0.822) is noticeably lower than Spearman's rho (0.927). This is <em>not</em> a weakness, Kendall and Spearman use different scales. Kendall's values are naturally more conservative because it counts individual pair agreements rather than measuring rank deviation. Think of it like comparing Celsius and Fahrenheit, different scales, same underlying temperature.</p>
<p><img src="screenshots/Correlation-Analysis-in-R-method-decision.webp" alt="Decision flowchart: which correlation method?" class="img-responsive img-zoomable" loading="lazy" width="1092" height="3056" /></p>
<p><em>Figure 2: Decision flowchart: which correlation method fits your data?</em></p>
<div class="callout callout-note"><div class="callout-label">Note</div><div class="callout-body"><strong>Kendall's tau values are typically lower than Spearman's rho for the same data.</strong> Don't compare them directly, they measure slightly different things. A tau of 0.7 and a rho of 0.85 can represent the same underlying relationship strength.</div></div>
<section class="tryit-block">
<p><strong>Try it:</strong> Create a small dataset of 8 paired observations where some values are tied. Compute both Kendall's tau and Spearman's rho. Do the ties change the relative gap between them?</p>
<div class="webr-container" data-block-title="Exercise: kendall and spearman with ties">
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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">Exercise: kendall and spearman with ties</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"># Try it: ties in small data</span></span>
<span class="cl">ex_x <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>
<span class="cl">ex_y <span class="o"><-</span> <span class="nf">c</span>(<span class="m">2</span>, <span class="m">3</span>, <span class="m">4</span>, <span class="m">3</span>, <span class="m">5</span>, <span class="m">5</span>, <span class="m">6</span>, <span class="m">7</span>)</span>
<span class="cl"><span class="c1"># your code here: compute Kendall and Spearman</span></span>
<span class="cl"><span class="c1">#> Expected: both positive, Kendall lower than Spearman</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">Kendall spearman with ties 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_x <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>
<span class="cl">ex_y <span class="o"><-</span> <span class="nf">c</span>(<span class="m">2</span>, <span class="m">3</span>, <span class="m">4</span>, <span class="m">3</span>, <span class="m">5</span>, <span class="m">5</span>, <span class="m">6</span>, <span class="m">7</span>)</span>
<span class="cl"></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"Spearman:"</span>, <span class="nf">round</span>(<span class="nf">cor</span>(ex_x, ex_y, method <span class="o">=</span> <span class="s">"spearman"</span>), <span class="m">4</span>),</span>
<span class="cl"> <span class="s">"\nKendall: "</span>, <span class="nf">round</span>(<span class="nf">cor</span>(ex_x, ex_y, method <span class="o">=</span> <span class="s">"kendall"</span>), <span class="m">4</span>))</span>
<span class="cl"><span class="c1">#> Spearman: 0.9272</span></span>
<span class="cl"><span class="c1">#> Kendall: 0.8528</span></span></div>
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<p><strong>Explanation:</strong> Both show strong positive correlation. Kendall handles the tied values (the repeated 2s and 4s in x, repeated 5s in y) using the tau-b correction, which adjusts the denominator for ties.</p>
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</section>
<h2>How do you test if a correlation is statistically significant?</h2>
<p>A correlation coefficient by itself doesn't tell you whether the relationship is real or just sampling noise. Is r = −0.87 genuinely strong, or could random data produce a number that large? That's where <code>cor.test()</code> comes in, it gives you a p-value and <a class="auto-link" href="Confidence-Intervals-in-R.html" title="Confidence Intervals in R: The Definition Most Textbooks State Incorrectly">confidence interval</a> alongside the correlation.</p>
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<div class="webr-editor" data-language="r"><span class="cl"><span class="c1"># Full significance test</span></span>
<span class="cl">test_result <span class="o"><-</span> <span class="nf">cor.test</span>(mtcars<span class="o">$</span>wt, mtcars<span class="o">$</span>mpg, method <span class="o">=</span> <span class="s">"pearson"</span>)</span>
<span class="cl">test_result</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$wt and mtcars$mpg</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">#> 95 percent confidence interval:</span></span>
<span class="cl"><span class="c1">#> -0.9338264 -0.7440872</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>Let's unpack each piece of this output:</p>
<ul>
<li><strong>t = −9.559:</strong> the test statistic. Larger absolute values mean stronger evidence against 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> (no correlation)</li>
<li><strong>df = 30:</strong> degrees of freedom (n − 2 = 32 − 2)</li>
<li><strong>p-value = 1.29 × 10⁻¹⁰:</strong> the probability of seeing a correlation this extreme if there were truly no relationship. This is astronomically small, the relationship is real</li>
<li><strong>95% CI: [−0.93, −0.74]:</strong> we're 95% confident the true correlation falls in this range. It's entirely negative and entirely strong</li>
<li><strong>cor = −0.868:</strong> the point estimate</li>
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<p>You can extract individual components for use in reports or further analysis.</p>
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<div class="webr-editor" data-language="r"><span class="cl"><span class="c1"># Extract components programmatically</span></span>
<span class="cl"><span class="nf">cat</span>(<span class="s">"Correlation:"</span>, test_result<span class="o">$</span>estimate,</span>
<span class="cl"> <span class="s">"\np-value: "</span>, test_result<span class="o">$</span>p.value,</span>
<span class="cl"> <span class="s">"\n95% CI: "</span>, test_result<span class="o">$</span>conf.int)</span>
<span class="cl"><span class="c1">#> Correlation: -0.8676594</span></span>
<span class="cl"><span class="c1">#> p-value: 1.293959e-10</span></span>
<span class="cl"><span class="c1">#> 95% CI: -0.9338264 -0.7440872</span></span></div>
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<p>The confidence interval is especially useful, it tells you how <em>precise</em> your estimate is. A wide interval means you need more data; a narrow one means you can trust the number.</p>