{"id":10889,"date":"2019-11-30T09:46:40","date_gmt":"2019-11-30T07:46:40","guid":{"rendered":"https:\/\/www.datanovia.com\/en\/?post_type=dt_lessons&#038;p=10889"},"modified":"2019-12-05T00:04:32","modified_gmt":"2019-12-04T22:04:32","slug":"kruskal-wallis-test-in-r","status":"publish","type":"dt_lessons","link":"https:\/\/www.datanovia.com\/en\/lessons\/kruskal-wallis-test-in-r\/","title":{"rendered":"Kruskal-Wallis Test in R"},"content":{"rendered":"<div id=\"rdoc\">\n<p><strong>Kruskal-Wallis test<\/strong> is a non-parametric alternative to the one-way ANOVA test. It extends the two-samples Wilcoxon test in the situation where there are more than two groups to compare. It\u2019s recommended when the assumptions of one-way ANOVA test are not met.<\/p>\n<p>This chapter describes how to compute the Kruskal-Wallis test using the R software. You will also learn how to calculate the <em>effect size<\/em> based on kruskal-Wallis <em>H-statistic<\/em>.<\/p>\n<p>Contents:<\/p>\n<div id=\"TOC\">\n<ul>\n<li><a href=\"#prerequisites\">Prerequisites<\/a><\/li>\n<li><a href=\"#data-preparation\">Data preparation<\/a><\/li>\n<li><a href=\"#summary-statistics\">summary statistics<\/a><\/li>\n<li><a href=\"#visualization\">Visualization<\/a><\/li>\n<li><a href=\"#computation\">Computation<\/a><\/li>\n<li><a href=\"#effect-size\">Effect size<\/a><\/li>\n<li><a href=\"#multiple-pairwise-comparisons\">Multiple pairwise-comparisons<\/a><\/li>\n<li><a href=\"#report\">Report<\/a><\/li>\n<li><a href=\"#references\">References<\/a><\/li>\n<\/ul>\n<\/div>\n<div class='dt-sc-hr-invisible-medium  '><\/div>\n<div class='dt-sc-ico-content type1'><div class='custom-icon' ><a href='https:\/\/www.datanovia.com\/en\/product\/practical-statistics-in-r-for-comparing-groups-numerical-variables\/' target='_blank'><span class='fa fa-book'><\/span><\/a><\/div><h4><a href='https:\/\/www.datanovia.com\/en\/product\/practical-statistics-in-r-for-comparing-groups-numerical-variables\/' target='_blank'> Related Book <\/a><\/h4>Practical Statistics in R II - Comparing Groups: Numerical Variables<\/div>\n<div class='dt-sc-hr-invisible-medium  '><\/div>\n<div id=\"prerequisites\" class=\"section level2\">\n<h2>Prerequisites<\/h2>\n<p>Make sure you have installed the following R packages:<\/p>\n<ul>\n<li><code>tidyverse<\/code> for data manipulation and visualization<\/li>\n<li><code>ggpubr<\/code> for creating easily publication ready plots<\/li>\n<li><code>rstatix<\/code> provides pipe-friendly R functions for easy statistical analyses.<\/li>\n<\/ul>\n<p>Load the packages:<\/p>\n<pre class=\"r\"><code>library(tidyverse)\r\nlibrary(ggpubr)\r\nlibrary(rstatix)<\/code><\/pre>\n<\/div>\n<div id=\"data-preparation\" class=\"section level2\">\n<h2>Data preparation<\/h2>\n<p>Here, we\u2019ll use the built-in R data set named <em>PlantGrowth<\/em>. It contains the weight of plants obtained under a control and two different treatment conditions.<\/p>\n<pre class=\"r\"><code>set.seed(1234)\r\nPlantGrowth %&gt;% sample_n_by(group, size = 1)<\/code><\/pre>\n<pre><code>## # A tibble: 3 x 2\r\n##   weight group\r\n##    &lt;dbl&gt; &lt;fct&gt;\r\n## 1   5.58 ctrl \r\n## 2   6.03 trt1 \r\n## 3   4.92 trt2<\/code><\/pre>\n<ul>\n<li>Re-order the group levels:<\/li>\n<\/ul>\n<pre class=\"r\"><code>PlantGrowth &lt;- PlantGrowth %&gt;%\r\n  reorder_levels(group, order = c(\"ctrl\", \"trt1\", \"trt2\"))<\/code><\/pre>\n<\/div>\n<div id=\"summary-statistics\" class=\"section level2\">\n<h2>summary statistics<\/h2>\n<p>Compute summary statistics by groups:<\/p>\n<pre class=\"r\"><code>PlantGrowth %&gt;% \r\n  group_by(group) %&gt;%\r\n  get_summary_stats(weight, type = \"common\")<\/code><\/pre>\n<pre><code>## # A tibble: 3 x 11\r\n##   group variable     n   min   max median   iqr  mean    sd    se    ci\r\n##   &lt;fct&gt; &lt;chr&gt;    &lt;dbl&gt; &lt;dbl&gt; &lt;dbl&gt;  &lt;dbl&gt; &lt;dbl&gt; &lt;dbl&gt; &lt;dbl&gt; &lt;dbl&gt; &lt;dbl&gt;\r\n## 1 ctrl  weight      10  4.17  6.11   5.16 0.743  5.03 0.583 0.184 0.417\r\n## 2 trt1  weight      10  3.59  6.03   4.55 0.662  4.66 0.794 0.251 0.568\r\n## 3 trt2  weight      10  4.92  6.31   5.44 0.467  5.53 0.443 0.14  0.317<\/code><\/pre>\n<\/div>\n<div id=\"visualization\" class=\"section level2\">\n<h2>Visualization<\/h2>\n<p>Create a box plot of <code>weight<\/code> by <code>group<\/code>:<\/p>\n<pre class=\"r\"><code>ggboxplot(PlantGrowth, x = \"group\", y = \"weight\")<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/dn-tutorials\/r-statistics-2-comparing-groups-means\/figures\/050-kruskal-wallis-test-in-r-box-plot-1.png\" width=\"288\" \/><\/p>\n<\/div>\n<div id=\"computation\" class=\"section level2\">\n<h2>Computation<\/h2>\n<p>Question: We want to know if there is any significant difference between the average weights of plants in the 3 experimental conditions.<\/p>\n<p>We\u2019ll use the pipe-friendly <code>kruskal_test()<\/code> function [rstatix package], a wrapper around the R base function <code>kruskal.test()<\/code>.<\/p>\n<pre class=\"r\"><code>res.kruskal &lt;- PlantGrowth %&gt;% kruskal_test(weight ~ group)\r\nres.kruskal<\/code><\/pre>\n<pre><code>## # A tibble: 1 x 6\r\n##   .y.        n statistic    df      p method        \r\n## * &lt;chr&gt;  &lt;int&gt;     &lt;dbl&gt; &lt;int&gt;  &lt;dbl&gt; &lt;chr&gt;         \r\n## 1 weight    30      7.99     2 0.0184 Kruskal-Wallis<\/code><\/pre>\n<\/div>\n<div id=\"effect-size\" class=\"section level2\">\n<h2>Effect size<\/h2>\n<p>The eta squared, based on the H-statistic, can be used as the measure of the Kruskal-Wallis test effect size. It is calculated as follow : <code>eta2[H] = (H - k + 1)\/(n - k)<\/code>; where <code>H<\/code> is the value obtained in the Kruskal-Wallis test; <code>k<\/code> is the number of groups; <code>n<\/code> is the total number of observations <span class=\"citation\">(M. T. Tomczak and Tomczak 2014)<\/span>.<\/p>\n<p>The eta-squared estimate assumes values from 0 to 1 and multiplied by 100 indicates the percentage of variance in the dependent variable explained by the independent variable.<\/p>\n<p>The interpretation values commonly in published literature are: 0.01- &lt; 0.06 (small effect), 0.06 - &lt; 0.14 (moderate effect) and &gt;= 0.14 (large effect).<\/p>\n<pre class=\"r\"><code>PlantGrowth %&gt;% kruskal_effsize(weight ~ group)<\/code><\/pre>\n<pre><code>## # A tibble: 1 x 5\r\n##   .y.        n effsize method  magnitude\r\n## * &lt;chr&gt;  &lt;int&gt;   &lt;dbl&gt; &lt;chr&gt;   &lt;ord&gt;    \r\n## 1 weight    30   0.222 eta2[H] large<\/code><\/pre>\n<div class=\"success\">\n<p>A large effect size is detected, eta2[H] = 0.22.<\/p>\n<\/div>\n<\/div>\n<div id=\"multiple-pairwise-comparisons\" class=\"section level2\">\n<h2>Multiple pairwise-comparisons<\/h2>\n<p>From the output of the Kruskal-Wallis test, we know that there is a significant difference between groups, but we don\u2019t know which pairs of groups are different.<\/p>\n<p>A significant Kruskal-Wallis test is generally followed up by <strong>Dunn\u2019s test<\/strong> to identify which groups are different. It\u2019s also possible to use the Wilcoxon\u2019s test to calculate pairwise comparisons between group levels with corrections for multiple testing.<\/p>\n<div class=\"warning\">\n<p>Compared to the Wilcoxon\u2019s test, the Dunn\u2019s test takes into account the rankings used by the Kruskal-Wallis test. It also does ties adjustments.<\/p>\n<\/div>\n<ul>\n<li><strong>Pairwise comparisons using Dunn\u2019s test<\/strong>:<\/li>\n<\/ul>\n<pre class=\"r\"><code># Pairwise comparisons\r\npwc &lt;- PlantGrowth %&gt;% \r\n  dunn_test(weight ~ group, p.adjust.method = \"bonferroni\") \r\npwc<\/code><\/pre>\n<pre><code>## # A tibble: 3 x 9\r\n##   .y.    group1 group2    n1    n2 statistic       p  p.adj p.adj.signif\r\n## * &lt;chr&gt;  &lt;chr&gt;  &lt;chr&gt;  &lt;int&gt; &lt;int&gt;     &lt;dbl&gt;   &lt;dbl&gt;  &lt;dbl&gt; &lt;chr&gt;       \r\n## 1 weight ctrl   trt1      10    10     -1.12 0.264   0.791  ns          \r\n## 2 weight ctrl   trt2      10    10      1.69 0.0912  0.273  ns          \r\n## 3 weight trt1   trt2      10    10      2.81 0.00500 0.0150 *<\/code><\/pre>\n<ul>\n<li><strong>Pairwise comparisons using Wilcoxon\u2019s test<\/strong>:<\/li>\n<\/ul>\n<pre class=\"r\"><code>pwc2 &lt;- PlantGrowth %&gt;% \r\n  wilcox_test(weight ~ group, p.adjust.method = \"bonferroni\")\r\npwc2<\/code><\/pre>\n<pre><code>## # A tibble: 3 x 9\r\n##   .y.    group1 group2    n1    n2 statistic     p p.adj p.adj.signif\r\n## * &lt;chr&gt;  &lt;chr&gt;  &lt;chr&gt;  &lt;int&gt; &lt;int&gt;     &lt;dbl&gt; &lt;dbl&gt; &lt;dbl&gt; &lt;chr&gt;       \r\n## 1 weight ctrl   trt1      10    10      67.5 0.199 0.597 ns          \r\n## 2 weight ctrl   trt2      10    10      25   0.063 0.189 ns          \r\n## 3 weight trt1   trt2      10    10      16   0.009 0.027 *<\/code><\/pre>\n<div class=\"success\">\n<p>The pairwise comparison shows that, only trt1 and trt2 are significantly different (Wilcoxon\u2019s test, p = 0.027).<\/p>\n<\/div>\n<\/div>\n<div id=\"report\" class=\"section level2\">\n<h2>Report<\/h2>\n<p>There was a statistically significant differences between treatment groups as assessed using the Kruskal-Wallis test (p = 0.018). Pairwise Wilcoxon test between groups showed that only the difference between trt1 and trt2 group was significant (Wilcoxon\u2019s test, p = 0.027)<\/p>\n<pre class=\"r\"><code># Visualization: box plots with p-values\r\npwc &lt;- pwc %&gt;% add_xy_position(x = \"group\")\r\nggboxplot(PlantGrowth, x = \"group\", y = \"weight\") +\r\n  stat_pvalue_manual(pwc, hide.ns = TRUE) +\r\n  labs(\r\n    subtitle = get_test_label(res.kruskal, detailed = TRUE),\r\n    caption = get_pwc_label(pwc)\r\n    )<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/dn-tutorials\/r-statistics-2-comparing-groups-means\/figures\/050-kruskal-wallis-test-in-r-kruskal-wallis-1.png\" width=\"480\" \/><\/p>\n<\/div>\n<div id=\"references\" class=\"section level2 unnumbered\">\n<h2>References<\/h2>\n<div id=\"refs\" class=\"references\">\n<div id=\"ref-tomczak2014\">\n<p>Tomczak, Maciej T., and Ewa Tomczak. 2014. \u201cThe Need to Report Effect Size Estimates Revisited. an Overview of Some Recommended Measures of Effect Size.\u201d Trends in SportSciences.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><!--end rdoc--><\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Kruskal-Wallis test is a non-parametric alternative to the one-way ANOVA test. It&#8217;s recommended when the assumptions of one-way ANOVA test are not met.  This chapter describes how to compute the Kruskal-Wallis test using the R software.<\/p>\n","protected":false},"author":1,"featured_media":8952,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"","class_list":["post-10889","dt_lessons","type-dt_lessons","status-publish","has-post-thumbnail","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Kruskal-Wallis Test in R: The Ultimate Guide - Datanovia<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.datanovia.com\/en\/lessons\/kruskal-wallis-test-in-r\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Kruskal-Wallis Test in R: The Ultimate Guide - Datanovia\" \/>\n<meta property=\"og:description\" content=\"The Kruskal-Wallis test is a non-parametric alternative to the one-way ANOVA test. 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