{"id":10890,"date":"2019-11-30T10:23:01","date_gmt":"2019-11-30T08:23:01","guid":{"rendered":"https:\/\/www.datanovia.com\/en\/?post_type=dt_lessons&#038;p=10890"},"modified":"2019-12-05T00:09:18","modified_gmt":"2019-12-04T22:09:18","slug":"friedman-test-in-r","status":"publish","type":"dt_lessons","link":"https:\/\/www.datanovia.com\/en\/lessons\/friedman-test-in-r\/","title":{"rendered":"Friedman Test in R"},"content":{"rendered":"<div id=\"rdoc\">\n<p>The <strong>Friedman test<\/strong> is a non-parametric alternative to the one-way repeated measures ANOVA test. It extends the <em>Sign test<\/em> in the situation where there are more than two groups to compare.<\/p>\n<p><strong>Friedman test<\/strong> is used to assess whether there are any statistically significant differences between the distributions of three or more paired groups. It\u2019s recommended when the normality assumptions of the one-way repeated measures ANOVA test is not met or when the dependent variable is measured on an ordinal scale.<\/p>\n<p>In this chapter, you\u2019ll learn how to:<\/p>\n<ul>\n<li><strong>Compute Friedman test in R<\/strong><\/li>\n<li><strong>Perform multiple pairwise-comparison between groups<\/strong>, to identify which pairs of groups are significantly different.<\/li>\n<li><strong>Determine the effect size of Friedman test using the Kendall\u2019s W<\/strong>.<\/li>\n<\/ul>\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>We\u2019ll use the self esteem score dataset measured over three time points. The data is available in the datarium package.<\/p>\n<pre class=\"r\"><code>data(\"selfesteem\", package = \"datarium\")\r\nhead(selfesteem, 3)<\/code><\/pre>\n<pre><code>## # A tibble: 3 x 4\r\n##      id    t1    t2    t3\r\n##   &lt;int&gt; &lt;dbl&gt; &lt;dbl&gt; &lt;dbl&gt;\r\n## 1     1  4.01  5.18  7.11\r\n## 2     2  2.56  6.91  6.31\r\n## 3     3  3.24  4.44  9.78<\/code><\/pre>\n<p>Gather columns <code>t1<\/code>, <code>t2<\/code> and <code>t3<\/code> into long format. Convert <code>id<\/code> and <code>time<\/code> variables into factor (or grouping) variables:<\/p>\n<pre class=\"r\"><code>selfesteem &lt;- selfesteem %&gt;%\r\n  gather(key = \"time\", value = \"score\", t1, t2, t3) %&gt;%\r\n  convert_as_factor(id, time)\r\nhead(selfesteem, 3)<\/code><\/pre>\n<pre><code>## # A tibble: 3 x 3\r\n##   id    time  score\r\n##   &lt;fct&gt; &lt;fct&gt; &lt;dbl&gt;\r\n## 1 1     t1     4.01\r\n## 2 2     t1     2.56\r\n## 3 3     t1     3.24<\/code><\/pre>\n<\/div>\n<div id=\"summary-statistics\" class=\"section level2\">\n<h2>Summary statistics<\/h2>\n<p>Compute some summary statistics of the self-esteem <code>score<\/code> by groups (<code>time<\/code>):<\/p>\n<pre class=\"r\"><code>selfesteem %&gt;%\r\n  group_by(time) %&gt;%\r\n  get_summary_stats(score, type = \"common\")<\/code><\/pre>\n<pre><code>## # A tibble: 3 x 11\r\n##   time  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 t1    score       10  2.05  4.00   3.21 0.571  3.14 0.552 0.174 0.395\r\n## 2 t2    score       10  3.91  6.91   4.60 0.89   4.93 0.863 0.273 0.617\r\n## 3 t3    score       10  6.31  9.78   7.46 1.74   7.64 1.14  0.361 0.817<\/code><\/pre>\n<\/div>\n<div id=\"visualization\" class=\"section level2\">\n<h2>Visualization<\/h2>\n<p>Create a box plot and add points corresponding to individual values<\/p>\n<pre class=\"r\"><code>ggboxplot(selfesteem, x = \"time\", y = \"score\", add = \"jitter\")<\/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\/051-friedman-test-visualization-1.png\" width=\"336\" \/><\/p>\n<\/div>\n<div id=\"computation\" class=\"section level2\">\n<h2>Computation<\/h2>\n<p>We\u2019ll use the pipe-friendly <code>friedman_test()<\/code> function [rstatix package], a wrapper around the R base function <code>friedman.test()<\/code>.<\/p>\n<pre class=\"r\"><code>res.fried &lt;- selfesteem %&gt;% friedman_test(score ~ time |id)\r\nres.fried<\/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;dbl&gt;    &lt;dbl&gt; &lt;chr&gt;        \r\n## 1 score    10      18.2     2 0.000112 Friedman test<\/code><\/pre>\n<div class=\"success\">\n<p>The self esteem score was statistically significantly different at the different time points during the diet, X2(2) = 18.2, p = 0.0001.<\/p>\n<\/div>\n<\/div>\n<div id=\"effect-size\" class=\"section level2\">\n<h2>Effect size<\/h2>\n<p>The Kendall\u2019s W can be used as the measure of the Friedman test effect size. It is calculated as follow : <code>W = X2\/N(K-1)<\/code>; where <code>W<\/code> is the Kendall\u2019s W value; <code>X2<\/code> is the Friedman test statistic value; <code>N<\/code> is the sample size. <code>k<\/code> is the number of measurements per subject <span class=\"citation\">(M. T. Tomczak and Tomczak 2014)<\/span>.<\/p>\n<p>The Kendall\u2019s W coefficient assumes the value from 0 (indicating no relationship) to 1 (indicating a perfect relationship).<\/p>\n<p>Kendall\u2019s W uses the Cohen\u2019s interpretation guidelines of 0.1 - &lt; 0.3 (small effect), 0.3 - &lt; 0.5 (moderate effect) and &gt;= 0.5 (large effect). Confidence intervals are calculated by bootstap.<\/p>\n<pre class=\"r\"><code>selfesteem %&gt;% friedman_effsize(score ~ time |id)<\/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 score    10   0.910 Kendall W large<\/code><\/pre>\n<div class=\"success\">\n<p>A large effect size is detected, W = 0.91.<\/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 Friedman 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 Friedman test can be followed up by pairwise <strong>Wilcoxon signed-rank tests<\/strong> for identifying which groups are different.<\/p>\n<div class=\"warning\">\n<p>Note that, the data must be correctly ordered by the blocking variable (<code>id<\/code>) so that the first observation for time <code>t1<\/code> will be paired with the first observation for time <code>t2<\/code>, and so on.<\/p>\n<\/div>\n<p><strong>Pairwise comparisons using paired Wilcoxon signed-rank test<\/strong>. P-values are adjusted using the Bonferroni multiple testing correction method.<\/p>\n<pre class=\"r\"><code># pairwise comparisons\r\npwc &lt;- selfesteem %&gt;%\r\n  wilcox_test(score ~ time, paired = TRUE, 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 score t1     t2        10    10         0 0.002 0.006 **          \r\n## 2 score t1     t3        10    10         0 0.002 0.006 **          \r\n## 3 score t2     t3        10    10         1 0.004 0.012 *<\/code><\/pre>\n<div class=\"success\">\n<p>All the pairwise differences are statistically significant.<\/p>\n<\/div>\n<div class=\"notice\">\n<p>Note that, it is also possible to perform pairwise comparisons using Sign Test, which may lack power in detecting differences in paired data sets. However, it is useful because it has few assumptions about the distributions of the data to compare.<\/p>\n<\/div>\n<p><strong>Pairwise comparisons using sign test<\/strong>:<\/p>\n<pre class=\"r\"><code>pwc2 &lt;- selfesteem %&gt;%\r\n  sign_test(score ~ time, p.adjust.method = \"bonferroni\")\r\npwc2<\/code><\/pre>\n<\/div>\n<div id=\"report\" class=\"section level2\">\n<h2>Report<\/h2>\n<p>The self-esteem score was statistically significantly different at the different time points using Friedman test, X2(2) = 18.2, p = 0.00011.<\/p>\n<p>Pairwise Wilcoxon signed rank test between groups revealed statistically significant differences in self esteem score between t1 and t2 (p = 0.006); t1 and t3 (0.006); t2 and t3 (0.012).<\/p>\n<pre class=\"r\"><code># Visualization: box plots with p-values\r\npwc &lt;- pwc %&gt;% add_xy_position(x = \"time\")\r\nggboxplot(selfesteem, x = \"time\", y = \"score\", add = \"point\") +\r\n  stat_pvalue_manual(pwc, hide.ns = TRUE) +\r\n  labs(\r\n    subtitle = get_test_label(res.fried,  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\/051-friedman-test-freedman-test-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 Friedman test is a non-parametric alternative to the one-way repeated measures ANOVA test. It extends the Sign test in the situation where there are more than two groups to compare. It&#8217;s recommended when the normality assumptions of the one-way repeated measures ANOVA test is not met or when the dependent variable is measured on an ordinal scale. In this chapter, you will learn how to compute Friedman test in R and to perform pairwise-comparison between groups.<\/p>\n","protected":false},"author":1,"featured_media":9081,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"","class_list":["post-10890","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>Friedman 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\/friedman-test-in-r\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Friedman Test in R: The Ultimate Guide - Datanovia\" \/>\n<meta property=\"og:description\" content=\"The Friedman test is a non-parametric alternative to the one-way repeated measures ANOVA test. 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