{"id":10892,"date":"2019-11-30T10:49:12","date_gmt":"2019-11-30T08:49:12","guid":{"rendered":"https:\/\/www.datanovia.com\/en\/?post_type=dt_lessons&#038;p=10892"},"modified":"2019-11-30T10:50:48","modified_gmt":"2019-11-30T08:50:48","slug":"normality-test-in-r","status":"publish","type":"dt_lessons","link":"https:\/\/www.datanovia.com\/en\/lessons\/normality-test-in-r\/","title":{"rendered":"Normality Test in R"},"content":{"rendered":"<div id=\"rdoc\">\n<p>Many of the statistical methods including correlation, regression, t tests, and analysis of variance assume that the data follows a normal distribution or a Gaussian distribution. These tests are called parametric tests, because their validity depends on the distribution of the data.<\/p>\n<p>Normality and the other assumptions made by these tests should be taken seriously to draw reliable interpretation and conclusions of the research.<\/p>\n<p>With large enough sample sizes (&gt; 30 or 40), there\u2019s a pretty good chance that the data will be normally distributed; or at least close enough to normal that you can get away with using parametric tests, such as t-test (central limit theorem).<\/p>\n<p>In this chapter, you will learn how to check the <strong>normality of the data in R<\/strong> by visual inspection (<em>QQ plots<\/em> and <strong>density distributions<\/strong>) and by significance tests (<em>Shapiro-Wilk test<\/em>).<\/p>\n<p>Contents:<\/p>\n<div id=\"TOC\">\n<ul>\n<li><a href=\"#prerequisites\">Prerequisites<\/a><\/li>\n<li><a href=\"#demo-data\">Demo data<\/a><\/li>\n<li><a href=\"#examples-of-distribution-shapes\">Examples of distribution shapes<\/a><\/li>\n<li><a href=\"#check-normality-in-r\">Check normality in R<\/a>\n<ul>\n<li><a href=\"#visual-methods\">Visual methods<\/a><\/li>\n<li><a href=\"#shapiro-wilks-normality-test\">Shapiro-Wilk\u2019s normality test<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#summary\">Summary<\/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>Start by loading the packages:<\/p>\n<pre class=\"r\"><code>library(tidyverse)\r\nlibrary(ggpubr)\r\nlibrary(rstatix)<\/code><\/pre>\n<\/div>\n<div id=\"demo-data\" class=\"section level2\">\n<h2>Demo data<\/h2>\n<p>We\u2019ll use the <code>ToothGrowth<\/code> dataset. Inspect the data by displaying some random rows by groups:<\/p>\n<pre class=\"r\"><code>set.seed(1234)\r\nToothGrowth %&gt;% sample_n_by(supp, dose, size = 1)<\/code><\/pre>\n<pre><code>## # A tibble: 6 x 3\r\n##     len supp   dose\r\n##   &lt;dbl&gt; &lt;fct&gt; &lt;dbl&gt;\r\n## 1  21.5 OJ      0.5\r\n## 2  25.8 OJ      1  \r\n## 3  26.4 OJ      2  \r\n## 4  11.2 VC      0.5\r\n## 5  18.8 VC      1  \r\n## 6  26.7 VC      2<\/code><\/pre>\n<\/div>\n<div id=\"examples-of-distribution-shapes\" class=\"section level2\">\n<h2>Examples of distribution shapes<\/h2>\n<ul>\n<li><strong>Normal distribution<\/strong><\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/dn-tutorials\/r-statistics-2-comparing-groups-means\/figures\/016-normality-test-in-r-examples-of-normal-distribution-1.png\" width=\"288\" \/><img decoding=\"async\" src=\"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/dn-tutorials\/r-statistics-2-comparing-groups-means\/figures\/016-normality-test-in-r-examples-of-normal-distribution-2.png\" width=\"288\" \/><\/p>\n<ul>\n<li><strong>Skewed distributions<\/strong><\/li>\n<\/ul>\n<p><img decoding=\"async\" src=\"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/dn-tutorials\/r-statistics-2-comparing-groups-means\/figures\/016-normality-test-in-r-skewed-distributions-1.png\" width=\"288\" \/><img decoding=\"async\" src=\"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/dn-tutorials\/r-statistics-2-comparing-groups-means\/figures\/016-normality-test-in-r-skewed-distributions-2.png\" width=\"288\" \/><\/p>\n<\/div>\n<div id=\"check-normality-in-r\" class=\"section level2\">\n<h2>Check normality in R<\/h2>\n<p>Question: We want to test if the variable <code>len<\/code> (tooth length) is normally distributed.<\/p>\n<div id=\"visual-methods\" class=\"section level3\">\n<h3>Visual methods<\/h3>\n<p><strong>Density plot<\/strong> and <strong>Q-Q plot<\/strong> can be used to check normality visually.<\/p>\n<ol style=\"list-style-type: decimal;\">\n<li><strong>Density plot<\/strong>: the density plot provides a visual judgment about whether the distribution is bell shaped.<\/li>\n<li><strong>QQ plot<\/strong>: QQ plot (or quantile-quantile plot) draws the correlation between a given sample and the normal distribution. A 45-degree reference line is also plotted. In a QQ plot, each observation is plotted as a single dot. If the data are normal, the dots should form a straight line.<\/li>\n<\/ol>\n<pre class=\"r\"><code>library(\"ggpubr\")\r\n# Density plot\r\nggdensity(ToothGrowth$len, fill = \"lightgray\")\r\n# QQ plot\r\nggqqplot(ToothGrowth$len)<\/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\/016-normality-test-in-r-density-and-qq-plot-1.png\" width=\"336\" \/><img decoding=\"async\" src=\"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/dn-tutorials\/r-statistics-2-comparing-groups-means\/figures\/016-normality-test-in-r-density-and-qq-plot-2.png\" width=\"336\" \/><\/p>\n<div class=\"success\">\n<p>As all the points fall approximately along this reference line, we can assume normality.<\/p>\n<\/div>\n<\/div>\n<div id=\"shapiro-wilks-normality-test\" class=\"section level3\">\n<h3>Shapiro-Wilk\u2019s normality test<\/h3>\n<p>Visual inspection, described in the previous section, is usually unreliable. It\u2019s possible to use a significance test comparing the sample distribution to a normal one in order to ascertain whether data show or not a serious deviation from normality.<\/p>\n<p>There are several methods for evaluate normality, including the <strong>Kolmogorov-Smirnov (K-S) normality test<\/strong> and the <strong>Shapiro-Wilk\u2019s test<\/strong>.<\/p>\n<div class=\"warning\">\n<p>The null hypothesis of these tests is that \u201csample distribution is normal\u201d. If the test is <strong>significant<\/strong>, the distribution is non-normal.<\/p>\n<\/div>\n<p><strong>Shapiro-Wilk\u2019s method<\/strong> is widely recommended for normality test and it provides better power than K-S. It is based on the correlation between the data and the corresponding normal scores <span class=\"citation\">(Ghasemi and Zahediasl 2012)<\/span>.<\/p>\n<div class=\"warning\">\n<p>Note that, normality test is sensitive to sample size. Small samples most often pass normality tests. Therefore, it\u2019s important to combine visual inspection and significance test in order to take the right decision.<\/p>\n<\/div>\n<p>The R function <code>shapiro_test()<\/code> [rstatix package] provides a pipe-friendly framework to compute Shapiro-Wilk test for one or multiple variables. It also supports a grouped data. It\u2019s a wrapper around R base function <code>shapiro.test()<\/code>.<\/p>\n<ul>\n<li>Shapiro test for one variable:<\/li>\n<\/ul>\n<pre class=\"r\"><code>ToothGrowth %&gt;% shapiro_test(len)<\/code><\/pre>\n<pre><code>## # A tibble: 1 x 3\r\n##   variable statistic     p\r\n##   &lt;chr&gt;        &lt;dbl&gt; &lt;dbl&gt;\r\n## 1 len          0.967 0.109<\/code><\/pre>\n<div class=\"warning\">\n<p>From the output above, the p-value &gt; 0.05 implying that the distribution of the data are not significantly different from normal distribution. In other words, we can assume the normality.<\/p>\n<\/div>\n<ul>\n<li>Shapiro test for grouped data:<\/li>\n<\/ul>\n<pre class=\"r\"><code>ToothGrowth %&gt;%\r\n  group_by(dose) %&gt;%\r\n  shapiro_test(len)<\/code><\/pre>\n<pre><code>## # A tibble: 3 x 4\r\n##    dose variable statistic     p\r\n##   &lt;dbl&gt; &lt;chr&gt;        &lt;dbl&gt; &lt;dbl&gt;\r\n## 1   0.5 len          0.941 0.247\r\n## 2   1   len          0.931 0.164\r\n## 3   2   len          0.978 0.902<\/code><\/pre>\n<ul>\n<li>Shapiro test for multiple variables:<\/li>\n<\/ul>\n<pre class=\"r\"><code>iris %&gt;% shapiro_test(Sepal.Length, Petal.Width)<\/code><\/pre>\n<pre><code>## # A tibble: 2 x 3\r\n##   variable     statistic            p\r\n##   &lt;chr&gt;            &lt;dbl&gt;        &lt;dbl&gt;\r\n## 1 Petal.Width      0.902 0.0000000168\r\n## 2 Sepal.Length     0.976 0.0102<\/code><\/pre>\n<\/div>\n<\/div>\n<div id=\"summary\" class=\"section level2\">\n<h2>Summary<\/h2>\n<p>This chapter describes how to check the normality of a data using QQ-plot and Shapiro-Wilk test.<\/p>\n<p>Note that, if your sample size is greater than 50, the normal QQ plot is preferred because at larger sample sizes the Shapiro-Wilk test becomes very sensitive even to a minor deviation from normality.<\/p>\n<p>Consequently, we should not rely on only one approach for assessing the normality. A better strategy is to combine visual inspection and statistical test.<\/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-ghasemi2012\">\n<p>Ghasemi, Asghar, and Saleh Zahediasl. 2012. \u201cNormality Tests for Statistical Analysis: A Guide for Non-Statisticians.\u201d <em>Int J Endocrinol Metab<\/em> 10 (2): 486\u201389. doi:<a href=\"https:\/\/doi.org\/10.5812\/ijem.3505\">10.5812\/ijem.3505<\/a>.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<p><!--end rdoc--><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Many of the statistical methods including correlation, regression, t tests, and analysis of variance assume that the data follows a normal distribution or a Gaussian distribution. In this chapter, you will learn how to check the normality of the data in R by visual inspection (QQ plots and density distributions) and by significance tests (Shapiro-Wilk test).<\/p>\n","protected":false},"author":1,"featured_media":9120,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"","class_list":["post-10892","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>Normality Test in R: The Definitive 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\/normality-test-in-r\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Normality Test in R: The Definitive Guide - Datanovia\" \/>\n<meta property=\"og:description\" content=\"Many of the statistical methods including correlation, regression, t tests, and analysis of variance assume that the data follows a normal distribution or a Gaussian distribution. 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