{"id":11686,"date":"2019-12-26T09:51:07","date_gmt":"2019-12-26T07:51:07","guid":{"rendered":"https:\/\/www.datanovia.com\/en\/?post_type=dt_lessons&#038;p=11686"},"modified":"2019-12-26T09:51:07","modified_gmt":"2019-12-26T07:51:07","slug":"one-sample-t-test-assumptions","status":"publish","type":"dt_lessons","link":"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/","title":{"rendered":"One Sample T-Test Assumptions"},"content":{"rendered":"<div id=\"rdoc\">\n<p>This article describes the <strong>one sample t-test assumptions<\/strong> and provides examples of R code to check whether the assumptions are met before calculating the t-test.<\/p>\n<p>Contents:<\/p>\n<div id=\"TOC\">\n<ul>\n<li><a href=\"#assumptions\">Assumptions<\/a><\/li>\n<li><a href=\"#check-one-sample-t-test-assumptions-in-r\">Check one-sample t-test assumptions in R<\/a>\n<ul>\n<li><a href=\"#prerequisites\">Prerequisites<\/a><\/li>\n<li><a href=\"#demo-data\">Demo data<\/a><\/li>\n<li><a href=\"#identify-outliers\">Identify outliers<\/a><\/li>\n<li><a href=\"#check-normality-assumption\">Check normality assumption<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#related-article\">Related article<\/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=\"assumptions\" class=\"section level2\">\n<h2>Assumptions<\/h2>\n<p>The one-sample t-test assumes the following characteristics about the data:<\/p>\n<ul>\n<li><strong>No significant outliers<\/strong> in the data<\/li>\n<li><strong>Normality<\/strong>. the data should be approximately normally distributed<\/li>\n<\/ul>\n<p>In this section, we\u2019ll perform some preliminary tests to check whether these assumptions are met.<\/p>\n<\/div>\n<div id=\"check-one-sample-t-test-assumptions-in-r\" class=\"section level2\">\n<h2>Check one-sample t-test assumptions in R<\/h2>\n<div id=\"prerequisites\" class=\"section level3\">\n<h3>Prerequisites<\/h3>\n<p>Make sure you have installed the following R packages:<\/p>\n<ul>\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<li><code>datarium<\/code>: contains required data sets for this chapter.<\/li>\n<\/ul>\n<p>Start by loading the following required packages:<\/p>\n<pre class=\"r\"><code>library(ggpubr)\r\nlibrary(rstatix)<\/code><\/pre>\n<\/div>\n<div id=\"demo-data\" class=\"section level3\">\n<h3>Demo data<\/h3>\n<p>Demo dataset: <code>mice<\/code> [in datarium package]. Contains the weight of 10 mice:<\/p>\n<pre class=\"r\"><code># Load and inspect the data\r\ndata(mice, package = \"datarium\")\r\nhead(mice, 3)<\/code><\/pre>\n<pre><code>## # A tibble: 3 x 2\r\n##   name  weight\r\n##   &lt;chr&gt;  &lt;dbl&gt;\r\n## 1 M_1     18.9\r\n## 2 M_2     19.5\r\n## 3 M_3     23.1<\/code><\/pre>\n<\/div>\n<div id=\"identify-outliers\" class=\"section level3\">\n<h3>Identify outliers<\/h3>\n<p>Outliers can be easily identified using boxplot methods, implemented in the R function <code>identify_outliers()<\/code> [rstatix package].<\/p>\n<pre class=\"r\"><code>mice %&gt;% identify_outliers(weight)<\/code><\/pre>\n<pre><code>## [1] name       weight     is.outlier is.extreme\r\n## &lt;0 rows&gt; (or 0-length row.names)<\/code><\/pre>\n<div class=\"success\">\n<p>There were no extreme outliers.<\/p>\n<\/div>\n<div class=\"warning\">\n<p>Note that, in the situation where you have extreme outliers, this can be due to: 1) data entry errors, measurement errors or unusual values.<\/p>\n<p>In this case, you could consider running the non parametric Wilcoxon test.<\/p>\n<\/div>\n<\/div>\n<div id=\"check-normality-assumption\" class=\"section level3\">\n<h3>Check normality assumption<\/h3>\n<p>The normality assumption can be checked by computing the Shapiro-Wilk test. If the data is normally distributed, the p-value should be greater than 0.05.<\/p>\n<pre class=\"r\"><code>mice %&gt;% shapiro_test(weight)<\/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 weight       0.923 0.382<\/code><\/pre>\n<div class=\"success\">\n<p>From the output, the p-value is greater than the significance level 0.05 indicating that the distribution of the data are not significantly different from the normal distribution. In other words, we can assume the normality.<\/p>\n<\/div>\n<p>You can also create a QQ plot of the <code>weight<\/code> data. QQ plot draws the correlation between a given data and the normal distribution.<\/p>\n<pre class=\"r\"><code>ggqqplot(mice, x = \"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\/081-one-sample-t-test-assumptions-qqplot-1.png\" width=\"288\" \/><\/p>\n<div class=\"success\">\n<p>All the points fall approximately along the (45-degree) reference line, for each group. So we can assume normality of the data.<\/p>\n<\/div>\n<div class=\"warning\">\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>If the data are not normally distributed, it\u2019s recommended to use a non-parametric test such as the <em>one-sample Wilcoxon signed-rank test<\/em>. This test is similar to the one-sample t-test, but focuses on the median rather than the mean.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"related-article\" class=\"section level2\">\n<h2>Related article<\/h2>\n<p><a href=\"\/?p=10861\">T-test in R<\/a><\/p>\n<\/div>\n<\/div>\n<p><!--end rdoc--><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Describes the one sample t-test assumptions and provides examples of R code to check whether the assumptions are met before calculating the t-test.<\/p>\n","protected":false},"author":1,"featured_media":8943,"parent":11667,"menu_order":81,"comment_status":"open","ping_status":"closed","template":"","class_list":["post-11686","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>One Sample T-Test Assumptions : Excellent Tutorial - Datanovia<\/title>\n<meta name=\"description\" content=\"Describes the one sample t-test assumptions and provides examples of R code to check whether the assumptions are met before calculating the t-test.\" \/>\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\/t-test-assumptions\/one-sample-t-test-assumptions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"One Sample T-Test Assumptions : Excellent Tutorial - Datanovia\" \/>\n<meta property=\"og:description\" content=\"Describes the one sample t-test assumptions and provides examples of R code to check whether the assumptions are met before calculating the t-test.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/\" \/>\n<meta property=\"og:site_name\" content=\"Datanovia\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/2019\/05\/X48411247_774695199537093_6992505721971539968_n.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1024\" \/>\n\t<meta property=\"og:image:height\" content=\"512\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data1\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/\",\"url\":\"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/\",\"name\":\"One Sample T-Test Assumptions : Excellent Tutorial - Datanovia\",\"isPartOf\":{\"@id\":\"https:\/\/www.datanovia.com\/en\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/2019\/05\/X48411247_774695199537093_6992505721971539968_n.jpg\",\"datePublished\":\"2019-12-26T07:51:07+00:00\",\"description\":\"Describes the one sample t-test assumptions and provides examples of R code to check whether the assumptions are met before calculating the t-test.\",\"breadcrumb\":{\"@id\":\"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/#primaryimage\",\"url\":\"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/2019\/05\/X48411247_774695199537093_6992505721971539968_n.jpg\",\"contentUrl\":\"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/2019\/05\/X48411247_774695199537093_6992505721971539968_n.jpg\",\"width\":1024,\"height\":512},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/www.datanovia.com\/en\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Lessons\",\"item\":\"https:\/\/www.datanovia.com\/en\/lessons\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"T-Test Assumptions\",\"item\":\"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"One Sample T-Test Assumptions\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/www.datanovia.com\/en\/#website\",\"url\":\"https:\/\/www.datanovia.com\/en\/\",\"name\":\"Datanovia\",\"description\":\"Data Mining and Statistics for Decision Support\",\"publisher\":{\"@id\":\"https:\/\/www.datanovia.com\/en\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/www.datanovia.com\/en\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/www.datanovia.com\/en\/#organization\",\"name\":\"Datanovia\",\"url\":\"https:\/\/www.datanovia.com\/en\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/www.datanovia.com\/en\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/2018\/09\/datanovia-logo.png\",\"contentUrl\":\"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/2018\/09\/datanovia-logo.png\",\"width\":98,\"height\":99,\"caption\":\"Datanovia\"},\"image\":{\"@id\":\"https:\/\/www.datanovia.com\/en\/#\/schema\/logo\/image\/\"}}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"One Sample T-Test Assumptions : Excellent Tutorial - Datanovia","description":"Describes the one sample t-test assumptions and provides examples of R code to check whether the assumptions are met before calculating the t-test.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/","og_locale":"en_US","og_type":"article","og_title":"One Sample T-Test Assumptions : Excellent Tutorial - Datanovia","og_description":"Describes the one sample t-test assumptions and provides examples of R code to check whether the assumptions are met before calculating the t-test.","og_url":"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/","og_site_name":"Datanovia","og_image":[{"width":1024,"height":512,"url":"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/2019\/05\/X48411247_774695199537093_6992505721971539968_n.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_misc":{"Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/","url":"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/","name":"One Sample T-Test Assumptions : Excellent Tutorial - Datanovia","isPartOf":{"@id":"https:\/\/www.datanovia.com\/en\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/#primaryimage"},"image":{"@id":"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/#primaryimage"},"thumbnailUrl":"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/2019\/05\/X48411247_774695199537093_6992505721971539968_n.jpg","datePublished":"2019-12-26T07:51:07+00:00","description":"Describes the one sample t-test assumptions and provides examples of R code to check whether the assumptions are met before calculating the t-test.","breadcrumb":{"@id":"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/#primaryimage","url":"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/2019\/05\/X48411247_774695199537093_6992505721971539968_n.jpg","contentUrl":"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/2019\/05\/X48411247_774695199537093_6992505721971539968_n.jpg","width":1024,"height":512},{"@type":"BreadcrumbList","@id":"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/one-sample-t-test-assumptions\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.datanovia.com\/en\/"},{"@type":"ListItem","position":2,"name":"Lessons","item":"https:\/\/www.datanovia.com\/en\/lessons\/"},{"@type":"ListItem","position":3,"name":"T-Test Assumptions","item":"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/"},{"@type":"ListItem","position":4,"name":"One Sample T-Test Assumptions"}]},{"@type":"WebSite","@id":"https:\/\/www.datanovia.com\/en\/#website","url":"https:\/\/www.datanovia.com\/en\/","name":"Datanovia","description":"Data Mining and Statistics for Decision Support","publisher":{"@id":"https:\/\/www.datanovia.com\/en\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.datanovia.com\/en\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/www.datanovia.com\/en\/#organization","name":"Datanovia","url":"https:\/\/www.datanovia.com\/en\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/www.datanovia.com\/en\/#\/schema\/logo\/image\/","url":"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/2018\/09\/datanovia-logo.png","contentUrl":"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/2018\/09\/datanovia-logo.png","width":98,"height":99,"caption":"Datanovia"},"image":{"@id":"https:\/\/www.datanovia.com\/en\/#\/schema\/logo\/image\/"}}]}},"multi-rating":{"mr_rating_results":[]},"_links":{"self":[{"href":"https:\/\/www.datanovia.com\/en\/wp-json\/wp\/v2\/dt_lessons\/11686","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.datanovia.com\/en\/wp-json\/wp\/v2\/dt_lessons"}],"about":[{"href":"https:\/\/www.datanovia.com\/en\/wp-json\/wp\/v2\/types\/dt_lessons"}],"author":[{"embeddable":true,"href":"https:\/\/www.datanovia.com\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.datanovia.com\/en\/wp-json\/wp\/v2\/comments?post=11686"}],"version-history":[{"count":0,"href":"https:\/\/www.datanovia.com\/en\/wp-json\/wp\/v2\/dt_lessons\/11686\/revisions"}],"up":[{"embeddable":true,"href":"https:\/\/www.datanovia.com\/en\/wp-json\/wp\/v2\/dt_lessons\/11667"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.datanovia.com\/en\/wp-json\/wp\/v2\/media\/8943"}],"wp:attachment":[{"href":"https:\/\/www.datanovia.com\/en\/wp-json\/wp\/v2\/media?parent=11686"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}