{"id":11667,"date":"2019-12-25T18:56:47","date_gmt":"2019-12-25T16:56:47","guid":{"rendered":"https:\/\/www.datanovia.com\/en\/?post_type=dt_lessons&#038;p=11667"},"modified":"2019-12-25T18:56:47","modified_gmt":"2019-12-25T16:56:47","slug":"t-test-assumptions","status":"publish","type":"dt_lessons","link":"https:\/\/www.datanovia.com\/en\/lessons\/t-test-assumptions\/","title":{"rendered":"T-Test Assumptions"},"content":{"rendered":"<div id=\"rdoc\">\n<p>This article describes the <strong>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>You will learn the assumptions of the different types of t-test, including the:<\/p>\n<ul>\n<li>one-sample t-test<\/li>\n<li>independent t-test<\/li>\n<li>paired t-test<\/li>\n<\/ul>\n<p>Contents:<\/p>\n<div id=\"TOC\">\n<ul>\n<li><a href=\"#assumptions\">Assumptions<\/a><\/li>\n<li><a href=\"#check-t-test-assumptions-in-r\">Check t-test assumptions in R<\/a>\n<ul>\n<li><a href=\"#prerequisites\">Prerequisites<\/a><\/li>\n<li><a href=\"#check-one-sample-t-test-assumptions\">Check one-sample t-test assumptions<\/a><\/li>\n<li><a href=\"#check-independent-t-test-assumptions\">Check independent t-test assumptions<\/a><\/li>\n<li><a href=\"#check-paired-t-test-assumptions\">Check paired t-test assumptions<\/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>T-test is a parametric test that assumes some characteristics about the data. This section shows the assumptions made by the different t-tests.<\/p>\n<ul>\n<li><strong>One-sample t-test<\/strong>:\n<ul>\n<li>no significant outliers in the data<\/li>\n<li>the data should be normally distributed.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Independent sample t-test<\/strong>:\n<ul>\n<li>no significant outliers in the two groups<\/li>\n<li>the two groups of samples (A and B), being compared, should be normally distributed.<\/li>\n<li>the variances of the two groups should not be significantly different. This assumption is made only by the original Student\u2019s t-test. It is relaxed in the Welch\u2019s t-test.<\/li>\n<\/ul>\n<\/li>\n<li><strong>Paired sample t-test<\/strong>:\n<ul>\n<li>No significant outliers in the difference between the two related groups<\/li>\n<li>the difference of pairs should follow a normal distribution.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>Before using a parametric test, some preliminary tests should be performed to make sure that the test assumptions are met.<\/p>\n<div class=\"warning\">\n<p>\nIn the situations where the assumptions are violated, non-parametric tests, such as Wilcoxon test, are recommended.\n<\/p>\n<\/div>\n<\/div>\n<div id=\"check-t-test-assumptions-in-r\" class=\"section level2\">\n<h2>Check 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>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<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(tidyverse)\r\nlibrary(ggpubr)\r\nlibrary(rstatix)<\/code><\/pre>\n<\/div>\n<div id=\"check-one-sample-t-test-assumptions\" class=\"section level3\">\n<h3>Check one-sample t-test assumptions<\/h3>\n<div id=\"demo-data\" class=\"section level4\">\n<h4>Demo data<\/h4>\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 = &quot;datarium&quot;)\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 level4\">\n<h4>Identify outliers<\/h4>\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>\nThere were no extreme outliers.\n<\/p>\n<\/div>\n<div class=\"warning\">\n<p>\nNote that, in the situation where you have extreme outliers, this can be due to: 1) data entry errors, measurement errors or unusual values.\n<\/p>\n<p>\nIn this case, you could consider running the non parametric Wilcoxon test.\n<\/p>\n<\/div>\n<\/div>\n<div id=\"check-normality-assumption\" class=\"section level4\">\n<h4>Check normality assumption<\/h4>\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>\nFrom 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.\n<\/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 = &quot;weight&quot;)<\/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\/080-t-test-assumptions-qqplot-1.png\" width=\"288\" \/><\/p>\n<div class=\"success\">\n<p>\nAll the points fall approximately along the (45-degree) reference line, for each group. So we can assume normality of the data.\n<\/p>\n<\/div>\n<div class=\"warning\">\n<p>\nNote 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.\n<\/p>\n<p>\nIf 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.\n<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"check-independent-t-test-assumptions\" class=\"section level3\">\n<h3>Check independent t-test assumptions<\/h3>\n<div id=\"demo-data-1\" class=\"section level4\">\n<h4>Demo data<\/h4>\n<p>Demo dataset: <code>genderweight<\/code> [in datarium package] containing the weight of 40 individuals (20 women and 20 men).<\/p>\n<p>Load the data and show some random rows by groups:<\/p>\n<pre class=\"r\"><code># Load the data\r\ndata(&quot;genderweight&quot;, package = &quot;datarium&quot;)\r\n# Show a sample of the data by group\r\nset.seed(123)\r\ngenderweight %&gt;% sample_n_by(group, size = 2)<\/code><\/pre>\n<pre><code>## # A tibble: 4 x 3\r\n##   id    group weight\r\n##   &lt;fct&gt; &lt;fct&gt;  &lt;dbl&gt;\r\n## 1 6     F       65.0\r\n## 2 15    F       65.9\r\n## 3 29    M       88.9\r\n## 4 37    M       77.0<\/code><\/pre>\n<\/div>\n<div id=\"identify-outliers-by-groups\" class=\"section level4\">\n<h4>Identify outliers by groups<\/h4>\n<pre class=\"r\"><code>genderweight %&gt;%\r\n  group_by(group) %&gt;%\r\n  identify_outliers(weight)<\/code><\/pre>\n<pre><code>## # A tibble: 2 x 5\r\n##   group id    weight is.outlier is.extreme\r\n##   &lt;fct&gt; &lt;fct&gt;  &lt;dbl&gt; &lt;lgl&gt;      &lt;lgl&gt;     \r\n## 1 F     20      68.8 TRUE       FALSE     \r\n## 2 M     31      95.1 TRUE       FALSE<\/code><\/pre>\n<div class=\"success\">\n<p>\nThere were no extreme outliers.\n<\/p>\n<\/div>\n<\/div>\n<div id=\"check-normality-by-groups\" class=\"section level4\">\n<h4>Check normality by groups<\/h4>\n<pre class=\"r\"><code># Compute Shapiro wilk test by goups\r\ndata(genderweight, package = &quot;datarium&quot;)\r\ngenderweight %&gt;%\r\n  group_by(group) %&gt;%\r\n  shapiro_test(weight)<\/code><\/pre>\n<pre><code>## # A tibble: 2 x 4\r\n##   group variable statistic     p\r\n##   &lt;fct&gt; &lt;chr&gt;        &lt;dbl&gt; &lt;dbl&gt;\r\n## 1 F     weight       0.938 0.224\r\n## 2 M     weight       0.986 0.989<\/code><\/pre>\n<pre class=\"r\"><code># Draw a qq plot by group\r\nggqqplot(genderweight, x = &quot;weight&quot;, facet.by = &quot;group&quot;)<\/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\/080-t-test-assumptions-independent-samples-normality-assumption-1.png\" width=\"480\" \/><\/p>\n<div class=\"success\">\n<p>\nFrom the output above, we can conclude that the data of the two groups are normally distributed.\n<\/p>\n<\/div>\n<\/div>\n<div id=\"check-the-equality-of-variances\" class=\"section level4\">\n<h4>Check the equality of variances<\/h4>\n<p>This can be done using the Levene\u2019s test. If the variances of groups are equal, the p-value should be greater than 0.05.<\/p>\n<pre class=\"r\"><code>genderweight %&gt;% levene_test(weight ~ group)<\/code><\/pre>\n<pre><code>## # A tibble: 1 x 4\r\n##     df1   df2 statistic      p\r\n##   &lt;int&gt; &lt;int&gt;     &lt;dbl&gt;  &lt;dbl&gt;\r\n## 1     1    38      6.12 0.0180<\/code><\/pre>\n<div class=\"success\">\n<p>\nThe p-value of the Levene\u2019s test is significant, suggesting that there is a significant difference between the variances of the two groups. Therefore, we\u2019ll use the Welch t-test, which doesn\u2019t assume the equality of the two variances.\n<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"check-paired-t-test-assumptions\" class=\"section level3\">\n<h3>Check paired t-test assumptions<\/h3>\n<div id=\"demo-data-2\" class=\"section level4\">\n<h4>Demo data<\/h4>\n<p>Here, we\u2019ll use a demo dataset <code>mice2<\/code> [datarium package], which contains the weight of 10 mice before and after the treatment.<\/p>\n<pre class=\"r\"><code># Wide format\r\ndata(&quot;mice2&quot;, package = &quot;datarium&quot;)\r\nhead(mice2, 3)<\/code><\/pre>\n<pre><code>##   id before after\r\n## 1  1    187   430\r\n## 2  2    194   404\r\n## 3  3    232   406<\/code><\/pre>\n<pre class=\"r\"><code># Transform into long data: \r\n# gather the before and after values in the same column\r\nmice2.long &lt;- mice2 %&gt;%\r\n  gather(key = &quot;group&quot;, value = &quot;weight&quot;, before, after)\r\nhead(mice2.long, 3)<\/code><\/pre>\n<pre><code>##   id  group weight\r\n## 1  1 before    187\r\n## 2  2 before    194\r\n## 3  3 before    232<\/code><\/pre>\n<p>First, start by computing the difference between groups:<\/p>\n<pre class=\"r\"><code>mice2 &lt;- mice2 %&gt;% mutate(differences = before - after)\r\nhead(mice2, 3)<\/code><\/pre>\n<pre><code>##   id before after differences\r\n## 1  1    187   430        -242\r\n## 2  2    194   404        -210\r\n## 3  3    232   406        -174<\/code><\/pre>\n<\/div>\n<div id=\"identify-outliers-1\" class=\"section level4\">\n<h4>Identify outliers<\/h4>\n<pre class=\"r\"><code>mice2 %&gt;% identify_outliers(differences)<\/code><\/pre>\n<pre><code>## [1] id          before      after       differences is.outlier  is.extreme \r\n## &lt;0 rows&gt; (or 0-length row.names)<\/code><\/pre>\n<div class=\"success\">\n<p>\nThere were no extreme outliers.\n<\/p>\n<\/div>\n<\/div>\n<div id=\"check-normality-assumption-1\" class=\"section level4\">\n<h4>Check normality assumption<\/h4>\n<pre class=\"r\"><code># Shapiro-Wilk normality test for the differences\r\nmice2 %&gt;% shapiro_test(differences) <\/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 differences     0.968 0.867<\/code><\/pre>\n<pre class=\"r\"><code># QQ plot for the difference\r\nggqqplot(mice2, &quot;differences&quot;)<\/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\/080-t-test-assumptions-paired-samples-normality-assumption-1.png\" width=\"288\" \/><\/p>\n<div class=\"success\">\n<p>\nFrom the output above, it can be assumed that the differences are normally distributed.\n<\/p>\n<\/div>\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 t-test assumptions and provides examples of R code to check whether the assumptions are met before calculating the t-test. You will learn the assumptions of the different types of t-test, including the one-sample t-test, independent t-test and paired t-test.<\/p>\n","protected":false},"author":1,"featured_media":8944,"parent":0,"menu_order":80,"comment_status":"open","ping_status":"closed","template":"","class_list":["post-11667","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>T-Test Assumptions : Excellent Tutorial You Will Love - Datanovia<\/title>\n<meta name=\"description\" content=\"Describes the t-test assumptions and provides examples of R code to check whether the assumptions are met before calculating the t-test. 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