{"id":10891,"date":"2019-11-30T10:39:35","date_gmt":"2019-11-30T08:39:35","guid":{"rendered":"https:\/\/www.datanovia.com\/en\/?post_type=dt_courses&#038;p=10891"},"modified":"2019-11-30T10:39:35","modified_gmt":"2019-11-30T08:39:35","slug":"statistical-tests-and-assumptions","status":"publish","type":"dt_courses","link":"https:\/\/www.datanovia.com\/en\/courses\/statistical-tests-and-assumptions\/","title":{"rendered":"Statistical Tests and Assumptions"},"content":{"rendered":"<div id=\"rdoc\">\n<h2>Course description<\/h2>\n<p>In this chapter, we\u2019ll introduce some research questions and the corresponding <strong>statistical tests<\/strong>, as well as, the <strong>assumptions<\/strong> of the tests.<\/p>\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=\"research-questions-and-statistics\" class=\"section level2\">\n<h2>Research questions and statistics<\/h2>\n<p>The most popular research questions include:<\/p>\n<ol style=\"list-style-type: decimal;\">\n<li>whether <strong>two variables<\/strong> (n = 2) are <strong>correlated<\/strong> (i.e., associated)<\/li>\n<li>whether <strong>multiple variables<\/strong> (n &gt; 2) are <strong>correlated<\/strong><\/li>\n<li>whether <strong>two groups<\/strong> (n = 2) of samples <strong>differ<\/strong> from each other<\/li>\n<li>whether <strong>multiple groups<\/strong> (n &gt;= 2) of samples <strong>differ<\/strong> from each other<\/li>\n<li>whether the <strong>variability<\/strong> of two or more samples differ<\/li>\n<\/ol>\n<p>Each of these questions can be answered using the following statistical tests:<\/p>\n<ol style=\"list-style-type: decimal;\">\n<li><strong>Correlation test<\/strong> between two variables<\/li>\n<li><strong>Correlation matrix<\/strong> between multiple variables<\/li>\n<li><strong>Comparing the means of two groups<\/strong>:\n<ul>\n<li><strong>Student\u2019s t-test<\/strong> (parametric)<\/li>\n<li><strong>Wilcoxon rank test<\/strong> (non-parametric)<\/li>\n<\/ul>\n<\/li>\n<li><strong>Comparing the means of more than two groups<\/strong>\n<ul>\n<li><strong>ANOVA test<\/strong> (analysis of variance, parametric): extension of t-test to compare more than two groups.<\/li>\n<li><strong>Kruskal-Wallis rank sum test<\/strong> (non-parametric): extension of Wilcoxon rank test to compare more than two groups<\/li>\n<\/ul>\n<\/li>\n<li><strong>Comparing the variances<\/strong>:\n<ul>\n<li>Comparing the variances of two groups: <strong>F-test<\/strong> (parametric)<\/li>\n<li>Comparison of the variances of more than two groups: <strong>Bartlett\u2019s test<\/strong> (parametric), <strong>Levene\u2019s test<\/strong> (parametric) and <strong>Fligner-Killeen test<\/strong> (non-parametric)<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<\/div>\n<div id=\"assumptions-of-statistical-tests\" class=\"section level2\">\n<h2>Assumptions of statistical tests<\/h2>\n<p>Many of the statistical methods including correlation, regression, t-test, and analysis of variance assume some characteristics about the data. Generally they assume that:<\/p>\n<ul>\n<li>the data are <strong>normally distributed<\/strong><\/li>\n<li>and the <strong>variances<\/strong> of the groups to be compared are <strong>homogeneous<\/strong> (equal).<\/li>\n<\/ul>\n<p>These assumptions should be taken seriously to draw reliable interpretation and conclusions of the research.<\/p>\n<p>These tests - correlation, t-test and ANOVA - are called <strong>parametric tests<\/strong>, because their validity depends on the distribution of the data.<\/p>\n<p>Before using parametric test, some preliminary tests should be performed to make sure that the test assumptions are met. In the situations where the assumptions are violated, <strong>non-paramatric<\/strong> tests are recommended.<\/p>\n<\/div>\n<div id=\"assessing-normality\" class=\"section level2\">\n<h2>Assessing normality<\/h2>\n<ol style=\"list-style-type: decimal;\">\n<li>With <strong>large enough sample sizes<\/strong> (n &gt; 30) the violation of the normality assumption should not cause major problems (central limit theorem). This implies that we can ignore the distribution of the data and use parametric tests.<\/li>\n<li>However, to be consistent, we can use <strong>Shapiro-Wilk\u2019s significance test<\/strong> comparing the sample distribution to a normal one in order to ascertain whether data show or not a serious deviation from normality <span class=\"citation\">(Ghasemi and Zahediasl 2012)<\/span>.<\/li>\n<\/ol>\n<\/div>\n<div id=\"assessing-equality-of-variances\" class=\"section level2\">\n<h2>Assessing equality of variances<\/h2>\n<p>The standard <strong>Student\u2019s t-test<\/strong> (comparing two independent samples) and the ANOVA test (comparing multiple samples) assume also that the samples to be compared have equal variances.<\/p>\n<p>If the samples, being compared, follow normal distribution, then it\u2019s possible to use:<\/p>\n<ul>\n<li><strong>F-test<\/strong> to compare the variances of two samples<\/li>\n<li><strong>Bartlett\u2019s Test<\/strong> or <strong>Levene\u2019s Test<\/strong> to compare the variances of multiple samples.<\/li>\n<\/ul>\n<\/div>\n<div id=\"summary\" class=\"section level2\">\n<h2>Summary<\/h2>\n<p>This chapter introduces the most commonly used statistical tests and their assumptions.<\/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>In this course, we&#8217;ll introduce some research questions and the corresponding statistical tests, as well as, the assumptions of the tests.<\/p>\n","protected":false},"author":1,"featured_media":8941,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"","class_list":["post-10891","dt_courses","type-dt_courses","status-publish","has-post-thumbnail","hentry","course_category-basic-statistics","course_category-biostatistics","course_category-comparing-means"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.2 - 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