{"id":11046,"date":"2019-12-07T23:57:36","date_gmt":"2019-12-07T21:57:36","guid":{"rendered":"https:\/\/www.datanovia.com\/en\/?post_type=dt_lessons&#038;p=11046"},"modified":"2019-12-07T23:57:36","modified_gmt":"2019-12-07T21:57:36","slug":"test-dhomogeneite-des-variances-dans-r","status":"publish","type":"dt_lessons","link":"https:\/\/www.datanovia.com\/en\/fr\/lessons\/test-dhomogeneite-des-variances-dans-r\/","title":{"rendered":"Test d&rsquo;Homog\u00e9n\u00e9it\u00e9 des Variances dans R"},"content":{"rendered":"<div id=\"rdoc\">\n<p>Ce chapitre d\u00e9crit les m\u00e9thodes de v\u00e9rification du <strong>test d\u2019homog\u00e9n\u00e9it\u00e9 des variances<\/strong> dans R sur deux groupes ou plus.<\/p>\n<p>Certains tests statistiques, comme le test T sur deux \u00e9chantillons ind\u00e9pendants et le test ANOVA, supposent que les variances sont \u00e9gales entre les groupes.<\/p>\n<p>Il existe diff\u00e9rents tests de variance qui peuvent \u00eatre utilis\u00e9s pour \u00e9valuer l\u2019\u00e9galit\u00e9 des variances. Il s\u2019agit notamment:<\/p>\n<ul>\n<li><strong>Test F<\/strong> : Comparez les variances de deux groupes. Les donn\u00e9es doivent \u00eatre normalement distribu\u00e9es.<\/li>\n<li><strong>Test de Bartlett<\/strong> : Comparer les variances de deux groupes ou plus. Les donn\u00e9es doivent \u00eatre normalement distribu\u00e9es.<\/li>\n<li><strong>Le test de Levene<\/strong> : Une alternative robuste au test de Bartlett qui est moins sensible aux \u00e9carts de normalit\u00e9.<\/li>\n<li><strong>Test de Fligner-Killeen<\/strong> : un test non param\u00e9trique qui est tr\u00e8s robuste contre les \u00e9carts de normalit\u00e9.<\/li>\n<\/ul>\n<div class=\"success\">\n<p>Il est \u00e0 noter que le test de Levene est le plus couramment utilis\u00e9 dans la litt\u00e9rature.<\/p>\n<\/div>\n<p>Vous apprendrez comment comparer les variances dans R en utilisant chacun des tests mentionn\u00e9s ci-dessus.<\/p>\n<p>Sommaire:<\/p>\n<div id=\"TOC\">\n<ul>\n<li><a href=\"#prerequis\">Pr\u00e9requis<\/a><\/li>\n<li><a href=\"#test-f-comparez-deux-variances\">Test F : Comparez deux variances<\/a><\/li>\n<li><a href=\"#compare-multiple-variances\">Compare multiple variances<\/a>\n<ul>\n<li><a href=\"#le-test-de-bartlett\">Le test de Bartlett<\/a><\/li>\n<li><a href=\"#le-test-de-levene\">Le test de Levene<\/a><\/li>\n<li><a href=\"#le-test-de-fligner-killeen\">Le test de Fligner-Killeen<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#resume\">R\u00e9sum\u00e9<\/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\/fr\/produit\/pratiques-des-statistiques-dans-r-pour-comparaison-de-groupes-variables-numeriques\/' target='_blank'><span class='fa fa-book'><\/span><\/a><\/div><h4><a href='https:\/\/www.datanovia.com\/en\/fr\/produit\/pratiques-des-statistiques-dans-r-pour-comparaison-de-groupes-variables-numeriques\/' target='_blank'> Livre Apparent\u00e9 <\/a><\/h4>Pratique des Statistiques dans R II - Comparaison de Groupes: Variables Num\u00e9riques<\/div>\n<div class='dt-sc-hr-invisible-medium  '><\/div>\n<div id=\"prerequis\" class=\"section level2\">\n<h2>Pr\u00e9requis<\/h2>\n<p>Charger le paquet <code>tidyverse<\/code> pour faciliter la manipulation des donn\u00e9es<\/p>\n<pre class=\"r\"><code>library(tidyverse)<\/code><\/pre>\n<p>Donn\u00e9es de d\u00e9monstration: <code>ToothGrowth<\/code>. Inspectez les donn\u00e9es en affichant quelques lignes al\u00e9atoires.<\/p>\n<pre class=\"r\"><code># Pr\u00e9paration des donn\u00e9es\r\nToothGrowth$dose &lt;- as.factor(ToothGrowth$dose)\r\n# Inspecter\r\nset.seed(123)\r\nsample_n(ToothGrowth, 6)<\/code><\/pre>\n<pre><code>##    len supp dose\r\n## 1 14.5   VC    1\r\n## 2 25.8   OJ    1\r\n## 3 25.5   VC    2\r\n## 4 25.5   OJ    2\r\n## 5 22.4   OJ    2\r\n## 6  7.3   VC  0.5<\/code><\/pre>\n<\/div>\n<div id=\"test-f-comparez-deux-variances\" class=\"section level2\">\n<h2>Test F : Comparez deux variances<\/h2>\n<p>Le <strong>test F<\/strong> est utilis\u00e9 pour \u00e9valuer si les variances de deux populations (A et B) sont \u00e9gales. Vous devez v\u00e9rifier si les donn\u00e9es sont normalement distribu\u00e9es (Chapitre @ref(normality-test-in-r)) avant d\u2019utiliser le test F.<\/p>\n<p><strong>Applications<\/strong>. La comparaison de deux variances est utile dans plusieurs cas, dont les suivants:<\/p>\n<ul>\n<li>Lorsque vous voulez effectuer un test-t \u00e0 deux \u00e9chantillons, vous devez v\u00e9rifier l\u2019\u00e9galit\u00e9 des variances des deux \u00e9chantillons<\/li>\n<li>Lorsque vous souhaitez comparer la variabilit\u00e9 d\u2019une nouvelle m\u00e9thode de mesure \u00e0 celle d\u2019une ancienne m\u00e9thode. La nouvelle m\u00e9thode r\u00e9duit-elle la variabilit\u00e9 de la mesure ?<\/li>\n<\/ul>\n<p>Les <strong>hypoth\u00e8ses statistiques<\/strong> sont les suivantes:<\/p>\n<ul>\n<li>Hypoth\u00e8se nulle (H0) : les variances des deux groupes sont \u00e9gales.<\/li>\n<li>Hypoth\u00e8se alternative (Ha) : les variances sont diff\u00e9rentes.<\/li>\n<\/ul>\n<p><strong>Calculs<\/strong>. La statistique du test F peut \u00eatre obtenue en calculant le rapport des deux variances <code>Var(A)\/Var(B)<\/code>. Plus ce rapport s\u2019\u00e9carte de 1, plus l\u2019\u00e9vidence des variances in\u00e9gales des population est forte.<\/p>\n<p>Le test F peut \u00eatre facilement calcul\u00e9 dans R \u00e0 l\u2019aide de la fonction <code>var.test()<\/code>. Dans le code R suivant, nous voulons tester l\u2019\u00e9galit\u00e9 des variances entre les deux groupes OJ et VC (dans la colonne \u201csupp\u201d) pour la variable <code>len<\/code>.<\/p>\n<pre class=\"r\"><code>res &lt;- var.test(len ~ supp, data = ToothGrowth)\r\nres<\/code><\/pre>\n<pre><code>## \r\n##  F test to compare two variances\r\n## \r\n## data:  len by supp\r\n## F = 0.6, num df = 30, denom df = 30, p-value = 0.2\r\n## alternative hypothesis: true ratio of variances is not equal to 1\r\n## 95 percent confidence interval:\r\n##  0.304 1.342\r\n## sample estimates:\r\n## ratio of variances \r\n##              0.639<\/code><\/pre>\n<p><strong>Interpr\u00e9tation<\/strong>. The p-value is p = 0.2 which is greater than the significance level 0.05. In conclusion, there is no significant difference between the two variances.<\/p>\n<\/div>\n<div id=\"compare-multiple-variances\" class=\"section level2\">\n<h2>Compare multiple variances<\/h2>\n<p>This section describes how to compare multiple variances in R using Bartlett, Levene or Fligner-Killeen tests.<\/p>\n<p><strong>Statistical hypotheses<\/strong>. For all these tests that follow, the null hypothesis is that all populations variances are equal, the alternative hypothesis is that at least two of them differ. Consequently, p-values less than 0.05 suggest variances are significantly different and the homogeneity of variance assumption has been violated.<\/p>\n<div id=\"le-test-de-bartlett\" class=\"section level3\">\n<h3>Le test de Bartlett<\/h3>\n<ol style=\"list-style-type: decimal;\">\n<li><strong>Le test de Bartlett with one independent variable<\/strong>:<\/li>\n<\/ol>\n<pre class=\"r\"><code>res &lt;- bartlett.test(weight ~ group, data = PlantGrowth)\r\nres<\/code><\/pre>\n<pre><code>## \r\n##  Bartlett test of homogeneity of variances\r\n## \r\n## data:  weight by group\r\n## Bartlett's K-squared = 3, df = 2, p-value = 0.2<\/code><\/pre>\n<p>From the output, it can be seen that the p-value of 0.237 is not less than the significance level of 0.05. Cela signifie qu\u2019il n\u2019y a aucune preuve que la variance de la croissance des plantes soit statistiquement diff\u00e9rente pour les trois groupes de traitement.<\/p>\n<ol style=\"list-style-type: decimal;\" start=\"2\">\n<li><strong>Test de Bartlett avec plusieurs variables ind\u00e9pendantes<\/strong> : la fonction <strong>interaction<\/strong>() doit \u00eatre utilis\u00e9e pour r\u00e9duire plusieurs facteurs en une seule variable contenant toutes les combinaisons des facteurs.<\/li>\n<\/ol>\n<pre class=\"r\"><code>bartlett.test(len ~ interaction(supp,dose), data=ToothGrowth)<\/code><\/pre>\n<pre><code>## \r\n##  Bartlett test of homogeneity of variances\r\n## \r\n## data:  len by interaction(supp, dose)\r\n## Bartlett's K-squared = 7, df = 5, p-value = 0.2<\/code><\/pre>\n<\/div>\n<div id=\"le-test-de-levene\" class=\"section level3\">\n<h3>Le test de Levene<\/h3>\n<p>La fonction <code>leveneTest()<\/code> [package <strong>car<\/strong>] peut \u00eatre utilis\u00e9e.<\/p>\n<pre class=\"r\"><code>library(car)\r\n# Test de Levene avec une variable ind\u00e9pendante\r\nleveneTest(weight ~ group, data = PlantGrowth)<\/code><\/pre>\n<pre><code>## Levene's Test for Homogeneity of Variance (center = median)\r\n##       Df F value Pr(&gt;F)\r\n## group  2    1.12   0.34\r\n##       27<\/code><\/pre>\n<pre class=\"r\"><code># Test de Levene avec de multiples variables ind\u00e9pendantes\r\nleveneTest(len ~ supp*dose, data = ToothGrowth)<\/code><\/pre>\n<pre><code>## Levene's Test for Homogeneity of Variance (center = median)\r\n##       Df F value Pr(&gt;F)\r\n## group  5    1.71   0.15\r\n##       54<\/code><\/pre>\n<\/div>\n<div id=\"le-test-de-fligner-killeen\" class=\"section level3\">\n<h3>Le test de Fligner-Killeen<\/h3>\n<p>Le test de Fligner-Killeen est l\u2019un des nombreux tests d\u2019homog\u00e9n\u00e9it\u00e9 des variances qui est le plus robuste contre les \u00e9carts de normalit\u00e9.<\/p>\n<p>La fonction R <code>fligner.test()<\/code> peut \u00eatre utilis\u00e9e pour calculer le test:<\/p>\n<pre class=\"r\"><code>fligner.test(weight ~ group, data = PlantGrowth)<\/code><\/pre>\n<pre><code>## \r\n##  Fligner-Killeen test of homogeneity of variances\r\n## \r\n## data:  weight by group\r\n## Fligner-Killeen:med chi-squared = 2, df = 2, p-value = 0.3<\/code><\/pre>\n<\/div>\n<\/div>\n<div id=\"resume\" class=\"section level2\">\n<h2>R\u00e9sum\u00e9<\/h2>\n<p>Cet article pr\u00e9sente diff\u00e9rents tests pour \u00e9valuer l\u2019\u00e9galit\u00e9 des variances entre les groupes, une hypoth\u00e8se faite par le test t \u00e0 deux \u00e9chantillons ind\u00e9pendants et les tests ANOVA.<\/p>\n<p>La m\u00e9thode couramment utilis\u00e9e est le test de Levene disponible dans le package R <code>car<\/code>. Un wrapper <code>levene_test()<\/code> est \u00e9galement fourni dans le paquet <code>rstatix<\/code>.<\/p>\n<\/div>\n<\/div>\n<p><!--end rdoc--><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Certains tests statistiques, comme le test T sur deux \u00e9chantillons ind\u00e9pendants et le test ANOVA, supposent que les variances sont \u00e9gales entre les groupes. Ce chapitre d\u00e9crit les m\u00e9thodes de v\u00e9rification de l&rsquo;homog\u00e9n\u00e9it\u00e9 des variances dans R sur deux groupes ou plus. Ces tests comprennent : le test F, test de Bartlett, test de Levene et test de Fligner-Killeen.<\/p>\n","protected":false},"author":1,"featured_media":11047,"parent":0,"menu_order":0,"comment_status":"open","ping_status":"closed","template":"","class_list":["post-11046","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>Test d&#039;Homog\u00e9n\u00e9it\u00e9 des Variances dans R: Excellente R\u00e9f\u00e9rence - 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\/fr\/lessons\/test-dhomogeneite-des-variances-dans-r\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Test d&#039;Homog\u00e9n\u00e9it\u00e9 des Variances dans R: Excellente R\u00e9f\u00e9rence - Datanovia\" \/>\n<meta property=\"og:description\" content=\"Certains tests statistiques, comme le test T sur deux \u00e9chantillons ind\u00e9pendants et le test ANOVA, supposent que les variances sont \u00e9gales entre les groupes. 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Ces tests comprennent : le test F, test de Bartlett, test de Levene et test de Fligner-Killeen.","og_url":"https:\/\/www.datanovia.com\/en\/fr\/lessons\/test-dhomogeneite-des-variances-dans-r\/","og_site_name":"Datanovia","og_image":[{"width":1024,"height":512,"url":"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/2019\/05\/P1040395.JPG.jpg","type":"image\/jpeg"}],"twitter_card":"summary_large_image","twitter_misc":{"Dur\u00e9e de lecture estim\u00e9e":"5 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/www.datanovia.com\/en\/fr\/lessons\/test-dhomogeneite-des-variances-dans-r\/","url":"https:\/\/www.datanovia.com\/en\/fr\/lessons\/test-dhomogeneite-des-variances-dans-r\/","name":"Test d'Homog\u00e9n\u00e9it\u00e9 des Variances dans R: Excellente R\u00e9f\u00e9rence - Datanovia","isPartOf":{"@id":"https:\/\/www.datanovia.com\/en\/fr\/#website"},"primaryImageOfPage":{"@id":"https:\/\/www.datanovia.com\/en\/fr\/lessons\/test-dhomogeneite-des-variances-dans-r\/#primaryimage"},"image":{"@id":"https:\/\/www.datanovia.com\/en\/fr\/lessons\/test-dhomogeneite-des-variances-dans-r\/#primaryimage"},"thumbnailUrl":"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/2019\/05\/P1040395.JPG.jpg","datePublished":"2019-12-07T21:57:36+00:00","breadcrumb":{"@id":"https:\/\/www.datanovia.com\/en\/fr\/lessons\/test-dhomogeneite-des-variances-dans-r\/#breadcrumb"},"inLanguage":"fr-FR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/www.datanovia.com\/en\/fr\/lessons\/test-dhomogeneite-des-variances-dans-r\/"]}]},{"@type":"ImageObject","inLanguage":"fr-FR","@id":"https:\/\/www.datanovia.com\/en\/fr\/lessons\/test-dhomogeneite-des-variances-dans-r\/#primaryimage","url":"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/2019\/05\/P1040395.JPG.jpg","contentUrl":"https:\/\/www.datanovia.com\/en\/wp-content\/uploads\/2019\/05\/P1040395.JPG.jpg","width":1024,"height":512},{"@type":"BreadcrumbList","@id":"https:\/\/www.datanovia.com\/en\/fr\/lessons\/test-dhomogeneite-des-variances-dans-r\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/www.datanovia.com\/en\/fr\/"},{"@type":"ListItem","position":2,"name":"Le\u00e7ons","item":"https:\/\/www.datanovia.com\/en\/fr\/lessons\/"},{"@type":"ListItem","position":3,"name":"Test d&rsquo;Homog\u00e9n\u00e9it\u00e9 des Variances dans R"}]},{"@type":"WebSite","@id":"https:\/\/www.datanovia.com\/en\/fr\/#website","url":"https:\/\/www.datanovia.com\/en\/fr\/","name":"Datanovia","description":"Exploration de Donn\u00e9es et Statistiques pour l'Aide \u00e0 la D\u00e9cision","publisher":{"@id":"https:\/\/www.datanovia.com\/en\/fr\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.datanovia.com\/en\/fr\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"fr-FR"},{"@type":"Organization","@id":"https:\/\/www.datanovia.com\/en\/fr\/#organization","name":"Datanovia","url":"https:\/\/www.datanovia.com\/en\/fr\/","logo":{"@type":"ImageObject","inLanguage":"fr-FR","@id":"https:\/\/www.datanovia.com\/en\/fr\/#\/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\/fr\/#\/schema\/logo\/image\/"}}]}},"multi-rating":{"mr_rating_results":[]},"_links":{"self":[{"href":"https:\/\/www.datanovia.com\/en\/fr\/wp-json\/wp\/v2\/dt_lessons\/11046","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.datanovia.com\/en\/fr\/wp-json\/wp\/v2\/dt_lessons"}],"about":[{"href":"https:\/\/www.datanovia.com\/en\/fr\/wp-json\/wp\/v2\/types\/dt_lessons"}],"author":[{"embeddable":true,"href":"https:\/\/www.datanovia.com\/en\/fr\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.datanovia.com\/en\/fr\/wp-json\/wp\/v2\/comments?post=11046"}],"version-history":[{"count":0,"href":"https:\/\/www.datanovia.com\/en\/fr\/wp-json\/wp\/v2\/dt_lessons\/11046\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.datanovia.com\/en\/fr\/wp-json\/wp\/v2\/media\/11047"}],"wp:attachment":[{"href":"https:\/\/www.datanovia.com\/en\/fr\/wp-json\/wp\/v2\/media?parent=11046"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}