{"id":15316,"date":"2020-03-15T17:33:57","date_gmt":"2020-03-15T16:33:57","guid":{"rendered":"https:\/\/www.datanovia.com\/en\/?post_type=dt_lessons&#038;p=15316"},"modified":"2020-03-15T17:33:57","modified_gmt":"2020-03-15T16:33:57","slug":"hypotheses-du-test-t-apparie","status":"publish","type":"dt_lessons","link":"https:\/\/www.datanovia.com\/en\/fr\/lessons\/hypotheses-du-test-t\/hypotheses-du-test-t-apparie\/","title":{"rendered":"Hypoth\u00e8ses du test T Appari\u00e9"},"content":{"rendered":"<div id=\"rdoc\">\n<p>Cet article d\u00e9crit les <strong>hypoth\u00e8ses du test t appari\u00e9<\/strong> et fournit des exemples de code R pour v\u00e9rifier si les hypoth\u00e8ses sont respect\u00e9es avant de calculer le test t. On appelle aussi cela:<\/p>\n<ul>\n<li><em>hypoth\u00e8ses du test t \u00e0 \u00e9chantillons appari\u00e9s<\/em>,<\/li>\n<li><em>hypoth\u00e8ses pour test t \u00e0 \u00e9chantillons appari\u00e9es<\/em> et<\/li>\n<li><em>hypoth\u00e8ses du test t d\u00e9pendant<\/em><\/li>\n<\/ul>\n<p>La proc\u00e9dure de l\u2019analyse du test t appari\u00e9 est la suivante:<\/p>\n<ol style=\"list-style-type: decimal;\">\n<li>Calculer la diff\u00e9rence (<span class=\"math inline\">\\(d\\)<\/span>) entre chaque paire de valeur<\/li>\n<li>Calculer la moyenne (<span class=\"math inline\">\\(m\\)<\/span>) et l\u2019\u00e9cart-type (<span class=\"math inline\">\\(s\\)<\/span>) de <span class=\"math inline\">\\(d\\)<\/span><\/li>\n<li>Comparer la diff\u00e9rence moyenne \u00e0 0. S\u2019il y a une diff\u00e9rence significative entre les deux paires d\u2019\u00e9chantillons, alors la moyenne de d (<span class=\"math inline\">\\(m\\)<\/span>) devrait \u00eatre loin de 0.<\/li>\n<\/ol>\n<p>Sommaire:<\/p>\n<div id=\"TOC\">\n<ul>\n<li><a href=\"#hypoth\u00e8ses\">Hypoth\u00e8ses<\/a><\/li>\n<li><a href=\"#v\u00e9rifier-les-hypoth\u00e8ses-du-test-t-appari\u00e9-dans-r\">V\u00e9rifier les hypoth\u00e8ses du test t appari\u00e9 dans R<\/a>\n<ul>\n<li><a href=\"#pr\u00e9requis\">Pr\u00e9requis<\/a><\/li>\n<li><a href=\"#donn\u00e9es-de-d\u00e9monstration\">Donn\u00e9es de d\u00e9monstration<\/a><\/li>\n<li><a href=\"#identifier-les-valeurs-aberrantes\">Identifier les valeurs aberrantes<\/a><\/li>\n<li><a href=\"#v\u00e9rifier-la-normalit\u00e9-par-groupes\">V\u00e9rifier la normalit\u00e9 par groupes<\/a><\/li>\n<\/ul>\n<\/li>\n<li><a href=\"#article-apparent\u00e9\">Article apparent\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=\"hypoth\u00e8ses\" class=\"section level2\">\n<h2>Hypoth\u00e8ses<\/h2>\n<p>Le test t des \u00e9chantillons appari\u00e9s suppose les caract\u00e9ristiques suivantes au sujet des donn\u00e9es:<\/p>\n<ul>\n<li><strong>les deux groupes sont appari\u00e9s<\/strong>.<\/li>\n<li><strong>Aucune valeur aberrante significative<\/strong> dans la diff\u00e9rence entre les deux groupes appari\u00e9s<\/li>\n<li><strong>Normalit\u00e9<\/strong>. la diff\u00e9rence des paires suit une distribution normale.<\/li>\n<\/ul>\n<p>Dans cette section, nous effectuerons quelques tests pr\u00e9liminaires pour v\u00e9rifier si ces hypoth\u00e8ses sont respect\u00e9es.<\/p>\n<\/div>\n<div id=\"v\u00e9rifier-les-hypoth\u00e8ses-du-test-t-appari\u00e9-dans-r\" class=\"section level2\">\n<h2>V\u00e9rifier les hypoth\u00e8ses du test t appari\u00e9 dans R<\/h2>\n<div id=\"pr\u00e9requis\" class=\"section level3\">\n<h3>Pr\u00e9requis<\/h3>\n<p>Assurez-vous d\u2019avoir install\u00e9 les paquets R suivants:<\/p>\n<ul>\n<li><code>tidyverse<\/code> pour la manipulation et la visualisation des donn\u00e9es<\/li>\n<li><code>ggpubr<\/code> pour cr\u00e9er facilement des graphiques pr\u00eats \u00e0 la publication<\/li>\n<li><code>rstatix<\/code> contient des fonctions R facilitant les analyses statistiques.<\/li>\n<li><code>datarium<\/code>: contient les jeux de donn\u00e9es requis pour ce chapitre.<\/li>\n<\/ul>\n<p>Commencez par charger les packages requis suivants:<\/p>\n<pre class=\"r\"><code>library(tidyverse)\r\nlibrary(ggpubr)\r\nlibrary(rstatix)<\/code><\/pre>\n<\/div>\n<div id=\"donn\u00e9es-de-d\u00e9monstration\" class=\"section level3\">\n<h3>Donn\u00e9es de d\u00e9monstration<\/h3>\n<p>Ici, nous utiliserons un jeu de donn\u00e9es de d\u00e9monstration <code>mice2<\/code> [package datarium], qui contient le poids de 10 souris avant et apr\u00e8s le traitement.<\/p>\n<pre class=\"r\"><code># Format large\r\ndata(\"mice2\", package = \"datarium\")\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># Transformez en donn\u00e9es longues : \r\n# rassembler les valeurs de `before` (avant) et `after` (apr\u00e8s) dans la m\u00eame colonne\r\nmice2.long &lt;- mice2 %&gt;%\r\n  gather(key = \"group\", value = \"weight\", 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>Tout d\u2019abord, commencez par calculer la diff\u00e9rence entre les groupes:<\/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=\"identifier-les-valeurs-aberrantes\" class=\"section level3\">\n<h3>Identifier les valeurs aberrantes<\/h3>\n<p>Les valeurs aberrantes peuvent \u00eatre facilement identifi\u00e9es \u00e0 l\u2019aide des m\u00e9thodes boxplot, impl\u00e9ment\u00e9es dans la fonction R <code>identify_outliers()<\/code> [paquet rstatix].<\/p>\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>Il n\u2019y avait pas de valeurs extr\u00eames aberrantes.<\/p>\n<\/div>\n<div class=\"warning\">\n<p>Notez que, dans le cas o\u00f9 vous avez des valeurs extr\u00eames aberrantes, cela peut \u00eatre d\u00fb \u00e0 : 1) erreurs de saisie de donn\u00e9es, erreurs de mesure ou valeurs inhabituelles.<\/p>\n<p>Vous pouvez quand m\u00eame inclure la valeur aberrante dans l\u2019analyse si vous ne croyez pas que le r\u00e9sultat sera affect\u00e9 de fa\u00e7on substantielle. Cela peut \u00eatre \u00e9valu\u00e9 en comparant le r\u00e9sultat du test t avec et sans la valeur aberrante.<\/p>\n<p>Il est \u00e9galement possible de conserver les valeurs aberrantes dans les donn\u00e9es et d\u2019effectuer un test Wilcoxon ou un test t robuste en utilisant le progiciel WRS2.<\/p>\n<\/div>\n<\/div>\n<div id=\"v\u00e9rifier-la-normalit\u00e9-par-groupes\" class=\"section level3\">\n<h3>V\u00e9rifier la normalit\u00e9 par groupes<\/h3>\n<p>L\u2019hypoth\u00e8se de normalit\u00e9 peut \u00eatre v\u00e9rifi\u00e9e en calculant le test de Shapiro-Wilk pour chaque groupe. Si les donn\u00e9es sont normalement distribu\u00e9es, la p-value doit \u00eatre sup\u00e9rieure \u00e0 0,05.<\/p>\n<pre class=\"r\"><code>mice2 %&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<div class=\"success\">\n<p>D\u2019apr\u00e8s le r\u00e9sultat, les deux p-values sont sup\u00e9rieures au seuil de significativit\u00e9 0,05, ce qui indique que la distribution des donn\u00e9es n\u2019est pas significativement diff\u00e9rente de la distribution normale. En d\u2019autres termes, nous pouvons supposer que la normalit\u00e9.<\/p>\n<\/div>\n<p>Vous pouvez \u00e9galement cr\u00e9er des QQ plots pour chaque groupe. Le graphique QQ plot dessine la corr\u00e9lation entre une donn\u00e9e d\u00e9finie et la distribution normale.<\/p>\n<pre class=\"r\"><code>ggqqplot(mice2, \"differences\")<\/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\/083-paired-t-test-assumptions-qqplot-1.png\" width=\"288\" \/><\/p>\n<div class=\"success\">\n<p>Tous les points se situent approximativement le long de la ligne de r\u00e9f\u00e9rence (45 degr\u00e9s), pour chaque groupe. Nous pouvons donc supposer la normalit\u00e9 des donn\u00e9es.<\/p>\n<\/div>\n<div class=\"warning\">\n<p>Notez que, si la taille de votre \u00e9chantillon est sup\u00e9rieure \u00e0 50, le graphique de normalit\u00e9 QQ plot est pr\u00e9f\u00e9r\u00e9 parce qu\u2019avec des \u00e9chantillons de plus grande taille, le test de Shapiro-Wilk devient tr\u00e8s sensible m\u00eame \u00e0 un \u00e9cart mineur par rapport \u00e0 la distribution normale.<\/p>\n<p>Dans le cas o\u00f9 les donn\u00e9es ne sont pas normalement distribu\u00e9es, il est recommand\u00e9 d\u2019utiliser le test de Wilcoxon non param\u00e9trique.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"article-apparent\u00e9\" class=\"section level2\">\n<h2>Article apparent\u00e9<\/h2>\n<p><a href=\"https:\/\/www.datanovia.com\/en\/fr\/lessons\/test-t-dans-r\/\">Test t dans R<\/a><\/p>\n<\/div>\n<\/div>\n<p><!--end rdoc--><\/p>\n","protected":false},"excerpt":{"rendered":"<p>D\u00e9crit les hypoth\u00e8ses du test t appari\u00e9 et fournit des exemples de code R pour v\u00e9rifier si les hypoth\u00e8ses sont respect\u00e9es avant de calculer le test t.<\/p>\n","protected":false},"author":1,"featured_media":15317,"parent":15307,"menu_order":83,"comment_status":"open","ping_status":"closed","template":"","class_list":["post-15316","dt_lessons","type-dt_lessons","status-publish","has-post-thumbnail","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.2 - 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