{"id":15303,"date":"2020-03-15T16:25:09","date_gmt":"2020-03-15T15:25:09","guid":{"rendered":"https:\/\/www.datanovia.com\/en\/?post_type=dt_lessons&#038;p=15303"},"modified":"2020-03-15T16:25:09","modified_gmt":"2020-03-15T15:25:09","slug":"formule-du-test-t-independant","status":"publish","type":"dt_lessons","link":"https:\/\/www.datanovia.com\/en\/fr\/lessons\/formule-du-test-t\/formule-du-test-t-independant\/","title":{"rendered":"Formule du Test-T Ind\u00e9pendant"},"content":{"rendered":"<div id=\"rdoc\">\n<p>Cet article d\u00e9crit la <strong>formule du test t ind\u00e9pendant<\/strong>, qui est utilis\u00e9e pour comparer les moyennes de deux groupes ind\u00e9pendants. La formule du test t ind\u00e9pendant est \u00e9galement appel\u00e9e:<\/p>\n<ul>\n<li><em>formule du test t non appari\u00e9<\/em>,<\/li>\n<li><em>formule du test t pour \u00e9chantillons ind\u00e9pendants<\/em>,<\/li>\n<li><em>formule du test t \u00e0 deux \u00e9chantillons<\/em>,<\/li>\n<li><em>formule du test t pour 2 \u00e9chantillons<\/em> et<\/li>\n<li><em>\u00e9quation du test t \u00e0 deux \u00e9chantillons<\/em><\/li>\n<\/ul>\n<p>Le t-test pour \u00e9chantillons ind\u00e9pendants se pr\u00e9sente sous deux formes diff\u00e9rentes:<\/p>\n<ul>\n<li>le <em>test t standard de Student<\/em>, qui suppose que la variance des deux groupes est \u00e9gale.<\/li>\n<li>le <em>test t de Welch<\/em>, qui est moins restrictif que le test original de Student. Il s\u2019agit du test o\u00f9 vous ne pr\u00e9sumez pas que la variance est la m\u00eame dans les deux groupes, ce qui donne les degr\u00e9s de libert\u00e9 fractionnaires suivants.<\/li>\n<\/ul>\n<p>Dans cet article, vous apprendrez la <em>formule du test T de Student<\/em> et la <em>formule du test T de Weltch<\/em>.<\/p>\n<p>Sommaire:<\/p>\n<div id=\"TOC\">\n<ul>\n<li><a href=\"#formule\">Formule<\/a><\/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=\"formule\" class=\"section level2\">\n<h2>Formule<\/h2>\n<ol style=\"list-style-type: decimal;\">\n<li><strong>Test t classique \u00e0 deux \u00e9chantillons ind\u00e9pendants<\/strong> (test t de Student). Si les variances des deux groupes sont \u00e9quivalentes (<strong>homosc\u00e9dasticit\u00e9<\/strong>), la valeur du test t, comparant les deux \u00e9chantillons (<span class=\"math inline\">\\(A\\)<\/span> et <span class=\"math inline\">\\(B\\)<\/span>), peut \u00eatre calcul\u00e9e comme suit.<\/li>\n<\/ol>\n<p><span class=\"math display\">\\[<br \/>\nt = \\frac{m_A - m_B}{\\sqrt{ \\frac{S^2}{n_A} + \\frac{S^2}{n_B} }}<br \/>\n\\]<\/span><\/p>\n<p>o\u00f9,<\/p>\n<ul>\n<li><span class=\"math inline\">\\(m_A\\)<\/span> et <span class=\"math inline\">\\(m_B\\)<\/span> repr\u00e9sentent la valeur moyenne des groupes A et B, respectivement.<\/li>\n<li><span class=\"math inline\">\\(n_A\\)<\/span> et <span class=\"math inline\">\\(n_B\\)<\/span> repr\u00e9sentent les tailles des groupes A et B, respectivement.<\/li>\n<li><span class=\"math inline\">\\(S^2\\)<\/span> est un estimateur de la variance mise en commun des deux groupes. Il peut \u00eatre calcul\u00e9 comme suit :<\/li>\n<\/ul>\n<p><span class=\"math display\">\\[<br \/>\nS^2 = \\frac{\\sum{(x-m_A)^2}+\\sum{(x-m_B)^2}}{n_A+n_B-2}<br \/>\n\\]<\/span><\/p>\n<p>avec des degr\u00e9s de libert\u00e9 (df) : <span class=\"math inline\">\\(df = n_A + n_B - 2\\)<\/span>.<\/p>\n<ol style=\"list-style-type: decimal;\" start=\"2\">\n<li><strong>Statistique t de Welch<\/strong>. Si les variances des deux groupes compar\u00e9s sont diff\u00e9rentes (<strong>h\u00e9t\u00e9rosc\u00e9dasticit\u00e9<\/strong>), il est possible d\u2019utiliser le test t de Welch, qui est une adaptation du test t de Student. La statistique t de Welch est calcul\u00e9e comme suit :<\/li>\n<\/ol>\n<p><span class=\"math display\">\\[<br \/>\nt = \\frac{m_A - m_B}{\\sqrt{ \\frac{S_A^2}{n_A} + \\frac{S_B^2}{n_B} }}<br \/>\n\\]<\/span><\/p>\n<p>o\u00f9, <span class=\"math inline\">\\(S_A\\)<\/span> et <span class=\"math inline\">\\(S_B\\)<\/span> sont les \u00e9cart-types des deux groupes A et B, respectivement.<\/p>\n<p>Contrairement au t-test classique de Student, la formule du t-test de Welch implique que la variance de chacun des deux groupes (<span class=\"math inline\">\\(S_A^2\\)<\/span> et <span class=\"math inline\">\\(S_B^2\\)<\/span>) compar\u00e9s. En d\u2019autres termes, il n\u2019utilise pas la variance group\u00e9e <span class=\"math inline\">\\(S\\)<\/span>.<\/p>\n<p>Le <strong>degr\u00e9 de libert\u00e9<\/strong> du <strong>test t de Welch<\/strong> est estim\u00e9 comme suit :<\/p>\n<p><span class=\"math display\">\\[<br \/>\ndf = (\\frac{S_A^2}{n_A}+ \\frac{S_B^2}{n_B})^2 \/ (\\frac{S_A^4}{n_A^2(n_A-1)} + \\frac{S_B^4}{n_B^2(n_B-1)} )<br \/>\n\\]<\/span><\/p>\n<div class=\"success\">\n<p>Une p-value peut \u00eatre calcul\u00e9e pour la valeur absolue correspondante de la statistique t (|t|).<\/p>\n<p>Si la p-value est inf\u00e9rieure ou \u00e9gale au seuil de significativit\u00e9 0,05, nous pouvons rejeter l\u2019hypoth\u00e8se nulle et accepter l\u2019hypoth\u00e8se alternative. En d\u2019autres termes, nous pouvons conclure que les valeurs moyennes des groupes A et B sont significativement diff\u00e9rentes.<\/p>\n<\/div>\n<div class=\"warning\">\n<p>Notez que le test t de Welch est consid\u00e9r\u00e9 comme le plus prudent. Habituellement, les r\u00e9sultats du <strong>test t classique de Student<\/strong> et du <strong>test t de Welch<\/strong> sont tr\u00e8s similaires, \u00e0 moins que la taille des groupes et les \u00e9carts types soient tr\u00e8s diff\u00e9rents.<\/p>\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 la formule du test t ind\u00e9pendant, qui est utilis\u00e9e pour comparer les moyennes de deux groupes ind\u00e9pendants. Vous apprendrez la formule du test t de Student et la formule du test t de Weltch.<\/p>\n","protected":false},"author":1,"featured_media":15304,"parent":15299,"menu_order":76,"comment_status":"open","ping_status":"closed","template":"","class_list":["post-15303","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>Formule du Test-T Ind\u00e9pendant: Excellent Tutoriel \u00e0 Lire - Datanovia<\/title>\n<meta name=\"description\" content=\"D\u00e9crit la formule du test t ind\u00e9pendant, qui est utilis\u00e9e pour comparer les moyennes de deux groupes ind\u00e9pendants. 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