{"id":179766,"date":"2022-11-21T09:30:57","date_gmt":"2022-11-21T09:30:57","guid":{"rendered":"https:\/\/datascientest.com\/?p=179766"},"modified":"2023-11-09T13:55:58","modified_gmt":"2023-11-09T13:55:58","slug":"test-du-khi-2","status":"publish","type":"post","link":"https:\/\/datascientest.com\/test-du-khi-2","title":{"rendered":"Chi-2 : En savoir plus sur ce test statistique essentiel"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"179766\" class=\"elementor elementor-179766\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b6af5c0 e-flex e-con-boxed e-con\" data-id=\"b6af5c0\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3c260a5 elementor-widget elementor-widget-heading\" data-id=\"3c260a5\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">Le test du khi2 (ou chi-squared) est un test statistique pour des variables prenant un nombre fini de valeurs possibles (donc des variables cat\u00e9gorielles). Pour rappel, un test statistique est une m\u00e9thode permettant d\u2019accepter ou non une hypoth\u00e8se, appel\u00e9e hypoth\u00e8se nulle, selon son ad\u00e9quation aux donn\u00e9es.<\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-794b63d e-flex e-con-boxed e-con\" data-id=\"794b63d\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-fce60fc elementor-widget elementor-widget-heading\" data-id=\"fce60fc\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">\u00c0 quoi sert le test du khi-2 ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-29e30d9 elementor-widget elementor-widget-text-editor\" data-id=\"29e30d9\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p>L\u2019avantage du test khi-deux est sa grande diversit\u00e9 d\u2019utilisation :<\/p><ul><li>Test d\u2019<strong>ad\u00e9quation<\/strong> \u00e0 une loi ou une famille de lois d\u00e9finies \u00e0 priori, par exemple : la taille d\u2019une population suit-elle une loi normale ? :<\/li><li>Test d\u2019<strong>ind\u00e9pendance<\/strong>, exemple : la couleur des cheveux est elle ind\u00e9pendante du sexe ?<\/li><li>Test d\u2019<strong>homog\u00e9n\u00e9it\u00e9<\/strong> : deux s\u00e9ries de donn\u00e9es sont-elles identiquement distribu\u00e9es?<\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-995b062 e-flex e-con-boxed e-con\" data-id=\"995b062\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d2326c2 elementor-widget elementor-widget-heading\" data-id=\"d2326c2\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Comment fonctionne le test ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e528ee6 elementor-widget elementor-widget-text-editor\" data-id=\"e528ee6\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Son principe est de comparer la proximit\u00e9 ou l\u2019\u00e9loignement entre la loi de l&rsquo;\u00e9chantillon et une loi th\u00e9orique, avec la statistique dite de <strong>Pearson <span class=\"katex-eq\" data-katex-display=\"false\"><\/span> \\chi_{Pearson} [\\latex]<\/strong>, bas\u00e9e sur la distance du khi-2.<\/p><p>Premier probl\u00e8me : Ne disposant que d\u2019un nombre limit\u00e9 de donn\u00e9es, nous ne pouvons pas conna\u00eetre parfaitement la loi de l\u2019\u00e9chantillon, mais seulement une approximation de celle-ci, la mesure empirique.<\/p><p>La mesure empirique <strong><span class=\"katex-eq\" data-katex-display=\"false\"><\/span> \\widehat{\\mathbb{P}}_{n,X} [\\latex]<\/strong> repr\u00e9sente la fr\u00e9quence des diff\u00e9rentes valeurs observ\u00e9es :<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6364a70 elementor-widget elementor-widget-shortcode\" data-id=\"6364a70\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\forall x \\in \\mathbb{X} \\quad   \\widehat{\\mathbb{P}}_{n,X} (x) = \\frac{1}{n} \\sum_{k=1}^{n} 1_{X_{k} =x}<\/span><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bfe43b9 elementor-widget elementor-widget-text-editor\" data-id=\"bfe43b9\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p style=\"text-align: center;\"><i><span style=\"font-weight: 400;\">Formule mesure empirique<\/span><\/i><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ca55691 elementor-widget elementor-widget-text-editor\" data-id=\"ca55691\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p style=\"text-align: center;\">avec<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6aadabc elementor-widget elementor-widget-shortcode\" data-id=\"6aadabc\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><span class=\"katex-eq\" data-katex-display=\"false\"> X_{1},... ,{X_n}<\/span> = l'\u00e9chantillon<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2ea8b71 elementor-widget elementor-widget-shortcode\" data-id=\"2ea8b71\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><span class=\"katex-eq\" data-katex-display=\"false\"> {\\mathbb{X}} <\/span> = l\u2019ensemble des valeurs possibles<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-248f549 elementor-widget elementor-widget-text-editor\" data-id=\"248f549\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\tOn d\u00e9finit la statistique de Pearson comme :\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a396e7f elementor-widget elementor-widget-shortcode\" data-id=\"a396e7f\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\chi_{Pearson} = n \\times \\chi_{2}(\\widehat{\\mathbb{P}}_{n,X}, P_{theorique} ) = n \\times \\sum_{x \\in  \\mathbb{X}} \\frac{(\\widehat{\\mathbb{P}}_{n,X} (x)- P_{theorique}(x))^{2}}{P_{theorique}(x)}<\/span><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6da2fff elementor-widget elementor-widget-text-editor\" data-id=\"6da2fff\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p style=\"text-align: center;\"><em>Formule statistiques de Pearson<\/em><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-33d2638 elementor-widget elementor-widget-text-editor\" data-id=\"33d2638\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p style=\"text-align: left;\">Sous l\u2019hypoth\u00e8se nulle , c\u2019est \u00e0 dire qu\u2019on a bien \u00e9galit\u00e9 entre la loi de l\u2019\u00e9chantillon et la loi th\u00e9orique, cette statistique de Pearson va converger vers la loi du khi-2 \u00e0 d degr\u00e9s de libert\u00e9s. Le nombre d de degr\u00e9s de libert\u00e9s d\u00e9pend des dimensions du probl\u00e8me, en g\u00e9n\u00e9ral c&rsquo;est le nombre de valeurs possibles -1.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-14594d4 e-flex e-con-boxed e-con\" data-id=\"14594d4\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t<div class=\"elementor-element elementor-element-57a9280 e-con-full e-flex e-con\" data-id=\"57a9280\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-b925bf2 elementor-widget elementor-widget-text-editor\" data-id=\"b925bf2\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Pour rappel, la loi du khi-2 \u00e0 d degr\u00e9s de libert\u00e9s<br \/><br \/>centr\u00e9es r\u00e9duites ind\u00e9pendantes.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-538eee2 e-con-full e-flex e-con\" data-id=\"538eee2\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-cabff63 elementor-widget elementor-widget-shortcode\" data-id=\"cabff63\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\chi^{2}_{loi}(d)\n<\/span><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-57706ea e-con-full e-flex e-con\" data-id=\"57706ea\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;full&quot;}\">\n\t\t\t\t<div class=\"elementor-element elementor-element-c6290db elementor-widget elementor-widget-text-editor\" data-id=\"c6290db\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>est celle d\u2019une somme de carr\u00e9s de d gaussiennes\u00a0<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-01fbe02 elementor-widget elementor-widget-shortcode\" data-id=\"01fbe02\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><span class=\"katex-eq\" data-katex-display=\"false\"> chi^{2}_{loi}(d) := \\sum_{k=1}^{d} X_{k} \\quad avec \\quad X_{k}  \\sim  \\mathbb{N}(0,1)<\/span><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c2c8462 elementor-widget elementor-widget-text-editor\" data-id=\"c2c8462\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p style=\"text-align: left;\">Sinon, cette statistique va diverger \u00e0 l\u2019infini, ce qui traduit l\u2019\u00e9loignement entre des distributions empiriques et th\u00e9oriques.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-83e5dc1 elementor-widget elementor-widget-shortcode\" data-id=\"83e5dc1\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><span class=\"katex-eq\" data-katex-display=\"false\"> Sous \\quad H_{0}  \\quad  \\lim_{n\\rightarrow  \\infty } \\chi_{Pearson} = \\chi^{2}_{loi}(d). \\\\\nSous \\quad H_{1}  \\quad  \\lim_{n\\rightarrow  \\infty } \\chi_{Pearson} = \\infty\n<\/span><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-409983e elementor-widget elementor-widget-text-editor\" data-id=\"409983e\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p style=\"text-align: center;\"><em>Formule limite<\/em><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-dc2c58d e-flex e-con-boxed e-con\" data-id=\"dc2c58d\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-ba77fd7 elementor-widget elementor-widget-heading\" data-id=\"ba77fd7\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Quels sont ses avantages ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c227329 elementor-widget elementor-widget-text-editor\" data-id=\"c227329\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>On dispose donc d\u2019une r\u00e8gle de d\u00e9cision simple : si la statistique de Pearson d\u00e9passe une certain seuil, on rejette l\u2019hypoth\u00e8se de d\u00e9part (la distribution th\u00e9orique ne colle pas aux donn\u00e9es), sinon on l\u2019accepte. L\u2019avantage du test Khi-2 est que ce seuil d\u00e9pend seulement de la loi du Khi2 et du niveau de confiance alpha, il est donc ind\u00e9pendant de la loi de l&rsquo;\u00e9chantillon.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-4b58c94 e-flex e-con-boxed e-con\" data-id=\"4b58c94\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-f4031d2 elementor-widget elementor-widget-heading\" data-id=\"f4031d2\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Une application, le test d\u2019ind\u00e9pendance :<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2913727 elementor-widget elementor-widget-text-editor\" data-id=\"2913727\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Prenons un exemple pour illustrer ce test : on veut savoir si les sexes des deux premiers enfants X et Y d\u2019un couple sont ind\u00e9pendants ?<\/p><p>On a rassembl\u00e9 les donn\u00e9es dans une table de contingence :<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-52f2b70 elementor-widget elementor-widget-shortcode\" data-id=\"52f2b70\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\begin{array}{|c|c|c|c|}\n\t\\hline X \/ Y &amp; Enfant 2 : fils &amp; Enfant 2 : fille &amp; Total \\\\\n\t\\hline Enfant 1 : fils &amp; 857  &amp;  801 &amp; 1658 \\\\\n\t\\hline Enfant 1 : fille  &amp; 813 &amp; 828 &amp; 1641\\\\\n\t\\hline Total  &amp; 1670 &amp; 1629 &amp; 3299\n\\end{array}\n<\/span><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c103712 elementor-widget elementor-widget-text-editor\" data-id=\"c103712\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>La <strong>Statistique de Pearson<\/strong> va d\u00e9terminer si la mesure empirique de la loi conjointe (X,Y) est \u00e9gale au produit des mesures empiriques marginales, ce qui caract\u00e9rise l\u2019ind\u00e9pendance :<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-03da5b8 elementor-widget elementor-widget-shortcode\" data-id=\"03da5b8\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\chi_{Pearson} = n \\times \\chi2\n(\\widehat{\\mathbb{P}}_{X \\times Y}, \\widehat{\\mathbb{P}}_{X} \\times \\widehat{\\mathbb{P}}_{Y}) = \n\\sum_{x \\in  \\{fille, fils\\}, y\\in \\{fille, fils\\} } \\frac{(Observation_{x,y} - Theory_{x,y})^{2}}{Theory_{x,y}}\n\n<\/span><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7e9aa9f elementor-widget elementor-widget-text-editor\" data-id=\"7e9aa9f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Ici Observation(x,y) est la fr\u00e9quence de la valeur (x,y) :<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-17c998a elementor-widget elementor-widget-shortcode\" data-id=\"17c998a\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\forall x,y \\in \\{fille, fils\\} \\quad\nObservation_{x,y} = \\frac{1}{n} \\sum_{k=1}^{n} 1_{(X_{k},Y_{k}) =(x,y)}\n<\/span><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-db29310 elementor-widget elementor-widget-text-editor\" data-id=\"db29310\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Par exemple:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2ee6279 elementor-widget elementor-widget-shortcode\" data-id=\"2ee6279\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><span class=\"katex-eq\" data-katex-display=\"false\"> Observation(fille,fille)= \\frac{828}{3299} =0.251\n<\/span><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-5cbb6a2 elementor-widget elementor-widget-text-editor\" data-id=\"5cbb6a2\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\tPour Theory(x,y), X et Y sont suppos\u00e9s ind\u00e9pendants, la loi th\u00e9orique devrait donc \u00eatre le produit des lois marginales :\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-bc10c5e elementor-widget elementor-widget-shortcode\" data-id=\"bc10c5e\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\forall x,y \\in \\{fille, fils\\} \\quad\nTheory_{x,y} = Observation^{X} \\times Observation^{Y} = \\sum_{y\\in\\{fille, fils\\}}Observation_{x,y} \\times\n\\sum_{x\\in\\{fille, fils\\}}Observation_{x,y}\n<\/span><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-753aed0 elementor-widget elementor-widget-text-editor\" data-id=\"753aed0\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Ainsi la probabilit\u00e9 th\u00e9orique pour(fils,fils) est:<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-73b350f elementor-widget elementor-widget-shortcode\" data-id=\"73b350f\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><span class=\"katex-eq\" data-katex-display=\"false\"> Theory(fils,fils)=\\frac{857+801}{3299} \\times \\frac{857+813}{3299}  =\\frac{1658 \\times 1670}{3299^{2}}=0.254<\/span><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9b1b87a elementor-widget elementor-widget-text-editor\" data-id=\"9b1b87a\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Calculons la statistique du test via le code python suivant :<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-a5b8eb2 elementor-widget elementor-widget-shortcode\" data-id=\"a5b8eb2\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><script src=\"https:\/\/gist.github.com\/robinTdatascientest\/8e3a8d20848edc75719ef94ee58dd804.js\"><\/script><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-86c1a12 elementor-widget elementor-widget-text-editor\" data-id=\"86c1a12\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Dans notre cas, les variables X et Y ont seulement 2 valeurs possibles : filles ou gar\u00e7ons, la dimension du probl\u00e8me est donc de (2-1)(2-1) soit 1.<\/p><p>On compare donc la statistique du test au quantile du khi2 \u00e0 1 degr\u00e9 de libert\u00e9, via la fonction chi2.ppf de scipy.stats. Elle est inf\u00e9rieure au quantile, et la p-valeur sup\u00e9rieure au niveau de confiance = 0.05, on ne peut pas rejeter l&rsquo;hypoth\u00e8se nulle avec un confiance 95%,et l\u2019on conclut donc \u00e0 l\u2019ind\u00e9pendance du sexe des 2 premiers enfants.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-8700138 e-flex e-con-boxed e-con\" data-id=\"8700138\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-a695879 elementor-widget elementor-widget-heading\" data-id=\"a695879\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Quelles sont ses limites ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-be4f012 elementor-widget elementor-widget-text-editor\" data-id=\"be4f012\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>S\u2019il semble tr\u00e8s pratique, le test du khi-2 conna\u00eet cependant des limites : il constate seulement l\u2019existence de corr\u00e9lations, mais ne d\u00e9tecte ni l\u2019intensit\u00e9 de celles-ci ni des causalit\u00e9s.<\/p><p>Il repose sur l\u2019approximation de la loi du khi2 avec la statistique de Pearson, v\u00e9rifi\u00e9e seulement si l\u2019on dispose d\u2019un nombre suffisant de donn\u00e9es. Dans la pratique cette condition de validit\u00e9 est la suivante :<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-71d4b0d elementor-widget elementor-widget-shortcode\" data-id=\"71d4b0d\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><span class=\"katex-eq\" data-katex-display=\"false\"> \\forall x \\in \\mathbb{X} \\quad n \\times P_{theorique}(x) (1- P_{theorique}(x)) \\geq 5<\/span><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4d69b2c elementor-widget elementor-widget-text-editor\" data-id=\"4d69b2c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Le test exact de Fisher permet de pallier ce d\u00e9faut mais n\u00e9cessite une puissance calcul \u00e9lev\u00e9e (dans la pratique, on le limite au cas tables contingences 2*2).<\/p><p>Les tests statistiques sont essentiels en <a href=\"https:\/\/datascientest.com\/data-science-definition\">Data Science<\/a> pour v\u00e9rifier la pertinence des variables explicatives et valider les hypoth\u00e8ses de sa mod\u00e9lisation. Vous pourrez retrouver davantage d\u2019informations sur le khi-2 et d\u2019autres tests statistiques dans notre <strong>module 104 &#8211; Statistiques Exploratoires<\/strong>.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-464cd31 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"464cd31\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/formation-data-scientist\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">D\u00e9couvrir la formation Data Scientist<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-08f5bb7 e-flex e-con-boxed e-con\" data-id=\"08f5bb7\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-caaba1d elementor-widget elementor-widget-heading\" data-id=\"caaba1d\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">R\u00e9f\u00e9rences :<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e093abf elementor-widget elementor-widget-text-editor\" data-id=\"e093abf\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><a href=\"https:\/\/docs.scipy.org\/doc\/scipy\/reference\/generated\/scipy.stats.chi2.html\">https:\/\/docs.scipy.org\/doc\/scipy\/reference\/generated\/scipy.stats.chi2.html<\/a><\/p><p><a href=\"https:\/\/docs.scipy.org\/doc\/scipy\/reference\/generated\/scipy.stats.chi2_contingency.html\">https:\/\/docs.scipy.org\/doc\/scipy\/reference\/generated\/scipy.stats.chi2_contingency.html<\/a><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-3bf514c e-flex e-con-boxed e-con\" data-id=\"3bf514c\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d4b3de5 elementor-widget elementor-widget-html\" data-id=\"d4b3de5\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<script type=\"application\/ld+json\">\r\n{\r\n  \"@context\": \"https:\/\/schema.org\",\r\n  \"@type\": \"FAQPage\",\r\n  \"mainEntity\": [{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"Comment fonctionne le test ?\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"Son principe est de comparer la proximit\u00e9 ou l\u2019\u00e9loignement entre la loi de l'\u00e9chantillon et une loi th\u00e9orique, avec la statistique dite de Pearson <span class=\"katex-eq\" data-katex-display=\"false\"><\/span> \\chi_{Pearson} [\\latex], bas\u00e9e sur la distance du khi-2. Premier probl\u00e8me : Ne disposant que d\u2019un nombre limit\u00e9 de donn\u00e9es, nous ne pouvons pas conna\u00eetre parfaitement la loi de l\u2019\u00e9chantillon, mais seulement une approximation de celle-ci, la mesure empirique.\"\r\n    }\r\n  },{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"Quels sont ses avantages ?\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"On dispose donc d\u2019une r\u00e8gle de d\u00e9cision simple : si la statistique de Pearson d\u00e9passe une certain seuil, on rejette l\u2019hypoth\u00e8se de d\u00e9part (la distribution th\u00e9orique ne colle pas aux donn\u00e9es), sinon on l\u2019accepte. L\u2019avantage du test Khi-2 est que ce seuil d\u00e9pend seulement de la loi du Khi2 et du niveau de confiance alpha, il est donc ind\u00e9pendant de la loi de l'\u00e9chantillon.\"\r\n    }\r\n  },{\r\n    \"@type\": \"Question\",\r\n    \"name\": \"Quelles sont ses limites ?\",\r\n    \"acceptedAnswer\": {\r\n      \"@type\": \"Answer\",\r\n      \"text\": \"S\u2019il semble tr\u00e8s pratique, le test du khi-2 conna\u00eet cependant des limites : il constate seulement l\u2019existence de corr\u00e9lations, mais ne d\u00e9tecte ni l\u2019intensit\u00e9 de celles-ci ni des causalit\u00e9s. Il repose sur l\u2019approximation de la loi du khi2 avec la statistique de Pearson, v\u00e9rifi\u00e9e seulement si l\u2019on dispose d\u2019un nombre suffisant de donn\u00e9es.\"\r\n    }\r\n  }]\r\n}\r\n<\/script>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Le test du khi2 (ou chi-squared) est un test statistique pour des variables prenant un nombre fini de valeurs possibles (donc des variables cat\u00e9gorielles). Pour rappel, un test statistique est une m\u00e9thode permettant d\u2019accepter ou non une hypoth\u00e8se, appel\u00e9e hypoth\u00e8se nulle, selon son ad\u00e9quation aux donn\u00e9es. \u00c0 quoi sert le test du khi-2 ? L\u2019avantage [&hellip;]<\/p>\n","protected":false},"author":77,"featured_media":181783,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2497],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Chi-2 : En savoir plus sur ce test statistique essentiel<\/title>\n<meta name=\"description\" content=\"Un test statistique est une m\u00e9thode permettant d\u2019accepter ou non une hypoth\u00e8se. D\u00e9couvrez tout ce qu&#039;il y a \u00e0 savoir concernant le test Khi-2.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/datascientest.com\/test-du-khi-2\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Chi-2 : En savoir plus sur ce test statistique essentiel\" \/>\n<meta property=\"og:url\" content=\"https:\/\/datascientest.com\/test-du-khi-2\" \/>\n<meta property=\"og:site_name\" content=\"Formation Data Science | DataScientest.com\" \/>\n<meta property=\"article:published_time\" content=\"2022-11-21T09:30:57+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-11-09T13:55:58+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/Illu_BLOG_test_chi2.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1024\" \/>\n\t<meta property=\"og:image:height\" content=\"562\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Raphael Kassel\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"Raphael Kassel\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/datascientest.com\/test-du-khi-2\",\"url\":\"https:\/\/datascientest.com\/test-du-khi-2\",\"name\":\"Chi-2 : En savoir plus sur ce test statistique essentiel\",\"isPartOf\":{\"@id\":\"https:\/\/datascientest.com\/#website\"},\"datePublished\":\"2022-11-21T09:30:57+00:00\",\"dateModified\":\"2023-11-09T13:55:58+00:00\",\"author\":{\"@id\":\"https:\/\/datascientest.com\/#\/schema\/person\/6eca16f63daaafcbc96e15549b9d4ee1\"},\"description\":\"Un test statistique est une m\u00e9thode permettant d\u2019accepter ou non une hypoth\u00e8se. D\u00e9couvrez tout ce qu'il y a \u00e0 savoir concernant le test Khi-2.\",\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/datascientest.com\/test-du-khi-2\"]}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/datascientest.com\/#website\",\"url\":\"https:\/\/datascientest.com\/\",\"name\":\"Formation Data Science | DataScientest.com\",\"description\":\"Leader de la formation en Data Science\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/datascientest.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"fr-FR\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/datascientest.com\/#\/schema\/person\/6eca16f63daaafcbc96e15549b9d4ee1\",\"name\":\"Raphael Kassel\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/datascientest.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/11\/raph.jpeg\",\"contentUrl\":\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/11\/raph.jpeg\",\"caption\":\"Raphael Kassel\"},\"description\":\"Raphael Kassel est le Head of Data Programs chez DataScientest. Il supervise une \u00e9quipe Data, impl\u00e9mente de nouveaux parcours comme \\\"Chef de projet IA\\\" et \\\"Data Product Manager\\\", et contribue \u00e0 la modernisation des op\u00e9rations du groupe. En collaboration \u00e9troite avec l'\u00e9quipe de d\u00e9veloppement, il adapte l'accompagnement acad\u00e9mique aux \u00e9volutions de l'\u00e9quipe data et \u00e0 l'internationalisation.\",\"sameAs\":[\"https:\/\/www.linkedin.com\/in\/raphaelkassel\/\",\"Data Science\"],\"url\":\"https:\/\/datascientest.com\/author\/raphaelkassel\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Chi-2 : En savoir plus sur ce test statistique essentiel","description":"Un test statistique est une m\u00e9thode permettant d\u2019accepter ou non une hypoth\u00e8se. D\u00e9couvrez tout ce qu'il y a \u00e0 savoir concernant le test Khi-2.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/datascientest.com\/test-du-khi-2","og_locale":"fr_FR","og_type":"article","og_title":"Chi-2 : En savoir plus sur ce test statistique essentiel","og_url":"https:\/\/datascientest.com\/test-du-khi-2","og_site_name":"Formation Data Science | DataScientest.com","article_published_time":"2022-11-21T09:30:57+00:00","article_modified_time":"2023-11-09T13:55:58+00:00","og_image":[{"width":1024,"height":562,"url":"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/11\/Illu_BLOG_test_chi2.png","type":"image\/png"}],"author":"Raphael Kassel","twitter_card":"summary_large_image","twitter_misc":{"\u00c9crit par":"Raphael Kassel","Dur\u00e9e de lecture estim\u00e9e":"5 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/datascientest.com\/test-du-khi-2","url":"https:\/\/datascientest.com\/test-du-khi-2","name":"Chi-2 : En savoir plus sur ce test statistique essentiel","isPartOf":{"@id":"https:\/\/datascientest.com\/#website"},"datePublished":"2022-11-21T09:30:57+00:00","dateModified":"2023-11-09T13:55:58+00:00","author":{"@id":"https:\/\/datascientest.com\/#\/schema\/person\/6eca16f63daaafcbc96e15549b9d4ee1"},"description":"Un test statistique est une m\u00e9thode permettant d\u2019accepter ou non une hypoth\u00e8se. D\u00e9couvrez tout ce qu'il y a \u00e0 savoir concernant le test Khi-2.","inLanguage":"fr-FR","potentialAction":[{"@type":"ReadAction","target":["https:\/\/datascientest.com\/test-du-khi-2"]}]},{"@type":"WebSite","@id":"https:\/\/datascientest.com\/#website","url":"https:\/\/datascientest.com\/","name":"Formation Data Science | DataScientest.com","description":"Leader de la formation en Data Science","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/datascientest.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"fr-FR"},{"@type":"Person","@id":"https:\/\/datascientest.com\/#\/schema\/person\/6eca16f63daaafcbc96e15549b9d4ee1","name":"Raphael Kassel","image":{"@type":"ImageObject","inLanguage":"fr-FR","@id":"https:\/\/datascientest.com\/#\/schema\/person\/image\/","url":"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/11\/raph.jpeg","contentUrl":"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/11\/raph.jpeg","caption":"Raphael Kassel"},"description":"Raphael Kassel est le Head of Data Programs chez DataScientest. Il supervise une \u00e9quipe Data, impl\u00e9mente de nouveaux parcours comme \"Chef de projet IA\" et \"Data Product Manager\", et contribue \u00e0 la modernisation des op\u00e9rations du groupe. En collaboration \u00e9troite avec l'\u00e9quipe de d\u00e9veloppement, il adapte l'accompagnement acad\u00e9mique aux \u00e9volutions de l'\u00e9quipe data et \u00e0 l'internationalisation.","sameAs":["https:\/\/www.linkedin.com\/in\/raphaelkassel\/","Data Science"],"url":"https:\/\/datascientest.com\/author\/raphaelkassel"}]}},"_links":{"self":[{"href":"https:\/\/datascientest.com\/wp-json\/wp\/v2\/posts\/179766"}],"collection":[{"href":"https:\/\/datascientest.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/datascientest.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/datascientest.com\/wp-json\/wp\/v2\/users\/77"}],"replies":[{"embeddable":true,"href":"https:\/\/datascientest.com\/wp-json\/wp\/v2\/comments?post=179766"}],"version-history":[{"count":0,"href":"https:\/\/datascientest.com\/wp-json\/wp\/v2\/posts\/179766\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/datascientest.com\/wp-json\/wp\/v2\/media\/181783"}],"wp:attachment":[{"href":"https:\/\/datascientest.com\/wp-json\/wp\/v2\/media?parent=179766"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/datascientest.com\/wp-json\/wp\/v2\/categories?post=179766"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/datascientest.com\/wp-json\/wp\/v2\/tags?post=179766"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}