{"id":800590,"date":"2019-02-04T21:38:22","date_gmt":"2019-02-05T04:38:22","guid":{"rendered":"https:\/\/www.questionpro.com\/blog\/coefficient-de-correlation-de-spearmans-rank\/"},"modified":"2019-02-04T21:38:22","modified_gmt":"2019-02-04T21:38:22","slug":"coefficient-de-correlation-de-spearmans-rank","status":"publish","type":"post","link":"https:\/\/www.questionpro.com\/blog\/fr\/coefficient-de-correlation-de-spearmans-rank\/","title":{"rendered":"Coefficient de corr\u00e9lation de Spearman : Formule + Calcul"},"content":{"rendered":"<h2><strong>Coefficient de corr\u00e9lation de Spearman : D\u00e9finition<\/strong><\/h2>\n<p><span style=\"font-weight: 400;\">Le coefficient de corr\u00e9lation de rang de Spearman ou coefficient de corr\u00e9lation de Spearman est une mesure non param\u00e9trique de la corr\u00e9lation de rang (d\u00e9pendance statistique du rang entre deux variables).  <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Nomm\u00e9 d&rsquo;apr\u00e8s Charles Spearman, il est souvent d\u00e9sign\u00e9 par la lettre grecque <strong>\u00ab\u00a0\u03c1\u00a0\u00bb <\/strong>(rho) et est principalement utilis\u00e9 pour l&rsquo;<a href=\"https:\/\/www.questionpro.com\/blog\/data-analysis-simple-and-complex-a-primer\/\">analyse de donn\u00e9es<\/a>.  <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Il mesure la force et la direction de l&rsquo;association entre deux variables class\u00e9es. Mais avant de parler du coefficient de corr\u00e9lation de Spearman, il est important de comprendre la corr\u00e9lation de Pearson. La corr\u00e9lation de Pearson est une mesure statistique de la force d&rsquo;une relation lin\u00e9aire entre des donn\u00e9es appari\u00e9es.  <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Pour le calcul et le test de signification de la variable de classement, il faut que les donn\u00e9es suivantes soient vraies :  <\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Niveau d&rsquo;<a href=\"https:\/\/www.questionpro.com\/blog\/interval-scale\/\">intervalle<\/a> ou de <a href=\"https:\/\/www.questionpro.com\/blog\/ratio-scale\/\">rapport<\/a> <\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Lin\u00e9aire  <\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Distribu\u00e9 bivariant  <\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Si vos donn\u00e9es ne r\u00e9pondent pas aux hypoth\u00e8ses ci-dessus, vous aurez besoin du coefficient de Spearman. Il est n\u00e9cessaire de savoir ce qu&rsquo;est une fonction monotone pour comprendre le coefficient de corr\u00e9lation de Spearman. Une fonction monotone est une fonction qui soit ne diminue jamais, soit n&rsquo;augmente jamais en fonction de l&rsquo;augmentation de la variable ind\u00e9pendante. Une fonction monotone peut \u00eatre expliqu\u00e9e \u00e0 l&rsquo;aide de l&rsquo;image ci-dessous :<\/span><\/p>\n<p><em><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-67390 size-full\" src=\"https:\/\/www.questionpro.com\/blog\/wp-content\/uploads\/2019\/02\/1-2.jpg\" alt=\"Coefficient de corr\u00e9lation de Spearman Ran\" width=\"977\" height=\"314\"><\/em><\/p>\n<p><span style=\"font-weight: 400;\">L&rsquo;image explique trois concepts de la fonction monotone :<\/span><\/p>\n<ol>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Augmentation monotone : Lorsque la variable \u00ab\u00a0x\u00a0\u00bb augmente et que la variable \u00ab\u00a0y\u00a0\u00bb ne diminue jamais.  <\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">D\u00e9croissance monotone : Lorsque la variable \u00ab\u00a0x\u00a0\u00bb augmente mais que la variable \u00ab\u00a0y\u00a0\u00bb n&rsquo;augmente jamais.<\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Non monotone : Lorsque la variable \u00ab\u00a0x\u00a0\u00bb augmente et que la variable \u00ab\u00a0y\u00a0\u00bb augmente parfois et diminue parfois.  <\/span><\/li>\n<\/ol>\n<p><span style=\"font-weight: 400;\">La relation monotone est moins restrictive que la relation lin\u00e9aire utilis\u00e9e dans le coefficient de Pearson. Bien que la monotonicit\u00e9 ne soit pas l&rsquo;exigence ultime du coefficient de corr\u00e9lation de Spearman, il ne sera pas utile de rechercher la corr\u00e9lation de Spearman sans d\u00e9terminer la force et la direction d&rsquo;une relation monotone si l&rsquo;on sait d\u00e9j\u00e0 que la relation entre les variables n&rsquo;est pas monotone.<\/span><\/p>\n<p style=\"text-align: center;\">En savoir plus : <a href=\"https:\/\/www.questionpro.com\/article\/turf-analysis.html\">Analyse du gazon \u00e0 l&rsquo;aide d&rsquo;exemples<\/a><\/p>\n<h3><strong>Coefficient de corr\u00e9lation de Spearman : Formule et calcul avec exemple<\/strong><\/h3>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-67263 size-full\" src=\"https:\/\/www.questionpro.com\/blog\/wp-content\/uploads\/2019\/02\/2019-02-01_1548-1.png\" alt=\"Coefficient de corr\u00e9lation de rang de Spearman\" width=\"277\" height=\"111\">Ici,<\/p>\n<p><span style=\"font-weight: 400;\"><em>n=<\/em> nombre de points de donn\u00e9es des deux variables  <\/span><\/p>\n<p><span style=\"font-weight: 400;\"><em>di=<\/em> diff\u00e9rence de rangs du \u00ab\u00a0i\u00e8me\u00a0\u00bb \u00e9l\u00e9ment<\/span><\/p>\n<p><span style=\"font-weight: 400;\">Le coefficient de Spearman, \u2374, peut prendre une valeur comprise entre +1 et -1 o\u00f9,  <\/span><\/p>\n<ul>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Une valeur \u2374 de +1 signifie une association parfaite du rang  <\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Une valeur \u2374 de 0 signifie qu&rsquo;il n&rsquo;y a pas d&rsquo;association entre les rangs.  <\/span><\/li>\n<li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Une valeur \u2374 de -1 signifie une association n\u00e9gative parfaite entre les rangs.  <\/span><\/li>\n<\/ul>\n<p><span style=\"font-weight: 400;\">Plus la valeur \u2374 est proche de 0, plus l&rsquo;association entre les deux rangs est faible.  <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Nous devons \u00eatre en mesure de classer les donn\u00e9es avant de proc\u00e9der au calcul du coefficient de corr\u00e9lation de rang de Spearman. Il est important d&rsquo;observer si, en augmentant une variable, l&rsquo;autre variable suit une relation monotone.  <\/span><\/p>\n<p><span style=\"font-weight: 400;\">\u00c0 chaque niveau, vous devrez comparer les valeurs des deux variables. Voici comment se d\u00e9roulent les calculs :  <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Les notes de 9 \u00e9l\u00e8ves en histoire et en g\u00e9ographie sont mentionn\u00e9es dans le tableau ci-dessous.<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>\u00c9tape 1 &#8211;<\/strong> Cr\u00e9er un tableau des donn\u00e9es obtenues.  <\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>\u00c9tape 2 &#8211;<\/strong> Commencez par classer les deux ensembles de donn\u00e9es. Le classement des donn\u00e9es peut \u00eatre r\u00e9alis\u00e9 en attribuant le rang \u00ab\u00a01\u00a0\u00bb au plus grand nombre de la colonne, \u00ab\u00a02\u00a0\u00bb au deuxi\u00e8me plus grand nombre et ainsi de suite. La valeur la plus faible est g\u00e9n\u00e9ralement la moins bien class\u00e9e. Cette op\u00e9ration doit \u00eatre effectu\u00e9e pour les deux s\u00e9ries de mesures.  <\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>\u00c9tape 3 &#8211;<\/strong> Ajoutez une troisi\u00e8me colonne d \u00e0 votre ensemble de donn\u00e9es, d repr\u00e9sentant ici la diff\u00e9rence entre les rangs. Par exemple, si le classement du premier \u00e9tudiant en physique est de 3 et celui en math\u00e9matiques de 5, la diff\u00e9rence de classement est de 3. Dans la quatri\u00e8me colonne, \u00e9levez au carr\u00e9 vos valeurs <em>d.<\/em>  <\/span><\/p>\n<table class=\"table-border\">\n<tbody>\n<tr>\n<td style=\"text-align: center;\" width=\"16.6%\"><span style=\"font-weight: 400;\">L&rsquo;histoire  <\/span><\/td>\n<td style=\"text-align: center;\" width=\"16.6%\"><span style=\"font-weight: 400;\">Rang<\/span><\/td>\n<td style=\"text-align: center;\" width=\"16.6%\"><span style=\"font-weight: 400;\">G\u00e9ographie<\/span><\/td>\n<td style=\"text-align: center;\" width=\"16.6%\"><span style=\"font-weight: 400;\">Rang<\/span><\/td>\n<td style=\"text-align: center;\" width=\"16.6%\"><span style=\"font-weight: 400;\">d<\/span><\/td>\n<td style=\"text-align: center;\" width=\"16.6%\"><span style=\"font-weight: 400;\">d carr\u00e9  <\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">35<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">30<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">4<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">23<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">5<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">33<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">3<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">4<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">47<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">45<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">17<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">6<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">23<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">6<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">10<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">7<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">8<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">8<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">43<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">2<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">49<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">9<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">8<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">12<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">7<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">1<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">1<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">6<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">9<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">9<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">28<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">31<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">4<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">0<\/span><\/td>\n<td style=\"text-align: center;\"><span style=\"font-weight: 400;\">0<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><\/td>\n<td style=\"text-align: center;\"><strong>12<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><span style=\"font-weight: 400;\"><strong>\u00c9tape 4 &#8211;<\/strong> Additionnez toutes les valeurs de votre carr\u00e9 <em>d<\/em>, ce qui donne <strong>12<\/strong> (\u2211d carr\u00e9).<\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>\u00c9tape 5-<\/strong> Ins\u00e9rer ces valeurs dans la formule  <\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-67263 size-full\" src=\"https:\/\/www.questionpro.com\/blog\/wp-content\/uploads\/2019\/02\/2019-02-01_1548-1.png\" alt=\"Coefficient de corr\u00e9lation de rang de Spearman\" width=\"277\" height=\"111\"><\/p>\n<p style=\"padding-left: 80px;\"><span style=\"font-weight: 400;\">=1-(6*12)\/<\/span><span style=\"font-weight: 400;\">(9(81-1))<\/span><\/p>\n<p style=\"padding-left: 80px;\"><span style=\"font-weight: 400;\">=1-72\/720<\/span><\/p>\n<p style=\"padding-left: 80px;\"><span style=\"font-weight: 400;\">=1-01<\/span><\/p>\n<p style=\"padding-left: 80px;\"><span style=\"font-weight: 400;\">=0.9<\/span><\/p>\n<p><span style=\"font-weight: 400;\">La corr\u00e9lation de rang de Spearman pour ces donn\u00e9es est de 0,9 et, comme indiqu\u00e9 ci-dessus, si la valeur <strong>\u2374<\/strong> est proche de +1, l&rsquo;association de rang est parfaite.<\/span><\/p>\n<p style=\"text-align: center;\">En savoir plus : <a href=\"https:\/\/www.questionpro.com\/blog\/what-is-conjoint-analysis\/\">Analyse conjointe &#8211; D\u00e9finition, types, exemple, algorithme et mod\u00e8le<\/a><\/p>\n<h3><strong>Comment r\u00e9aliser un coefficient de corr\u00e9lation avec QuestionPro<\/strong><\/h3>\n<p><span style=\"font-weight: 400;\">Dans cette section, vous apprendrez comment ex\u00e9cuter le coefficient de corr\u00e9lation de rang de Spearman pour votre enqu\u00eate.  <\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>\u00c9tape 1 :<\/strong> Allez dans Mes enqu\u00eates \u2192S\u00e9lectionnez Enqu\u00eate\u2192Analytique  <\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>\u00c9tape 2 :<\/strong> Cliquez sur Analyse corr\u00e9lationnelle sous Analyse  <\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-67264 size-full\" src=\"https:\/\/www.questionpro.com\/blog\/wp-content\/uploads\/2019\/02\/SCOC1-1-1.png\" alt=\"Coefficient de corr\u00e9lation de rang de Spearman\" width=\"900\" height=\"499\"><br \/>\n<span style=\"font-weight: 400;\"><strong>\u00c9tape 3 :<\/strong> Cliquez sur le bouton G\u00e9n\u00e9rer le coefficient de Spearman pour obtenir un rapport d\u00e9taill\u00e9.<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-67265 size-full\" src=\"https:\/\/www.questionpro.com\/blog\/wp-content\/uploads\/2019\/02\/SCOC2-1-1.png\" alt=\"Coefficient de corr\u00e9lation de rang de Spearman\" width=\"900\" height=\"556\"><br \/>\n<span style=\"font-weight: 400;\">Dans l&rsquo;exemple ci-dessus, le coefficient de corr\u00e9lation de Spearman est utilis\u00e9 pour d\u00e9terminer la relation entre les deux variables, l&rsquo;exp\u00e9rience professionnelle et le revenu mensuel. D&rsquo;une mani\u00e8re g\u00e9n\u00e9rale, le revenu mensuel devrait augmenter avec l&rsquo;exp\u00e9rience professionnelle, ce qui signifie qu&rsquo;il devrait y avoir une association positive entre les deux variables, comme le prouve la valeur rs de 0,97.<\/span><\/p>\n<p style=\"text-align: center;\">En savoir plus : <a href=\"https:\/\/www.questionpro.com\/blog\/gap-analysis\/\">Analyse des \u00e9carts &#8211; D\u00e9finition, m\u00e9thode et mod\u00e8le avec exemple <\/a> <\/p>\n<p style=\"text-align: center;\"><a class=\"square-cta secondary-lined-cta\" href=\"https:\/\/www.questionpro.com\/a\/showEntry.do?mode=workforce&amp;classID=1024&amp;sourceRef=blog-workforce\" target=\"_blank\" rel=\"noopener noreferrer\"><strong>Cr\u00e9er un compte gratuit<\/strong><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Coefficient de corr\u00e9lation de Spearman : D\u00e9finition Le coefficient de corr\u00e9lation de rang de Spearman ou coefficient de corr\u00e9lation de [&hellip;]<\/p>\n","protected":false},"author":86,"featured_media":632510,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[1536],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.4 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Coefficient de corr\u00e9lation de Spearman : Formule + Calcul .<\/title>\n<meta name=\"description\" content=\"Le coefficient de corr\u00e9lation de Spearman permet de classer la corr\u00e9lation entre deux variables class\u00e9es ou entre une variable class\u00e9e et une variable de mesure.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" 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