{"id":296,"date":"2014-10-06T13:19:03","date_gmt":"2014-10-06T11:19:03","guid":{"rendered":"http:\/\/wordpress.callac.online\/index.php\/test-de-student-et-test-de-wilcoxon\/"},"modified":"2023-10-14T20:14:40","modified_gmt":"2023-10-14T18:14:40","slug":"test-de-student-et-test-de-wilcoxon","status":"publish","type":"page","link":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/le-logiciel-r\/les-tests-avec-r\/test-de-student-et-test-de-wilcoxon\/","title":{"rendered":"Test de Student et test de Wilcoxon"},"content":{"rendered":"

Un fichier de donn\u00e9es<\/h2>\n

Travaillons sur une enqu\u00eate de satisfactions dans un h\u00f4pital, r\u00e9cup\u00e9r\u00e9 lors d’un cours de FUN (France Unit\u00e9 Num\u00e9rique). Les fichiers sont disponibles ici<\/a>.<\/p>\n

Par la suite, ces donn\u00e9es seront stock\u00e9es dans la variable satis<\/em> .<\/p>\n

Dans ces donn\u00e9es comme souvent, les observations sont en lignes et les variables en colonnes.<\/p>\n

Un exemple<\/h2>\n

On cherche \u00e0 savoir s’il y a une diff\u00e9rence d’\u00e2ge entre les patients recommandant l’h\u00f4pital et les autres.<\/p>\n

Pr\u00e9parons les donn\u00e9es.<\/p>\n

satis$recommander.b<-ifelse(satis$recommander==2,1,0)<\/pre>\n
Le test de Student<\/h2>\n
Ce test sert \u00e0 comparer les moyennes d’une variable quantitative pour deux groupes d’une population (d\u00e9terminer par une variable binaire).<\/p>\n
Pour pouvoir l’utiliser, il faut respecter les conditions suivantes :
\n– les effectifs doivent \u00eatre raisonnables (n>30) ;
\n– la variable quantitative doit suivre une loi normale ;
\n– les variances des deux groupes doivent \u00eatre voisines.<\/p>\n
On utilise l’instruction t.test<\/em>.<\/p>\n
V\u00e9rifions les conditions<\/h2>\n
– La loi normale de l’\u00e2ge<\/strong><\/p>\n
hist(satis$age)<\/pre>\n
\"histo_age_01-2.png\"<\/p>\n
On voit que l’\u00e2ge suit environ une loi normale.<\/p>\n
– Les effectifs dans les sous-groupes<\/strong><\/p>\n
library(prettyR)\ntapply(satis$age,satis$recommander.b,valid.n)<\/pre>\n

\n0   1
\n136 269
\n<\/code><\/p>\n
– Les \u00e9cart-types dans les sous-groupes<\/strong><\/p>\n
tapply(satis$age,satis$recommander.b,sd)<\/pre>\n

\n0        1
\n18.38549 16.10392
\n<\/code><\/p>\n
Les \u00e9cart-types ne sont pas trop \u00e9loign\u00e9s.<\/p>\n
Toutes les conditions sont respect\u00e9es<\/p>\n
Application du test de Student<\/h2>\n
NB : attention au ~<\/code> qui remplace la virgule habituelle !<\/p>\n
t.test(satis$age~satis$recommander.b,var.equal=TRUE)<\/pre>\n

\nTwo Sample t-test<\/code><\/p>\n

\n<\/code><\/p>\n
data:  satis$age by satis$recommander.b
\nt = -1.2159, df = 403, p-value = 0.2247
\nalternative hypothesis: true difference in means is not equal to 0
\n95 percent confidence interval:
\n-5.658504  1.333772
\nsample estimates:
\nmean in group 0 mean in group 1
\n53.55882        55.72119
\n<\/code><\/p>\n
La moyenne d’\u00e2ge est sup\u00e9rieure dans le groupe qui recommande l’\u00e9tablissement, mais la valeur de $p$ est sup\u00e9rieure \u00e0 $5~\\%$.<\/p>\n
Le test de Wilcoxon<\/h2>\n
Si le test de Student n’est pas applicable, on peut utiliser le test de Wilcoxon.<\/p>\n
Celui-ci ne donne pas les moyennes. Commen\u00e7ons par les calculer :<\/p>\n
tapply(satis$age,satis$recommander.b,mean)<\/pre>\n

\n0        1
\n53.55882 55.72119
\n<\/code><\/p>\n
Appliquons le test.<\/p>\n
NB : attention au ~<\/code> qui remplace la virgule habituelle !<\/p>\n
wilcox.test(satis$age~satis$recommander.b)<\/pre>\n

\nWilcoxon rank sum test with continuity correction<\/code><\/p>\n

\n<\/code><\/p>\n
data:  satis$age by satis$recommander.b
\nW = 17023.5, p-value = 0.2543
\nalternative hypothesis: true location shift is not equal to 0
\n<\/code><\/p>\n
La valeur de $p$ est aussi sup\u00e9rieure \u00e0 $5~\\%$.<\/p>\n","protected":false},"excerpt":{"rendered":"
Un fichier de donn\u00e9es Travaillons sur une enqu\u00eate de satisfactions dans un h\u00f4pital, r\u00e9cup\u00e9r\u00e9 lors d’un cours de FUN (France Unit\u00e9 Num\u00e9rique). Les fichiers sont disponibles ici. Par la suite,…<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2089,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-296","page","type-page","status-publish","hentry"],"yoast_head":"\nTest de Student et test de Wilcoxon - Maths & Num\u00e9rique<\/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:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/le-logiciel-r\/les-tests-avec-r\/test-de-student-et-test-de-wilcoxon\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Test de Student et test de Wilcoxon - Maths & Num\u00e9rique\" \/>\n<meta property=\"og:description\" content=\"Un fichier de donn\u00e9es Travaillons sur une enqu\u00eate de satisfactions dans un h\u00f4pital, r\u00e9cup\u00e9r\u00e9 lors d’un cours de FUN (France Unit\u00e9 Num\u00e9rique). 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