{"id":3169,"date":"2015-07-20T12:48:53","date_gmt":"2015-07-20T11:48:53","guid":{"rendered":"https:\/\/abcdr.guyader.pro\/?p=3169"},"modified":"2018-04-08T00:02:14","modified_gmt":"2018-04-07T23:02:14","slug":"comment-comparer-deux-moyennes-grace-au-test-de-student-t-test","status":"publish","type":"post","link":"https:\/\/thinkr.fr\/abcdr\/comment-comparer-deux-moyennes-grace-au-test-de-student-t-test\/","title":{"rendered":"Comment comparer deux moyennes avec R gr\u00e2ce au test de Student ? t.test"},"content":{"rendered":"

Le test de Student permet de tester l\u2019\u00e9galit\u00e9 de deux moyennes. L\u2019hypoth\u00e8se H0 est \u00ab\u00a0les moyennes sont \u00e9gales\u00a0\u00bb ou \u00ab\u00a0la moyenne vaut une valeur x\u00a0\u00bb.<\/p>\n

Pour r\u00e9aliser ce test il est n\u00e9cessaire d\u2019avoir un \u00e9chantillonnage al\u00e9atoire de chaque individu et que les ces deux \u00e9chantillons suivent une loi Normale. Pour tester l\u2019hypoth\u00e8se H0 on utilise la fonction t.test().<\/b><\/p>\n


data(iris)\n\nA<-subset(iris,Species==\"setosa\")[,2]\n\n#On isole la 2\u00e8me colonne : la largeur des s\u00e9pales\n\n<\/code><\/pre>\n
\u00a0<\/p>\n
On commence par tester la normalit\u00e9 de cette variable gr\u00e2ce au test de Shapiro\u00a0:<\/p>\n

shapiro.test(A)\n\n\u00a0\n\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Shapiro-Wilk normality test\n\n\u00a0\n\ndata:\u00a0 A\n\nW = 0.9717, p-value = 0.2715\n\n<\/code><\/pre>\n
\u00a0<\/p>\n
La p-value est sup\u00e9rieur \u00e0 0.05 on accepte donc l’hypoth\u00e8se de normalit\u00e9\u00a0: la variable correspondant \u00e0 la largeur des s\u00e9pales suit donc une loi Normale.<\/p>\n
On compare la moyenne de la variable et la valeur de 0.5cm\u00a0:<\/p>\n

t.test(x=A,mu=0.5)\n\n\u00a0\n\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 One Sample t-test\n\n\u00a0\n\ndata:\u00a0 A\n\nt = 54.6189, df = 49, p-value < 2.2e-16\n\nalternative hypothesis: true mean is not equal to 0.5\n\n95 percent confidence interval:\n\n\u00a03.320271 3.535729\n\nsample estimates:\n\nmean of x\n\n\u00a0\u00a0\u00a0 3.428\n\n<\/code><\/pre>\n
Nous constatons que la p-value est bien sup\u00e9rieure \u00e0 0.05, nous rejetons donc l’hypoth\u00e8se H0\u00a0: moy(Sepal.Width) = 0.05, la moyenne de cette variable est donc significativement diff\u00e9rente de 0.05.<\/p>\n
Nous comparons la moyenne de la longueur des s\u00e9pales des esp\u00e8ces setosa et versicolor\u00a0:<\/p>\n

#On isole les 100 premi\u00e8res lignes qui correspondent aux donn\u00e9es des esp\u00e8ces Setosa et Versicolor.\n\nt.test(Sepal.Length~Species, data=iris[1:100,])\n\n\u00a0\n\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Welch Two Sample t-test\n\n\u00a0\n\ndata:\u00a0 Sepal.Length by Species\n\nt = -10.521, df = 86.538, p-value < 2.2e-16\n\nalternative hypothesis: true difference in means is not equal to 0\n\n95 percent confidence interval:\n\n\u00a0-1.1057074 -0.7542926\n\nsample estimates:\n\n\u00a0\u00a0\u00a0 mean in group setosa mean in group versicolor\n\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 5.006\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 5.936\n\n<\/code><\/pre>\n
\u00a0 
La probabilit\u00e9 critique est inf\u00e9rieure \u00e0 0.05 (< 2.2e-16). Nous rejetons donc l\u2019hypoth\u00e8se H0\u00a0: moy(Sepal.Width)setosa = moy(Sepal.Width)versicolor. Cela signifie qu\u2019en moyenne, la longueur des s\u00e9pales est significativement diff\u00e9rente d\u2019une esp\u00e8ce \u00e0 l\u2019autre. La longueur des s\u00e9pales d\u00e9pend donc de l\u2019esp\u00e8ce de l\u2019Iris.<\/p>\n","protected":false},"excerpt":{"rendered":"
Le test de Student permet de tester l\u2019\u00e9galit\u00e9 de deux moyennes. L\u2019hypoth\u00e8se H0 est \u00ab\u00a0les moyennes sont \u00e9gales\u00a0\u00bb ou \u00ab\u00a0la moyenne vaut une valeur x\u00a0\u00bb. Pour r\u00e9aliser ce test il est n\u00e9cessaire d\u2019avoir un \u00e9chantillonnage al\u00e9atoire de chaque individu et que les ces deux \u00e9chantillons suivent une loi Normale. Pour tester l\u2019hypoth\u00e8se H0 on utilise la fonction t.test(). data(iris) A<-subset(iris,Species==\u00a0\u00bbsetosa\u00a0\u00bb)[,2] #On isole la 2\u00e8me colonne : la largeur des s\u00e9pales \u00a0 On commence par tester la normalit\u00e9 de cette variable gr\u00e2ce au test de Shapiro\u00a0: shapiro.test(A) \u00a0 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Shapiro-Wilk normality test \u00a0 data:\u00a0 A W = 0.9717, p-value = 0.2715 \u00a0 La p-value est sup\u00e9rieurRead More →<\/a><\/p>\n","protected":false},"author":13,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"content-type":"","rop_custom_images_group":[],"rop_custom_messages_group":[],"rop_publish_now":"initial","rop_publish_now_accounts":{"twitter_399453572_399453572":""},"rop_publish_now_history":[],"rop_publish_now_status":"pending","jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[21],"tags":[],"class_list":{"0":"entry","1":"post","2":"publish","3":"author-helene","4":"post-3169","6":"format-standard","7":"category-test"},"acf":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p9O7Sx-P7","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/thinkr.fr\/abcdr\/wp-json\/wp\/v2\/posts\/3169","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thinkr.fr\/abcdr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thinkr.fr\/abcdr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thinkr.fr\/abcdr\/wp-json\/wp\/v2\/users\/13"}],"replies":[{"embeddable":true,"href":"https:\/\/thinkr.fr\/abcdr\/wp-json\/wp\/v2\/comments?post=3169"}],"version-history":[{"count":2,"href":"https:\/\/thinkr.fr\/abcdr\/wp-json\/wp\/v2\/posts\/3169\/revisions"}],"predecessor-version":[{"id":4289,"href":"https:\/\/thinkr.fr\/abcdr\/wp-json\/wp\/v2\/posts\/3169\/revisions\/4289"}],"wp:attachment":[{"href":"https:\/\/thinkr.fr\/abcdr\/wp-json\/wp\/v2\/media?parent=3169"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thinkr.fr\/abcdr\/wp-json\/wp\/v2\/categories?post=3169"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thinkr.fr\/abcdr\/wp-json\/wp\/v2\/tags?post=3169"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}