{"id":292,"date":"2014-10-04T18:36:57","date_gmt":"2014-10-04T16:36:57","guid":{"rendered":"http:\/\/wordpress.callac.online\/index.php\/intervalle-de-confiance-avec-r\/"},"modified":"2022-01-05T22:41:53","modified_gmt":"2022-01-05T21:41:53","slug":"intervalle-de-confiance-avec-r","status":"publish","type":"page","link":"https:\/\/wordpress.callac.online\/index.php\/logiciels-mathematiques\/le-logiciel-r\/les-tests-avec-r\/intervalle-de-confiance-avec-r\/","title":{"rendered":"Intervalle de confiance avec R"},"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

On dispose d’un \u00e9chantillon<\/h2>\n

Il faut deux conditions :
\n– le caract\u00e8re \u00e9tudi\u00e9 suit une loi normale ;
\n– l’\u00e9chantillon est al\u00e9atoire.<\/p>\n

Pour un \u00e9chantillon donn\u00e9, il n’y a pas de fonction R donnant l’intervalle de confiance au seuil de 95%.<\/p>\n

On doit donc calculer les deux bornes de l’intervalle :<\/p>\n \\left[\\overline{x} -1,96 \\times \\frac{\\sigma}{\\sqrt{n}}~;~\\overline{x} + 1,96 \\times \\frac{\\sigma}{\\sqrt{n}}\\right] <\/span>\n

o\u00f9 $\\overline{x}$ est la moyenne et $\\sigma$ l’\u00e9cart-type de l’\u00e9chantillon de taille $n$.<\/p>\n

Prenons l’exemple des \u00e2ges.<\/p>\n

library(prettyR)\ndescribe(satis$age)<\/pre>\n

\nNumeric
\nmean    median       var        sd   valid.n
\nx            58.21        60     317.2     17.81       528
\n<\/code><\/p>\n
58.21-1.96*17.81\/sqrt(528)<\/pre>\n

\n[1] 56.69084
\n<\/code><\/p>\n
58.21+1.96*17.81\/sqrt(528)<\/pre>\n

\n[1] 59.72916
\n<\/code><\/p>\n
On utilise la loi binomiale<\/h2>\n
La librairie binom<\/em> propose une dizaine de m\u00e9thode pour calculer l’intervalle de confiance au seuil de 95% gr\u00e2ce \u00e0 la fonction binom.confint<\/em>. On pourra choisir la m\u00e9thode \u00ab\u00a0exact\u00a0\u00bb.<\/p>\n
Prenons comme exemple les 269 personnes sur les 405 qui recommandent l’h\u00f4pital.<\/p>\n
library(binom)\nbinom.confint(269,405,method=\"exact\")<\/pre>\n

\nmethod   x   n      mean     lower     upper
\n1  exact 269 405 0.6641975 0.6158948 0.7100798
\n<\/code><\/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":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-292","page","type-page","status-publish","hentry"],"yoast_head":"\nIntervalle de confiance avec R - 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\/intervalle-de-confiance-avec-r\/\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Intervalle de confiance avec R - 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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