{"id":6804,"date":"2025-07-15T13:34:48","date_gmt":"2025-07-15T13:34:48","guid":{"rendered":"https:\/\/functiontranslator.com\/loi-student-n\/"},"modified":"2021-02-26T08:15:00","modified_gmt":"2021-02-26T08:15:00","slug":"t-dist","status":"publish","type":"post","link":"https:\/\/functiontranslator.com\/fr\/t-dist\/","title":{"rendered":"LOI.STUDENT.N"},"content":{"rendered":"

Description de la fonction LOI.STUDENT.N<\/h2>\n

La fonction LOI.STUDENT.N dans MS Excel et Google Sheets est utilis\u00e9e pour calculer la distribution de Student pour un ensemble sp\u00e9cifique de valeurs. Elle est couramment employ\u00e9e en statistique pour \u00e9valuer les probabilit\u00e9s relatives \u00e0 une variable suivant une distribution t, bas\u00e9e sur un \u00e9chantillon al\u00e9atoire.<\/p>\n

Syntaxe et exemples<\/h2>\n

Voici la syntaxe de la fonction LOI.STUDENT.N sous Excel :<\/p>\n

LOI.STUDENT.N(x, degr\u00e9s_de_libert\u00e9, cumulatif)<\/code><\/pre>\n
    \n
  • x<\/strong> : La valeur \u00e0 \u00e9valuer par la fonction.<\/li>\n
  • degr\u00e9s_de_libert\u00e9<\/strong> : Le nombre de degr\u00e9s de libert\u00e9 de la distribution.<\/li>\n
  • cumulatif<\/strong> : Un bool\u00e9en qui sp\u00e9cifie le type de fonction. TRUE pour la distribution cumulative, FALSE pour la densit\u00e9 de probabilit\u00e9.<\/li>\n<\/ul>\n
    Exemple :<\/p>\n\n\n\n
    Formule<\/th>\nValeur<\/th>\nDescription<\/th>\n<\/tr>\n
    =LOI.STUDENT.N(1.96, 10, VRAI)<\/code><\/td>\n0.966903<\/td>\nCalcule la probabilit\u00e9 cumul\u00e9e P(X<=1.96) avec un \u00e9chantillon de 10 degr\u00e9s de libert\u00e9.<\/td>\n<\/tr>\n<\/table>\n
    Applications pratiques<\/h2>\n
    La fonction LOI.STUDENT.N est essentielle dans des domaines tels que la statistique et l’\u00e9conom\u00e9trie pour effectuer des pr\u00e9dictions ou tester des hypoth\u00e8ses sur des \u00e9chantillons.<\/p>\n
    Exemple d’application : Test d’hypoth\u00e8se<\/h2>\n
    Imaginez un chercheur analysant l’efficacit\u00e9 d’un nouveau m\u00e9dicament sur un \u00e9chantillon de 15 patients, avec une am\u00e9lioration moyenne observ\u00e9e de 20 et un \u00e9cart-type de 5. Le chercheur souhaite tester l’hypoth\u00e8se selon laquelle l’am\u00e9lioration moyenne diff\u00e8re de 15 (am\u00e9lioration moyenne sous placebo).<\/p>\n
    # \u00c9tape 1 : Calculez la statistique t t = (Moyenne_\u00e9chantillon - Moyenne_null) \/ (\u00c9cart_type \/ SQRT(N)) = (20 - 15) \/ (5 \/ SQRT(15)) = 3.873 # \u00c9tape 2 : Utilisez LOI.STUDENT.N pour trouver la p-valeur (\u00e0 deux queues) p-valeur = (1 - LOI.STUDENT.N(ABS(3.873), 14, VRAI)) * 2 = (1 - 0.9985) * 2 = 0.003 <\/code><\/pre>\n
    Cette p-valeur tr\u00e8s faible nous am\u00e8ne \u00e0 rejeter l’hypoth\u00e8se nulle, sugg\u00e9rant que le m\u00e9dicament a un impact significatif compar\u00e9 au placebo.<\/p>\n
    Exemple d’application : Intervalles de confiance<\/h2>\n
    Dans le cas d’une \u00e9tude sur les performances scolaires, supposons un \u00e9chantillon de 25 notes avec une moyenne de 68 et un \u00e9cart-type de 10. Pour \u00e9tablir un intervalle de confiance de 95% pour cette moyenne :<\/p>\n
    # \u00c9tape 1 : Trouvez la valeur critique t t_critique = 2.064 # valeur \u00e0 95% pour 24 degr\u00e9s de libert\u00e9 # \u00c9tape 2 : Calculez l'intervalle de confiance IC_inf = Moyenne - t_critique * (\u00c9cart_type \/ SQRT(N)) = 68 - 2.064 * (10 \/ SQRT(25)) = 61.68 IC_sup = Moyenne + t_critique * (\u00c9cart_type \/ SQRT(N)) = 68 + 2.064 * (10 \/ SQRT(25)) = 74.32 <\/code><\/pre>\n
    Cet intervalle nous donne une confiance de 95% que la v\u00e9ritable moyenne des notes se situe entre 61.68 et 74.32.<\/p>\n","protected":false},"excerpt":{"rendered":"
    Renvoie la pRobabilit\u00e9 d\u2019une vaRiable al\u00e9atoiRe suivant la loi T de Student<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[315],"tags":[],"class_list":["post-6804","post","type-post","status-publish","format-standard","hentry","category-statistiques"],"acf":[],"yoast_head":"\nFonction T.DIST (LOI.STUDENT.N) dans Excel : comment \u00e7a marche, exemples et syntaxe<\/title>\n<meta name=\"description\" content=\"Pr\u00e9sentation de la fonction T.DIST (LOI.STUDENT.N) d\u2019Excel et Google Sheets. 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