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Puissance Et Taille D'échantillon

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Basic principles of power calculation and sample size estimation

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  • DOWNLOAD THIS BOOKS INTO AVAILABLE FORMAT (2019 Update) ......................................................................................................................... ......................................................................................................................... Download Full PDF EBOOK here { https://soo.gd/irt2 } ......................................................................................................................... Download Full EPUB Ebook here { https://soo.gd/irt2 } ......................................................................................................................... Download Full doc Ebook here { https://soo.gd/irt2 } ......................................................................................................................... Download PDF EBOOK here { https://soo.gd/irt2 } ......................................................................................................................... Download EPUB Ebook here { https://soo.gd/irt2 } ......................................................................................................................... Download doc Ebook here { https://soo.gd/irt2 } ......................................................................................................................... ......................................................................................................................... ................................................................................................................................... eBook is an electronic version of a traditional print book THIS can be read by using a personal computer or by using an eBook reader. (An eBook reader can be a software application for use on a computer such as Microsoft's free Reader application, or a book-sized computer THIS is used solely as a reading device such as Nuvomedia's Rocket eBook.) Users can purchase an eBook on diskette or CD, but the most popular method of getting an eBook is to purchase a downloadable file of the eBook (or other reading material) from a Web site (such as Barnes and Noble) to be read from the user's computer or reading device. Generally, an eBook can be downloaded in five minutes or less ......................................................................................................................... .............. Browse by Genre Available eBooks .............................................................................................................................. Art, Biography, Business, Chick Lit, Children's, Christian, Classics, Comics, Contemporary, Cookbooks, Manga, Memoir, Music, Mystery, Non Fiction, Paranormal, Philosophy, Poetry, Psychology, Religion, Romance, Science, Science Fiction, Self Help, Suspense, Spirituality, Sports, Thriller, Travel, Young Adult, Crime, Ebooks, Fantasy, Fiction, Graphic Novels, Historical Fiction, History, Horror, Humor And Comedy, ......................................................................................................................... ......................................................................................................................... .....BEST SELLER FOR EBOOK RECOMMEND............................................................. ......................................................................................................................... Blowout: Corrupted Democracy, Rogue State Russia, and the Richest, Most Destructive Industry on Earth,-- The Ride of a Lifetime: Lessons Learned from 15 Years as CEO of the Walt Disney Company,-- Call Sign Chaos: Learning to Lead,-- StrengthsFinder 2.0,-- Stillness Is the Key,-- She Said: Breaking the Sexual Harassment Story THIS Helped Ignite a Movement,-- Atomic Habits: An Easy & Proven Way to Build Good Habits & Break Bad Ones,-- Everything Is Figureoutable,-- What It Takes: Lessons in the Pursuit of Excellence,-- Rich Dad Poor Dad: What the Rich Teach Their Kids About Money THIS the Poor and Middle Class Do Not!,-- The Total Money Makeover: Classic Edition: A Proven Plan for Financial Fitness,-- Shut Up and Listen!: Hard Business Truths THIS Will Help You Succeed, ......................................................................................................................... .........................................................................................................................
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  • DOWNLOAD THAT BOOKS INTO AVAILABLE FORMAT (2019 Update) ......................................................................................................................... ......................................................................................................................... Download Full PDF EBOOK here { http://bit.ly/2m6jJ5M } ......................................................................................................................... Download Full EPUB Ebook here { http://bit.ly/2m6jJ5M } ......................................................................................................................... Download Full doc Ebook here { http://bit.ly/2m6jJ5M } ......................................................................................................................... Download PDF EBOOK here { http://bit.ly/2m6jJ5M } ......................................................................................................................... Download EPUB Ebook here { http://bit.ly/2m6jJ5M } ......................................................................................................................... Download doc Ebook here { http://bit.ly/2m6jJ5M } ......................................................................................................................... ......................................................................................................................... ................................................................................................................................... eBook is an electronic version of a traditional print book that can be read by using a personal computer or by using an eBook reader. (An eBook reader can be a software application for use on a computer such as Microsoft's free Reader application, or a book-sized computer that is used solely as a reading device such as Nuvomedia's Rocket eBook.) Users can purchase an eBook on diskette or CD, but the most popular method of getting an eBook is to purchase a downloadable file of the eBook (or other reading material) from a Web site (such as Barnes and Noble) to be read from the user's computer or reading device. Generally, an eBook can be downloaded in five minutes or less ......................................................................................................................... .............. Browse by Genre Available eBooks .............................................................................................................................. Art, Biography, Business, Chick Lit, Children's, Christian, Classics, Comics, Contemporary, Cookbooks, Manga, Memoir, Music, Mystery, Non Fiction, Paranormal, Philosophy, Poetry, Psychology, Religion, Romance, Science, Science Fiction, Self Help, Suspense, Spirituality, Sports, Thriller, Travel, Young Adult, Crime, Ebooks, Fantasy, Fiction, Graphic Novels, Historical Fiction, History, Horror, Humor And Comedy, ......................................................................................................................... ......................................................................................................................... .....BEST SELLER FOR EBOOK RECOMMEND............................................................. ......................................................................................................................... Blowout: Corrupted Democracy, Rogue State Russia, and the Richest, Most Destructive Industry on Earth,-- The Ride of a Lifetime: Lessons Learned from 15 Years as CEO of the Walt Disney Company,-- Call Sign Chaos: Learning to Lead,-- StrengthsFinder 2.0,-- Stillness Is the Key,-- She Said: Breaking the Sexual Harassment Story That Helped Ignite a Movement,-- Atomic Habits: An Easy & Proven Way to Build Good Habits & Break Bad Ones,-- Everything Is Figureoutable,-- What It Takes: Lessons in the Pursuit of Excellence,-- Rich Dad Poor Dad: What the Rich Teach Their Kids About Money That the Poor and Middle Class Do Not!,-- The Total Money Makeover: Classic Edition: A Proven Plan for Financial Fitness,-- Shut Up and Listen!: Hard Business Truths that Will Help You Succeed, ......................................................................................................................... .........................................................................................................................
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  • DOWNLOAD THAT BOOKS INTO AVAILABLE FORMAT (2019 Update) ......................................................................................................................... ......................................................................................................................... Download Full PDF EBOOK here { http://bit.ly/2m6jJ5M } ......................................................................................................................... Download Full EPUB Ebook here { http://bit.ly/2m6jJ5M } ......................................................................................................................... Download Full doc Ebook here { http://bit.ly/2m6jJ5M } ......................................................................................................................... Download PDF EBOOK here { http://bit.ly/2m6jJ5M } ......................................................................................................................... Download EPUB Ebook here { http://bit.ly/2m6jJ5M } ......................................................................................................................... Download doc Ebook here { http://bit.ly/2m6jJ5M } ......................................................................................................................... ......................................................................................................................... ................................................................................................................................... eBook is an electronic version of a traditional print book that can be read by using a personal computer or by using an eBook reader. (An eBook reader can be a software application for use on a computer such as Microsoft's free Reader application, or a book-sized computer that is used solely as a reading device such as Nuvomedia's Rocket eBook.) Users can purchase an eBook on diskette or CD, but the most popular method of getting an eBook is to purchase a downloadable file of the eBook (or other reading material) from a Web site (such as Barnes and Noble) to be read from the user's computer or reading device. Generally, an eBook can be downloaded in five minutes or less ......................................................................................................................... .............. Browse by Genre Available eBooks .............................................................................................................................. Art, Biography, Business, Chick Lit, Children's, Christian, Classics, Comics, Contemporary, Cookbooks, Manga, Memoir, Music, Mystery, Non Fiction, Paranormal, Philosophy, Poetry, Psychology, Religion, Romance, Science, Science Fiction, Self Help, Suspense, Spirituality, Sports, Thriller, Travel, Young Adult, Crime, Ebooks, Fantasy, Fiction, Graphic Novels, Historical Fiction, History, Horror, Humor And Comedy, ......................................................................................................................... ......................................................................................................................... .....BEST SELLER FOR EBOOK RECOMMEND............................................................. ......................................................................................................................... Blowout: Corrupted Democracy, Rogue State Russia, and the Richest, Most Destructive Industry on Earth,-- The Ride of a Lifetime: Lessons Learned from 15 Years as CEO of the Walt Disney Company,-- Call Sign Chaos: Learning to Lead,-- StrengthsFinder 2.0,-- Stillness Is the Key,-- She Said: Breaking the Sexual Harassment Story That Helped Ignite a Movement,-- Atomic Habits: An Easy & Proven Way to Build Good Habits & Break Bad Ones,-- Everything Is Figureoutable,-- What It Takes: Lessons in the Pursuit of Excellence,-- Rich Dad Poor Dad: What the Rich Teach Their Kids About Money That the Poor and Middle Class Do Not!,-- The Total Money Makeover: Classic Edition: A Proven Plan for Financial Fitness,-- Shut Up and Listen!: Hard Business Truths that Will Help You Succeed, ......................................................................................................................... .........................................................................................................................
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Puissance Et Taille D'échantillon

  1. 1. J’ai besoin de combien de monde ? Une question de puissance
  2. 2. Plan Notions de bases sur la puissance Taille d’échantillon pour le test Z: un exemple Conseils pour la planification d’expériences (plus) complexes
  3. 3. Avertissement La mathématique est l’art de donner le même nom à des choses différentes. -- Jules Henri Poincaré (1854-1912) [Mathématicien français]
  4. 4. Notions de base sur la puissance Le dilemme du juge: Le juge est confronté à 4 situations dans chaque cas Déclarer l’accusé coupable alors qu’il est coupable Déclarer l’accusé innocent alors qu’il est innocent Déclarer l’accusé coupable alors qu’il est innocent Déclarer l’accusé innocent alors qu’il est coupable
  5. 5. Notions de base sur la puissance H0 vraie H0 fausse Accepter H0 Pas Erreur de d’erreur type II Rejeter H0 Erreur de Pas type I d’erreur
  6. 6. Erreur de Type I Seuil du test ( ) P(Rejeter H0 | H0 vraie) On veut contrôler cette erreur le plus strictement possible, alors on la fixe à l’avance (0.1, 0.05, 0.01, etc.)
  7. 7. Erreur de Type II P(Accepter H0 | H0 fausse) On n’est pas si inquiet lorsque vient le temps de contrôler ce type d’erreur.
  8. 8. Puissance 1- P(Rejeter H0 | H0 fausse) C’est habituellement avec la puissance qu’on contrôle la probabilité d’erreur de type II
  9. 9. Taille d’échantillon pour le test Z Mise en situation: On veut vérifier si une moyenne ( ) est égale à une certaine valeur (x) sachant que l’écart- type de la population est On a donc les hypothèses suivante: H0: =x H1: x
  10. 10. Taille d’échantillon pour le test Z Mise en situation: On tire un échantillon de taille N et on calcul la moyenne de l’échantillon On obtient la statistique de test et sa distribution sous H0 X x ~ N (0,1) N
  11. 11. Taille d’échantillon pour le test Z On fait le test au seuil de 5%, ce qui veut dire: P(Rejeter H0 | H0 vraie) = 0.05 X x P >z 2 μ = x = 0.05 N
  12. 12. Taille d’échantillon pour le test Z On fait le test au seuil de 5%, ce qui veut dire: P(Rejeter H0 | H0 vraie) = 0.05 X x P > 1.96 μ = x = 0.05 N
  13. 13. Taille d’échantillon pour le test Z Calculons la puissance: P(Rejeter H0 | H0 fausse) Que veut dire « H0 fausse » ? x Que vaut ? On doit fixer la différence minimale détectable: x: =x+ X x ~ N ( ,1) N
  14. 14. Taille d’échantillon pour le test Z Calculons la puissance: P(Rejeter H0 | H0 fausse) X x P > 1.96 μ = x + N
  15. 15. Taille d’échantillon pour le test Z Calculons la puissance: P(Rejeter H0 | H0 fausse) X x P 1.96 > > 1.96 μ = x + N
  16. 16. Taille d’échantillon pour le test Z Calculons la puissance: P(Rejeter H0 | H0 fausse) P x 1.96 > X > x + 1.96 μ = x + N N
  17. 17. Taille d’échantillon pour le test Z Calculons la puissance: P(Rejeter H0 | H0 fausse) P 1.96 > X (x + ) > + 1.96 N N
  18. 18. Taille d’échantillon pour le test Z Calculons la puissance: P(Rejeter H0 | H0 fausse) 1.96 + 1.96 P N > X (x + ) > N N N N
  19. 19. Taille d’échantillon pour le test Z Calculons la puissance: P(Rejeter H0 | H0 fausse) P 1.96 N > X (x + ) > 1.96 N N
  20. 20. Taille d’échantillon pour le test Z Calculons la puissance: P(Rejeter H0 | H0 fausse) P X (x + ) > 1.96 N N
  21. 21. Taille d’échantillon pour le test Z Pour calculer la puissance, il faut connaître: N, et Autrement, pour calculer la taille d’échantillon, il faudrait connaître: , et la puissance
  22. 22. Taille d’échantillon pour le test Z Calculons la taille d’échantillon approximative: Fixons la puissance à 80% P X (x + ) > 1.96 N = 0.8 N
  23. 23. Taille d’échantillon pour le test Z Calculons la taille d’échantillon approximative: Fixons la puissance à 80% P X (x + ) > 1.96 N = 0.8 Si > 0 N P X (x + ) < 1.96 N = 0.8 Si <0 N
  24. 24. Taille d’échantillon pour le test Z On sait aussi que: P X (x + ) > 0.84 = 0.8 N
  25. 25. Taille d’échantillon pour le test Z On a donc: N 1.96 = 0.84
  26. 26. Taille d’échantillon pour le test Z On a donc: N 1.96 + 0.84 =
  27. 27. Taille d’échantillon pour le test Z On a donc: (1.96 + 0.84) = N
  28. 28. Taille d’échantillon pour le test Z On a donc: On arrondie toujours à l’entier supérieur 2 (1.96 + 0.84 ) =N
  29. 29. Étapes pour déterminer la taille d’échantillon Spécifier le test d’hypothèse Spécifier le seuil du test Spécifier l’effet détectable Spécifier des estimés pour les co- paramètres (e.g. l’écart-type) Spécifier la puissance du test pour l’effet détectable
  30. 30. Conseils pour des expériences plus complexes Spécifier le test d’hypothèse Choisir le paramètre qui est le plus important en fonction de la question de recherche Toujours faire un test bilatéral, à moins d’avoir une très bonne raison d’effectuer un test unilatéral
  31. 31. Étapes pour déterminer la taille d’échantillon Spécifier le seuil du test Le seuil peut être fixé comme on veut 10% si on peut être plus libéral quand on déclare la présence d’un effet 5% si on veut faire comme tout le monde 1% si on veut être plus conservateur ou plus certain de la présence d’un effet Plus le seuil est faible, plus la taille d’échantillon augmente
  32. 32. Étapes pour déterminer la taille d’échantillon Spécifier l’effet détectable On peut spécifier l’effet détectable par intervalle: L’effet espéré offre habituellement une borne supérieure On peut ensuite déterminer une borne inférieure en suggérant l’effet cliniquement significatif minimal On peut calculer la taille d’échantillon pour plusieurs propositions d’effet Plus l’effet est grand, plus la taille d’échantillon est petite
  33. 33. Étapes pour déterminer la taille d’échantillon Spécifier des estimés pour les co- paramètres (e.g. l’écart-type) On peut utiliser des valeurs historiques (obtenu dans d’autres études similaires) On peut élaborer une étude pilote pour estimer ces paramètres On peut essayer différentes valeurs pour un même paramètre (mais ça entraîne une plus grande incertitude sur la taille d’échantillon obtenue)
  34. 34. Étapes pour déterminer la taille d’échantillon Spécifier la puissance du test pour l’effet détectable Encore une fois, on peut la spécifier à notre goût 80% pour faire comme tout le monde 90% pour être plus conservateur parfois une faible augmentation dans la taille d’échantillon permet d’obtenir une grande augmentation dans la puissance Plus la puissance est élevée, plus la taille d’échantillon sera grande
  35. 35. Conseils pour les expériences complexes Simplifier au maximum les questions de recherche Calculer des tailles approximatives pour des tests plus simples Calculer des tailles pour plusieurs scénarios différents et choisir la taille la plus grande possible Aller voir un statisticien

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