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[null,null,null,null,null,null,"Objectif du labo Excel 3"]
[]
[null,null,null,null,null,null,"Utiliser Excel pour comparer deux moyennes à l'aide du test t de Student (signification statistique d'une différence) et de la mesure d'association Êta-carré (signification réelle d'une différence)"]

{"sheet":"Test t (démo)","index":1,"n_rows":106,"n_cols":12,"rows_kept":106,"cut":false,"hidden":false,"merged":[[105,1,106,11],[45,8,45,10],[46,8,46,11],[97,1,97,11],[71,1,71,5],[46,1,46,5],[49,1,49,5],[52,1,52,5],[52,7,52,11],[57,1,57,5],[69,1,69,11],[91,1,91,11],[93,1,93,11],[95,1,95,11],[59,7,59,11],[60,8,60,9],[61,8,61,10],[63,2,63,3],[65,1,65,11],[1,1,1,11],[3,1,3,11],[31,1,31,2],[31,4,31,5],[44,1,44,5],[44,7,44,11],[7,1,7,2],[7,3,7,4],[5,5,5,6],[5,3,6,4],[8,3,8,4],[9,3,9,4],[50,1,50,2]]}
[]
[null,"Test t de la différence entre deux moyennes - Démonstration"]
[]
[null,"Question de recherche: Y a-t-il une relation entre le sexe et le temps passé devant la télévision? (Fox, p.214)"]
[]
[null,null,null,"Temps passé devant la TV",null,"Sexe"]
[null,null,null,null,null,"Hommes","Femmes"]
[null,null,null,"Moyennes (heures)",null,2.75,3.01]
[null,null,null,"Écart-type",null,2.0299999999999998,2.23]
[null,null,null,"Nombres de cas (n)",null,855,1085]
[]
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[]
[]
[]
[]
[]
[]
[]
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[]
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[]
[]
[]
[]
[]
[null,null,null,"Sexe"]
[null,"Hommes (catégorie 1)",null,null,"Femmes (catégorie 2)"]
[null,"X1=",2.75,null,"X2=",3.01]
[null,"n1 =",855,null,"n2 =",1085]
[null,"s1 =",2.0299999999999998,null,"s2 =",2.2250000000000001]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"1. Formulons les hypothèses statistiques",null,null,null,null,null,"4. Calculons sw2, la variance combinée des deux échantillons"]
[null,null,null,null,null,null,null,"sw2 =","(Sx12 + Sx22) / dl"]
[null,"Hypothèse nulle: il n’y a pas de différence dans le nombre d’heures passées devant la TV chez les hommes et les femmes \n",null,null,null,null,null,"= ","(3523+5371)/1938"]
[null,"H0 : m1 = m2  ou de façon équivalente H0 : m1 - m2 = 0 ",null,null,null,null,null,"= ",{"$f":"(C56+F56) / (C62+F62)","v":4.5896788570691429}]
[]
[null,"Hypothèse alternative bilatérale: il y a une différence dans le nombre d’heures passées devant la TV chez les hommes et les femmes "]
[null,"Ha : m1 ¹ m2 "]
[]
[null,"2. Multiplions chaque variance par la taille de l'échantillon (variance pondérée)",null,null,null,null,null,"5. Calculons l'erreur type de la différence des moyennes sx1-x2"]
[null,"Sx12 =","s12 * n1",null,"Sx22 =","s22 * n2",null,"sx1-x22 =","sw2 * (1 / n1 + 1 / n2)"]
[null,null,"(2,03)2 * 855",null,null,"(2,225)2 * 1085",null,"= ",{"$f":"I48&\" *  (1/\"&C34&\" + 1/\"&F34&\")\"","v":"4.58967885706914 *  (1/855 + 1/1085)"}]
[null,null,{"$f":"C35*C35*C34","v":3523.3694999999989},null,null,{"$f":"F35*F35*F34","v":5371.4281250000004},null,"= ",{"$f":"I48 *  (C34 + F34)/(C34*F34)","v":9.5981642091402027E-3}]
[null,null,null,null,null,null,null,"sx1-x2 =",{"$f":"I56^0.5","v":9.7970221032414762E-2},{"$f":"\"    * (racine carrée de \"&FIXED(I56,4)&\")\"","v":"    * (racine carrée de 0.0096)"}]
[null,"3. Calculons le nombre de degrés de libertés"]
[null,null,null,"dl =","n1 + n2 - 2"]
[null,"dl1 =","n1-1",null,"dl2 =","n2-1",null,"6. Calculons la valeur du t "]
[null,"=",{"$f":"C34 &\" - 1\"","v":"855 - 1"},null,"=",{"$f":"F34 &\" - 1\"","v":"1085 - 1"},null,"t = ","(X1 - X2) / sx1-x2 "]
[null,"=",{"$f":"C34-1","v":854},null,"=",{"$f":"F34-1","v":1084},null,"= ","(2,75-3,01)/0,098"]
[null,null,null,null,null,null,null,"= ",{"$f":"(C33 - F33) / I57","v":-2.6538676473331146}]
[null,null,"dl = (dl1 + dl2) = ",null,{"$f":"C62+F62","v":1938},null,null,"abs(t) =",{"$f":"ABS(I63)","v":2.6538676473331146}]
[]
[null,"7. Choisissons un seuil de signification et trouvons la valeur critique en prenant en compte les degrés de liberté déjà calculés"]
[]
[null,null,"degrés de libertés (dl1 + dl2)",{"$f":"E64","v":1938},null,null,"a =",0.05,null,null,"valeur critique : ",1.96]
[]
[null,"8. Énonçons la règle de décision et représentons graphiquement la décision à l'aide de la distribution d'échantillonnage du t"]
[]
[null,"Rejet de H0 si tcalculé > tcritique "]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"9. Prenons une décision quant au rejet ou non de l'hypothèse nulle et concluons"]
[]
[null,"La valeur absolue du t calculé (2,65) étant supérieure à la valeur critique (1,96), nous rejetons l'hypothèse nulle, à l'effet qu'il n'y a pas de différence entre les deux groupes. Autrement dit, l'écart symbolisé par la valeur 2,65 est suffisamment significatif pour qu'on accepte plutôt l'hypothèse alternative."]
[]
[null,"On peut conclure à l'existence d'une relation entre le sexe et le temps passé devant la TV  dans la population de laquelle est tiré l'échantillon. Plus précisément, il y a une différence entre les hommes et les femmes quant au nombre d'heures quotidiennes utilisées pour regarder la TV. On est sûr au moins à 95% que cette différence est statistiquement significative."]
[]
[null,"Ëta-carré et taille de l'effet- Démonstration"]
[]
[]
[]
[null,null,"2,65*2,65/(2,65*2,65)+1938"]
[]
[null,null,{"$f":"(2.65*2.65)/((2.65*2.65)+1938)","v":3.6104980790710645E-3}]
[]
[null,"Interprétation: D'après la règle de Cohen (1988) ci-dessous, la valeur de l'êta-carré indique la présence d'effet de petite taille du sexe sur le nombre d'heures passées devant la TV. Autrement dit, la différence entre les hommes et les femmes quant au nombre d'heures passées devant la TV est faible."]

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[]
[null,"Test t de la différence entre deux moyennes - Exercice"]
[]
[null,"Question de recherche: Y a-t-il une relation entre le groupe d'appartenance et le quotient intellectuel (QI)?"]
[]
[null,null,null,"Groupe",null,null,null,"0. Sortons le diagramme des moyennes"]
[null,"Groupe 1",null,null,"Groupe 2"]
[null,"X1=",108.1,null,"X2=",98.4]
[null,"n1 =",100,null,"n2 =",100]
[null,"s12 =",289,null,"s22 =",196]
[]
[null,"Temps passé devant la TV",null,"Sexe"]
[null,null,null,"Groupe 1","Groupe 2"]
[null,"Moyennes (heures)",null,108.1,98.4]
[null,"Écart-type",null,{"$f":"SQRT(C10)","v":17},{"$f":"SQRT(F10)","v":14}]
[null,"Nombres de cas (n)",null,100,100]
[]
[null,"Différence entre les deux moyennes observées: "]
[]
[null,"1. Formulons les hypothèses statistiques",null,null,null,null,null,"4. Calculer sw2, la variance combinée des deux échantillons"]
[null,"Hypothèse nulle",null,"H0 : m1 = m2  ou  H0 : m1 - m2 = 0 ",null,null,null,"sw2 =","(Sx12 + Sx22) / dl"]
[null,null,null,null,null,null,null,"= "]
[null,null,null,null,null,null,null,"= "]
[]
[null,"Hypothèse alternative bilatérale",null,null,"Ha : m1 ¹ m2 "]
[]
[]
[null,"2. Multiplier chaque variance par la taille de l'échantillon (pondérée)",null,null,null,null,null,"5. Calculer l'erreur type de la différence des moyennes sx1-x2"]
[null,"Sx12 =","s12 * n1",null,"Sx22 =","s22 * n2",null,"sx1-x22 =","sw2 * (1 / n1 + 1 / n2)"]
[]
[null,null,null,null,null,null,null,"sx1-x22 ="]
[]
[null,"3. Calculer le nombre de degrés de libertés",null,null,null,null,null,"sx1-x2 =",null,"Racine carrée"]
[null,null,null,"dl =","n1 + n2 - 2"]
[null,"dl1 =","n1-1",null,"dl2 =","n2-1",null,"6. Calculer la valeur du t "]
[null,"=",null,null,"=",null,null,"t = ","(X1 - X2) / sx1-x2 "]
[]
[null,null,"dl = (dl1 + dl2) = ",null,null,null,null,"abs(t) ="]
[]
[null,"7. Choisissons un seuil de signification 0,05 et trouver la valeur critique en prenant en compte les degrés de liberté déjà calculés"]
[]
[null,null,"degrés de libertés ",null,null,null,"a =",0.05,null,null,"valeur critique : "]
[]
[null,"8. Énonçons la règle de décision et représenter graphiquement la décision à l'aide la distribution d'échantillonnage du t"]
[]
[null,"Rejet de H0 si tcalculé > tcritique "]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"9. Prendre une décision quant au rejet ou non de l'hypothèse nulle et conclure"]
[]
[]
[]
[]
[]
[]
[null,"Calculer la taille de l'effet du groupe sur le QI, si nécessaire"]
[]
[]
[null,null,null,"       t 2 ="]

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[]
[null,"Test t bilatéral et unilatéral (Décision)"]
[]
[null,"En vous basant sur la table statistique, trouvez la valeur critique du t et comparer-la à la valeur calculée pour prendre une décision d'acceptation (A) ou de rejet (R) de l'hypothèse nulle, selon la nature du test."]
[]
[null,"Test ","tcalculé ","Seuil de signification","Dl",null,"tcritique  ?","Décision A ou R de H0?"]
[null,"Bilatéral",2.4,0.05,null,5]
[null,"Unilatéral ",2.4,0.05,null,5]
[]
[null,"Que constatez-vous à propos de la différence entre un test bilatéral et un test unilatéral?"]
[]
[]
[]
[]
[]
[null,"           Test bilatéral",null,null,null,null,"                    Test unilatéral"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"H0 : m1 = m2  ou de façon équivalente H0 : m1 - m2 = 0 ",null,null,null,"H0 : m1 = m2"]
[]
[null,"Ha : m1 ¹ m2 ",null,null,null,"Ha : m1 > m2 "]

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[]
[null,"Test t de la différence entre deux moyennes (utilitaire d'analyse)"]
[]
[null,"Question de recherche: Y a-t-il une relation entre l'absentéisme des étudiants et la performance à l'examen?"]
[]
[]
[null,null,"Absentéisme",null,null,null,"Test d'égalité des espérances: deux observations de variances égales"]
[null,"Réguliers",null,"Irréguliers"]
[null,89,null,70,null,null,null,"Réguliers","Irréguliers"]
[null,97,null,64,null,null,"Moyenne",86.3,72.7]
[null,98,null,95,null,null,"Variance",159.78888888888955,156.23333333333318]
[null,79,null,67,null,null,"Observations",10,10]
[null,95,null,59,null,null,"Variance pondérée",158.01111111111135]
[null,68,null,89,null,null,"Différence hypothétique des moyennes",0]
[null,97,null,79,null,null,"Degré de liberté",18]
[null,65,null,80,null,null,"Statistique t",2.419246364254461]
[null,79,null,59]
[null,96,null,65,null,null,"Valeur critique de t (unilatéral)",1.7340636066175394]
[]
[null,null,null,null,null,null,"Valeur critique de t (bilatéral)",2.1009220402410378]
[]
[null,"1. Analysez brièvement la différence entre les moyennes"]
[]
[]
[]
[null,"2. Formulez les hypothèse nulle et alternative pour un test bilatéral"]
[]
[null,"H0 :","m1 = m2 "]
[]
[null,"Ha :","m1 ¹ m2 "]
[]
[null,"3. Prenez une décision au seuil de signification 0,05 et concluez"]
[]
[null,"a. Prenez une décision quant au rejet ou non de l'hypothèse nulle"]
[]
[null,"En comparant les valeurs du t calculé et du t critique"]
[]
[]
[]
[null,"En comparant les valeurs de la probabilité calculée et du seuil de signification critique 0,05"]
[]
[]
[]
[null,"b. Concluez sur la signification statistique de la relation étudiée"]
[]
[]
[]
[null,"c. Voici la représentation graphique de la décision pour le test bilatéral"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"4. Quelle est la signification réelle de la relation entre l'absentéisme et la performance?"]
[]
[null,null,null,null,null,"Interprétez la valeur de l'êta-carré en termes d'effet de taille"]
[]
[]
[null,"Eta-carré ",null,null,"Calcul"]
[null,null,null,null,"Résultat"]

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[]
[null,"Test t de la différence entre deux moyennes (exercice complémentaire)"]
[]
[null,"Comparativement aux gars, les filles passent-elles plus de temps sur Internet chez les étudiants de L2 sociologie?"]
[]
[null,null,"Sexe",null,null,null,"1. Sortez le test d'égalité des espérances (utilitaire d'analyse)"]
[null,null,"Filles","Gars"]
[null,null,4,8]
[null,null,4,3]
[null,null,6,4]
[null,null,8,5]
[null,null,18,5]
[null,null,8,4]
[null,null,18,3]
[null,null,24,2]
[null,null,17,4]
[null,"Temps sur",6,6]
[null,"Internet/jour",19,6]
[null,null,3,5]
[null,null,8,4]
[null,null,3,10]
[null,null,6,5]
[null,null,5,2]
[null,null,7,3]
[null,null,8,1]
[null,null,0,4]
[null,null,20,2]
[]
[null,"Source: Sondage auprès des étudiants de sociologie L2 (2021)"]
[]
[null,"2. Analysez brièvement la différence entre les moyennes"]
[]
[]
[]
[null,"3. Formulez les hypothèses statistiques pour un test unilatéral"]
[]
[null,"H0 :","m1 = m2 "]
[]
[null,"Ha :","m1  > m2 "]
[]
[null,"4. Prenez une décision au seuil de signification 0,05, concluez et représentez graphiquement la décison"]
[]
[null,"b. Prenez une décision quant au rejet ou non de l'hypothèse nulle"]
[]
[null,"En comparant les valeurs du t calculé et du t critique"]
[]
[]
[]
[null,"En comparant les valeurs du seuil de signification calculé et du seuil de signification critique 0,05"]
[]
[]
[]
[null,"c. Concluez sur la signification statistique de la relation étudiée"]
[]
[]
[]
[null,"d. Représentez graphiquement la décision pour un test unilatéral"]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[null,"5. Quelle est la signification réelle de la relation entre le sexe et le revenu annuel chez les Canadiens?"]
[]
[null,null,null,null,null,null,"Interprétez la valeur de l'êta-carré en termes d'effet de taille"]
[]
[]
[null,"Eta-carré =",null,null,"Calcul"]
[null,null,null,null,"Résultat"]

{"sheet":"Table t","index":6,"n_rows":103,"n_cols":17,"rows_kept":103,"cut":false,"hidden":false,"merged":[[1,1,1,11],[10,3,10,11],[12,3,12,11]]}
[]
[null,"Distribution du t de Student (table statistique)"]
[]
[]
[]
[]
[]
[]
[]
[]
[null,null,null,"Probabilité (seuil de signification pour un test unilatéral a)"]
[null,null,null,0.1,0.05,2.5000000000000001E-2,null,0.01,null,5.0000000000000001E-3,null,5.0000000000000001E-4]
[null,null,null,"Probabilité (seuil de signification pour un test bilatéral a)"]
[null,"dl",null,0.2,0.1,0.05,null,0.02,null,0.01,null,1E-3]
[]
[null,1,null,{"$f":"_xlfn.T.INV.2T(0.2,B16)","v":3.077683537175254},{"$f":"_xlfn.T.INV.2T(0.1,B16)","v":6.3137515146750438},{"$f":"_xlfn.T.INV.2T(0.05,B16)","v":12.706204736174707},null,{"$f":"_xlfn.T.INV.2T(0.02,B16)","v":31.820515953773956},null,{"$f":"_xlfn.T.INV.2T(0.01,B16)","v":63.656741162871583},null,{"$f":"_xlfn.T.INV.2T(0.001,B16)","v":636.61924876871956}]
[null,2,null,{"$f":"_xlfn.T.INV.2T(0.2,B17)","v":1.8856180831641267},{"$f":"_xlfn.T.INV.2T(0.1,B17)","v":2.9199855803537269},{"$f":"_xlfn.T.INV.2T(0.05,B17)","v":4.3026527297494637},null,{"$f":"_xlfn.T.INV.2T(0.02,B17)","v":6.9645567342832733},null,{"$f":"_xlfn.T.INV.2T(0.01,B17)","v":9.9248432009182928},null,{"$f":"_xlfn.T.INV.2T(0.001,B17)","v":31.599054576443621}]
[null,3,null,1.63774435369621,2.3533634348018233,3.1824463052837091,null,4.5407028585681335,null,5.8409093097333571,null,12.923978636687485,null,null,"a =",null,0.05]
[null,4,null,1.5332062740589443,2.1318467863266499,2.7764451051977934,null,3.7469473879791968,null,4.604094871349993,null,8.6103015813792751,null,null,"dl ="]
[null,5,null,1.4758840488244813,2.0150483733330233,2.570581835636315,null,3.3649299989072183,null,4.0321429835552278,null,6.8688266258811099,null,null,"t critique (Bil)=",null,{"$f":"_xlfn.T.INV.2T(Q18,Q19)","v":{"$error":"#NUM!"}}]
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