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{"sheet":"Beispiel 1","index":0,"n_rows":101,"n_cols":6,"rows_kept":101}
["Geschlecht (Frauen 1, Männer 2)","Raucher (Raucher 1, Nichtraucher 2)",{"$nulls":3},"Gibt es einen Zusammenhang zwischen Geschlecht und Rauchverhalten?"]
[1,1,{"$nulls":3},"Alpha = 0.05"]
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{"sheet":"Beispiel 1 (2)","index":1,"n_rows":101,"n_cols":14,"rows_kept":101}
["Geschlecht (Frauen 1, Männer 2)","Raucher (Raucher 1, Nichtraucher 2)",{"$nulls":3},"Gibt es einen Zusammenhang zwischen Geschlecht und Rauchverhalten?",{"$nulls":6},"Geschlecht","Raucherverhalten"]
[1,1,{"$nulls":3},"Alpha = 0.05",{"$nulls":6},1,1]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":3},"H0: die faktischen Häufigkeiten weichen nicht von den erwarteten ab",{"$nulls":6},1,1]
[1,1,{"$nulls":3},"HA: die faktischen Häufigkeiten weichen von den erwarteten ab.",{"$nulls":6},1,1]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":5},"Rauchverhalten",{"$nulls":4},1,1]
[1,1,{"$nulls":5},"Raucher","Nichtraucher",{"$nulls":3},1,1]
[1,1,{"$nulls":5},1,2,"Randsummen",null,null,1,1]
[1,1,null,null,"Geschlecht","Frauen",1,{"$f":"SUM(IF(($A$2:$A$101=$G10)*($B$2:$B$101=H$9),1,0))","v":12},{"$f":"SUM(IF(($A$2:$A$101=$G10)*($B$2:$B$101=I$9),1,0))","v":34},{"$f":"SUM(H10:I10)","v":46},null,null,1,1]
[1,1,{"$nulls":3},"Männer",2,{"$f":"SUM(IF(($A$2:$A$101=$G11)*($B$2:$B$101=H$9),1,0))","v":11},{"$f":"SUM(IF(($A$2:$A$101=$G11)*($B$2:$B$101=I$9),1,0))","v":43},{"$f":"SUM(H11:I11)","v":54},null,null,1,1]
[1,1,{"$nulls":3},"Randsummen",null,{"$f":"SUM(H10:H11)","v":23},{"$f":"SUM(I10:I11)","v":77},{"$f":"SUM(J9:J11)","v":100},null,null,1,1]
[1,1,{"$nulls":10},1,1]
[1,2,{"$nulls":10},1,2]
[1,2,null,null,"erwartete Häufigkeiten",null,null,{"$f":"H$12*$J10/$J$12","v":10.58},{"$f":"I$12*$J10/$J$12","v":35.42},{"$f":"SUM(H15:I15)","v":46},null,null,1,2]
[1,2,{"$nulls":5},{"$f":"H$12*$J11/$J$12","v":12.42},{"$f":"I$12*$J11/$J$12","v":41.58},{"$f":"SUM(H16:I16)","v":54},null,null,1,2]
[1,2,{"$nulls":3},"Randummen",null,{"$f":"SUM(H15:H16)","v":23},{"$f":"SUM(I15:I16)","v":77},{"$f":"SUM(J15:J16)","v":100},null,null,1,2]
[1,2,{"$nulls":10},1,2]
[1,2,{"$nulls":10},1,2]
[1,2,null,null,"Summanden der Teststatistik",null,null,{"$f":"(H10-H15)^2/H15","v":0.190586011342155},{"$f":"(I10-I15)^2/I15","v":0.05692828910220228},{"$nulls":3},1,2]
[1,2,{"$nulls":5},{"$f":"(H11-H16)^2/H16","v":0.1623510466988728},{"$f":"(I11-I16)^2/I16","v":0.04849446849446861},{"$nulls":3},1,2]
[1,2,{"$nulls":6},"Teststatistik",{"$f":"SUM(H20:I21)","v":0.4583598156376987},null,null,1,2]
[1,2,{"$nulls":6},"p-Wert",{"$f":"1-_xlfn.CHISQ.DIST(J22,1,1)","v":0.4983915147043183},null,null,1,2]
[1,2,{"$nulls":10},1,2]
[1,2,{"$nulls":4},"> 0.05",{"$nulls":5},1,2]
[1,2,{"$nulls":4},"also nicht signifikante Abweichungen der faktischen",{"$nulls":5},1,2]
[1,2,{"$nulls":4},"von den erwarteten Häufigkeiten",{"$nulls":5},1,2]
[1,2,{"$nulls":10},1,2]
[1,2,null,null,"Residuen",null,null,{"$f":"H10-H15","v":1.42},{"$f":"I10-I15","v":-1.4200000000000017},{"$nulls":3},1,2]
[1,2,{"$nulls":5},{"$f":"H11-H16","v":-1.42},{"$f":"I11-I16","v":1.4200000000000017},{"$nulls":3},1,2]
[1,2,{"$nulls":10},1,2]
[1,2,null,null,"Pearson-Residuen",null,null,{"$f":"(H10-H15)/SQRT(H15)","v":0.4365615779499554},{"$f":"(I10-I15)/SQRT(I15)","v":-0.2385964985120324},{"$nulls":3},1,2]
[1,2,{"$nulls":5},{"$f":"(H11-H16)/SQRT(H16)","v":-0.40292809122580764},{"$f":"(I11-I16)/SQRT(I16)","v":0.22021459646097172},{"$nulls":3},1,2]
[1,2,{"$nulls":10},1,2]
[1,2,{"$nulls":10},1,2]
[1,2,null,null,"standardisierte Pearson-Residuen",null,null,{"$f":"(H10-H15)/SQRT(H15*(1-H$12/$J$12)*(1-$J10/$J$12))","v":0.6770227585817913},{"$f":"(I10-I15)/SQRT(I15*(1-I$12/$J$12)*(1-$J10/$J$12))","v":-0.6770227585817922},{"$nulls":3},1,2]
[1,2,{"$nulls":5},{"$f":"(H11-H16)/SQRT(H16*(1-H$12/$J$12)*(1-$J11/$J$12))","v":-0.6770227585817913},{"$f":"(I11-I16)/SQRT(I16*(1-I$12/$J$12)*(1-$J11/$J$12))","v":0.6770227585817922},{"$nulls":3},1,2]
[1,2,{"$nulls":5},"es gibt keine Zellen mit signifikanten Abweichungen",{"$nulls":4},1,2]
[1,2,{"$nulls":10},1,2]
[1,2,null,null,"Ergebnisse mit R (Man liest die zwei Spalten rechts ein):",{"$nulls":7},1,2]
[1,2,null,null,"> rauch=read.table(\"clipboard\",header=T)",{"$nulls":7},1,2]
[1,2,null,null,"> head(rauch)",{"$nulls":7},1,2]
[1,2,null,null,"  Geschlecht Raucherverhalten",{"$nulls":7},1,2]
[1,2,null,null,"1          1                1",{"$nulls":7},1,2]
[1,2,null,null,"2          1                1",{"$nulls":7},1,2]
[1,2,null,null,"3          1                1",{"$nulls":7},1,2]
[1,2,null,null,"4          1                1",{"$nulls":7},1,2]
[2,1,null,null,"5          1                1",{"$nulls":7},2,1]
[2,1,null,null,"6          1                1",{"$nulls":7},2,1]
[2,1,null,null,"> tabrauch=table(rauch$Geschlecht,rauch$Raucherverhalten)",{"$nulls":7},2,1]
[2,1,null,null,"> rownames(tabrauch)=c(\"Frauen\",\"Maenner\")",{"$nulls":7},2,1]
[2,1,null,null,"> colnames(tabrauch)= c(\"Raucher\",\"Nichtraucher\")",{"$nulls":7},2,1]
[2,1,null,null,"> tabrauch",{"$nulls":7},2,1]
[2,1,null,null,"         ",{"$nulls":7},2,1]
[2,1,null,null,"          Raucher Nichtraucher",{"$nulls":7},2,1]
[2,1,null,null,"  Frauen       12           34",{"$nulls":7},2,1]
[2,1,null,null,"  Maenner      11           43",{"$nulls":7},2,1]
[2,1,null,null,"> ",{"$nulls":7},2,1]
[2,2,null,null,"> testrauch=chisq.test(rauch$Geschlecht,rauch$Raucherverhalten)",{"$nulls":7},2,2]
[2,2,null,null,"> testrauch",{"$nulls":7},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,null,null,"        Pearson's Chi-squared test with Yates' continuity correction",{"$nulls":7},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,null,null,"data:  rauch$Geschlecht and rauch$Raucherverhalten",{"$nulls":7},2,2]
[2,2,null,null,"X-squared = 0.1924, df = 1, p-value = 0.6609",{"$nulls":7},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,null,null,"> #Residuen",{"$nulls":7},2,2]
[2,2,null,null,"> testrauch$observed-testrauch$expected",{"$nulls":7},2,2]
[2,2,null,null,"                rauch$Raucherverhalten",{"$nulls":7},2,2]
[2,2,null,null,"rauch$Geschlecht     1     2",{"$nulls":7},2,2]
[2,2,null,null,"               1  1.42 -1.42",{"$nulls":7},2,2]
[2,2,null,null,"               2 -1.42  1.42",{"$nulls":7},2,2]
[2,2,null,null,"> #Pearson-Residuen",{"$nulls":7},2,2]
[2,2,null,null,"> testrauch$residuals",{"$nulls":7},2,2]
[2,2,null,null,"                rauch$Raucherverhalten",{"$nulls":7},2,2]
[2,2,null,null,"rauch$Geschlecht          1          2",{"$nulls":7},2,2]
[2,2,null,null,"               1  0.4365616 -0.2385965",{"$nulls":7},2,2]
[2,2,null,null,"               2 -0.4029281  0.2202146",{"$nulls":7},2,2]
[2,2,null,null,"> #standardisierte Pearson-Residuen",{"$nulls":7},2,2]
[2,2,null,null,"> testrauch$stdres",{"$nulls":7},2,2]
[2,2,null,null,"                rauch$Raucherverhalten",{"$nulls":7},2,2]
[2,2,null,null,"rauch$Geschlecht          1          2",{"$nulls":7},2,2]
[2,2,null,null,"               1  0.6770228 -0.6770228",{"$nulls":7},2,2]
[2,2,null,null,"               2 -0.6770228  0.6770228",{"$nulls":7},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,null,null,"Im Test erhält man nicht dieselben Ergebnisse wie mit Excel. Diese erhält man mit:",{"$nulls":7},2,2]
[2,2,null,null,"chisq.test(rauch$Geschlecht,rauch$Raucherverhalten,correct = F)",{"$nulls":7},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,{"$nulls":10},2,2]

{"sheet":"Beispiel 2","index":2,"n_rows":330,"n_cols":7,"rows_kept":330}
["Intensität von Gruppenarbeiten (1 hoch, 2 mittel, 3 gering)","Arbeitsklima (1 verbessert; 2 unverändert; 3 verschlechtert)",{"$nulls":4},"Wie verhält sich das Arbeitsklima bezüglich Intensität von Gruppenarbeiten?"]
[1,2,{"$nulls":4},"Alpha = 0.05"]
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{"sheet":"Beispiel 2 (2)","index":3,"n_rows":330,"n_cols":14,"rows_kept":330}
["Intensität von Gruppenarbeiten (1 hoch, 2 mittel, 3 gering)","Arbeitsklima (1 verbessert; 2 unverändert; 3 verschlechtert)",{"$nulls":4},"Wie verhält sich das Arbeitsklima bezüglich Intensität von Gruppenarbeiten?",{"$nulls":5},"Gruppenarbeit","Arbeitsklima"]
[1,2,{"$nulls":4},"H0: die faktischen Häufigkeiten weichen nicht von den erwarteten ab",{"$nulls":5},1,2]
[1,1,{"$nulls":4},"HA: die faktischen Häufigkeiten weichen von den erwarteten ab.",{"$nulls":5},1,1]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":4},"verbessert","unverändert","verschlechtert",{"$nulls":3},1,1]
[1,2,{"$nulls":4},1,2,3,"Randsummen",null,null,1,2]
[1,2,null,null,"hoch",1,{"$f":"SUM(IF(($A$2:$A$330=$F7)*($B$2:$B$330=G$6),1,0))","v":101},{"$f":"SUM(IF(($A$2:$A$330=$F7)*($B$2:$B$330=H$6),1,0))","v":48},{"$f":"SUM(IF(($A$2:$A$330=$F7)*($B$2:$B$330=I$6),1,0))","v":17},{"$f":"SUM(G7:I7)","v":166},null,null,1,2]
[2,3,null,null,"mittel",2,{"$f":"SUM(IF(($A$2:$A$330=$F8)*($B$2:$B$330=G$6),1,0))","v":41},{"$f":"SUM(IF(($A$2:$A$330=$F8)*($B$2:$B$330=H$6),1,0))","v":43},{"$f":"SUM(IF(($A$2:$A$330=$F8)*($B$2:$B$330=I$6),1,0))","v":8},{"$f":"SUM(G8:I8)","v":92},null,null,2,3]
[2,1,null,null,"gering",3,{"$f":"SUM(IF(($A$2:$A$330=$F9)*($B$2:$B$330=G$6),1,0))","v":20},{"$f":"SUM(IF(($A$2:$A$330=$F9)*($B$2:$B$330=H$6),1,0))","v":36},{"$f":"SUM(IF(($A$2:$A$330=$F9)*($B$2:$B$330=I$6),1,0))","v":15},{"$f":"SUM(G9:I9)","v":71},null,null,2,1]
[3,1,{"$nulls":3},"Randsummen",{"$f":"SUM(G7:G9)","v":162},{"$f":"SUM(H7:H9)","v":127},{"$f":"SUM(I7:I9)","v":40},{"$f":"SUM(J7:J9)","v":329},null,null,3,1]
[1,1,{"$nulls":10},1,1]
[2,2,{"$nulls":10},2,2]
[1,3,{"$nulls":10},1,3]
[2,1,null,null,"Erwwartete Häufigkeiten",{"$nulls":4},"Randsummen",null,null,2,1]
[2,2,{"$nulls":4},{"$f":"G$10*$J7/$J$10","v":81.73860182370821},64.0790273556231,20.182370820668694,{"$f":"SUM(G15:I15)","v":166},null,null,2,2]
[1,1,{"$nulls":4},45.30091185410334,35.51367781155015,11.185410334346505,{"$f":"SUM(G16:I16)","v":92},null,null,1,1]
[2,1,{"$nulls":4},34.96048632218845,27.407294832826747,8.632218844984802,{"$f":"SUM(G17:I17)","v":71},null,null,2,1]
[2,1,{"$nulls":3},"Randsummen",{"$f":"SUM(G15:G17)","v":162},{"$f":"SUM(H15:H17)","v":127},{"$f":"SUM(I15:I17)","v":40},{"$f":"SUM(J15:J17)","v":329},null,null,2,1]
[2,2,{"$nulls":10},2,2]
[2,1,{"$nulls":10},2,1]
[1,2,null,null,"Summanden des Chiquadrat-Testwertes",{"$nulls":7},1,2]
[2,1,{"$nulls":4},{"$f":"(G7-G15)^2/G15","v":4.538876998481372},4.0346292909233545,0.501798531512067,{"$nulls":3},2,1]
[1,1,{"$nulls":4},0.4083326807270681,1.5781249187052355,0.9071494647812876,{"$nulls":3},1,1]
[1,1,{"$nulls":4},6.4019747589820515,2.6939755470332476,4.697359690055226,{"$nulls":3},1,1]
[3,1,{"$nulls":6},"Testwert",{"$f":"SUM(G22:I24)","v":25.762221881200908},null,null,3,1]
[3,1,{"$nulls":6},"p-Werte",{"$f":"1-_xlfn.CHISQ.DIST(J25,4,1)","v":3.533693054669218E-5},null,null,3,1]
[1,2,{"$nulls":10},1,2]
[2,1,{"$nulls":5},"p-Werte < Alpha",{"$nulls":4},2,1]
[1,1,{"$nulls":4},"die beiden Häufigkeitstabellen unterscheiden sich",{"$nulls":5},1,1]
[3,2,{"$nulls":4},"signifikant.",{"$nulls":5},3,2]
[2,1,{"$nulls":10},2,1]
[2,2,null,null,"Residuen:",null,{"$f":"G7-G15","v":19.26139817629179},-16.079027355623097,-3.1823708206686945,{"$nulls":3},2,2]
[1,3,{"$nulls":4},-4.30091185410334,7.486322188449847,-3.1854103343465052,{"$nulls":3},1,3]
[1,1,{"$nulls":4},-14.960486322188451,8.592705167173253,6.367781155015198,{"$nulls":3},1,1]
[2,2,{"$nulls":10},2,2]
[1,3,{"$nulls":10},1,3]
[1,3,null,null,"Pearson-Residuen:",null,{"$f":"(G7-G15)/SQRT(G15)","v":2.130464033604269},-2.008638666092873,-0.7083773934225082,{"$nulls":3},1,3]
[1,1,{"$nulls":4},-0.6390091397836717,1.2562344202835853,-0.9524439431175398,{"$nulls":3},1,1]
[2,2,{"$nulls":4},-2.530212394045617,1.6413334661284549,2.1673393112420642,{"$nulls":3},2,2]
[1,1,{"$nulls":10},1,1]
[2,1,{"$nulls":10},2,1]
[3,2,null,null,"Standardisierte Pearson-Residuen",{"$nulls":7},3,2]
[1,1,{"$nulls":4},{"$f":"(G7-G15)/SQRT(G15*(1-G$10/$J$10)*(1-$J7/$J$10))","v":4.248328265669505},-3.6419017853908997,-1.0737863215417172,{"$nulls":3},1,1]
[3,2,{"$nulls":4},-1.0567458703121357,1.8889337614153368,-1.1973254887741391,{"$nulls":3},3,2]
[3,3,{"$nulls":4},-4.01037318880303,2.365414119895402,2.611343671801978,{"$nulls":3},3,3]
[1,2,{"$nulls":10},1,2]
[3,2,null,null,"es gibt signifikante Abweichungen in den Zellen (1,1), (1,2), (3,1), (3,2) und (3,3)",{"$nulls":7},3,2]
[2,2,{"$nulls":10},2,2]
[2,3,{"$nulls":10},2,3]
[1,2,{"$nulls":10},1,2]
[1,2,{"$nulls":10},1,2]
[2,2,{"$nulls":10},2,2]
[2,2,null,null,"Mit R:",{"$nulls":7},2,2]
[2,2,null,null,"> Gruppen=read.table(\"clipboard\",header=T)",{"$nulls":7},2,2]
[1,1,null,null,"> head(Gruppen)",{"$nulls":7},1,1]
[3,3,null,null,"  Gruppenarbeit Arbeitsklima",{"$nulls":7},3,3]
[1,1,null,null,"1             1            2",{"$nulls":7},1,1]
[3,2,null,null,"2             1            1",{"$nulls":7},3,2]
[2,2,null,null,"3             1            1",{"$nulls":7},2,2]
[3,1,null,null,"4             1            1",{"$nulls":7},3,1]
[3,1,null,null,"5             1            2",{"$nulls":7},3,1]
[1,2,null,null,"6             1            2",{"$nulls":7},1,2]
[1,2,null,null,"> tabgrup=table(Gruppen$Gruppenarbeit,Gruppen$Arbeitsklima)",{"$nulls":7},1,2]
[3,3,null,null,"> rownames(tabgrup)=c(\"hoch\",\"mittel\",\"tief\")",{"$nulls":7},3,3]
[1,1,null,null,"> colnames(tabgrup)= c(\"verbessert\",\"unverändert\",\"verschlechtert\")",{"$nulls":7},1,1]
[1,2,null,null,"> tabgrup",{"$nulls":7},1,2]
[3,3,null,null,"        ",{"$nulls":7},3,3]
[3,1,null,null,"         verbessert unverändert verschlechtert",{"$nulls":7},3,1]
[1,2,null,null,"  hoch          101          48             17",{"$nulls":7},1,2]
[3,1,null,null,"  mittel         41          43              8",{"$nulls":7},3,1]
[3,2,null,null,"  tief           20          36             15",{"$nulls":7},3,2]
[1,3,null,null,"> ",{"$nulls":7},1,3]
[1,3,null,null,"> testgrup=chisq.test(Gruppen$Gruppenarbeit,Gruppen$Arbeitsklima)",{"$nulls":7},1,3]
[1,1,null,null,"> testgrup",{"$nulls":7},1,1]
[1,2,{"$nulls":10},1,2]
[1,1,null,null,"        Pearson's Chi-squared test",{"$nulls":7},1,1]
[1,1,{"$nulls":10},1,1]
[1,1,null,null,"data:  Gruppen$Gruppenarbeit and Gruppen$Arbeitsklima",{"$nulls":7},1,1]
[1,1,null,null,"X-squared = 25.762, df = 4, p-value = 3.534e-05",{"$nulls":7},1,1]
[2,1,{"$nulls":10},2,1]
[3,2,null,null,"> #Residuen",{"$nulls":7},3,2]
[1,1,null,null,"> testgrup$observed-testgrup$expected",{"$nulls":7},1,1]
[1,1,null,null,"                     Gruppen$Arbeitsklima",{"$nulls":7},1,1]
[1,1,null,null,"Gruppen$Gruppenarbeit          1          2          3",{"$nulls":7},1,1]
[1,1,null,null,"                    1  19.261398 -16.079027  -3.182371",{"$nulls":7},1,1]
[2,1,null,null,"                    2  -4.300912   7.486322  -3.185410",{"$nulls":7},2,1]
[1,3,null,null,"                    3 -14.960486   8.592705   6.367781",{"$nulls":7},1,3]
[1,1,null,null,"> #Pearson-Residuen",{"$nulls":7},1,1]
[1,1,null,null,"> testgrup$residuals",{"$nulls":7},1,1]
[1,1,null,null,"                     Gruppen$Arbeitsklima",{"$nulls":7},1,1]
[2,1,null,null,"Gruppen$Gruppenarbeit          1          2          3",{"$nulls":7},2,1]
[2,1,null,null,"                    1  2.1304640 -2.0086387 -0.7083774",{"$nulls":7},2,1]
[1,1,null,null,"                    2 -0.6390091  1.2562344 -0.9524439",{"$nulls":7},1,1]
[3,1,null,null,"                    3 -2.5302124  1.6413335  2.1673393",{"$nulls":7},3,1]
[3,3,null,null,"> #standardisierte Pearson-Residuen",{"$nulls":7},3,3]
[2,1,null,null,"> testgrup$stdres",{"$nulls":7},2,1]
[1,1,null,null,"                     Gruppen$Arbeitsklima",{"$nulls":7},1,1]
[1,2,null,null,"Gruppen$Gruppenarbeit         1         2         3",{"$nulls":7},1,2]
[3,3,null,null,"                    1  4.248328 -3.641902 -1.073786",{"$nulls":7},3,3]
[1,1,null,null,"                    2 -1.056746  1.888934 -1.197325",{"$nulls":7},1,1]
[1,3,null,null,"                    3 -4.010373  2.365414  2.611344",{"$nulls":7},1,3]
[1,2,{"$nulls":10},1,2]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[1,2,{"$nulls":10},1,2]
[1,2,{"$nulls":10},1,2]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[2,1,{"$nulls":10},2,1]
[3,3,{"$nulls":10},3,3]
[1,1,{"$nulls":10},1,1]
[3,2,{"$nulls":10},3,2]
[1,2,{"$nulls":10},1,2]
[1,2,{"$nulls":10},1,2]
[2,1,{"$nulls":10},2,1]
[3,2,{"$nulls":10},3,2]
[3,2,{"$nulls":10},3,2]
[1,1,{"$nulls":10},1,1]
[2,2,{"$nulls":10},2,2]
[1,1,{"$nulls":10},1,1]
[1,2,{"$nulls":10},1,2]
[1,1,{"$nulls":10},1,1]
[2,2,{"$nulls":10},2,2]
[1,2,{"$nulls":10},1,2]
[1,3,{"$nulls":10},1,3]
[3,1,{"$nulls":10},3,1]
[1,2,{"$nulls":10},1,2]
[2,2,{"$nulls":10},2,2]
[1,3,{"$nulls":10},1,3]
[1,1,{"$nulls":10},1,1]
[2,1,{"$nulls":10},2,1]
[1,2,{"$nulls":10},1,2]
[1,2,{"$nulls":10},1,2]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[3,2,{"$nulls":10},3,2]
[3,2,{"$nulls":10},3,2]
[3,2,{"$nulls":10},3,2]
[2,2,{"$nulls":10},2,2]
[1,1,{"$nulls":10},1,1]
[2,1,{"$nulls":10},2,1]
[1,2,{"$nulls":10},1,2]
[1,2,{"$nulls":10},1,2]
[1,2,{"$nulls":10},1,2]
[3,1,{"$nulls":10},3,1]
[1,2,{"$nulls":10},1,2]
[1,1,{"$nulls":10},1,1]
[1,2,{"$nulls":10},1,2]
[3,1,{"$nulls":10},3,1]
[3,1,{"$nulls":10},3,1]
[1,1,{"$nulls":10},1,1]
[2,2,{"$nulls":10},2,2]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[1,2,{"$nulls":10},1,2]
[2,2,{"$nulls":10},2,2]
[1,1,{"$nulls":10},1,1]
[2,1,{"$nulls":10},2,1]
[3,1,{"$nulls":10},3,1]
[2,2,{"$nulls":10},2,2]
[1,1,{"$nulls":10},1,1]
[2,2,{"$nulls":10},2,2]
[2,3,{"$nulls":10},2,3]
[1,1,{"$nulls":10},1,1]
[3,3,{"$nulls":10},3,3]
[1,2,{"$nulls":10},1,2]
[1,2,{"$nulls":10},1,2]
[2,3,{"$nulls":10},2,3]
[2,1,{"$nulls":10},2,1]
[1,1,{"$nulls":10},1,1]
[1,2,{"$nulls":10},1,2]
[2,2,{"$nulls":10},2,2]
[2,3,{"$nulls":10},2,3]
[1,2,{"$nulls":10},1,2]
[1,3,{"$nulls":10},1,3]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[2,2,{"$nulls":10},2,2]
[1,1,{"$nulls":10},1,1]
[2,2,{"$nulls":10},2,2]
[2,1,{"$nulls":10},2,1]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[2,3,{"$nulls":10},2,3]
[3,3,{"$nulls":10},3,3]
[3,2,{"$nulls":10},3,2]
[1,3,{"$nulls":10},1,3]
[1,3,{"$nulls":10},1,3]
[2,2,{"$nulls":10},2,2]
[1,1,{"$nulls":10},1,1]
[2,2,{"$nulls":10},2,2]
[3,1,{"$nulls":10},3,1]
[2,1,{"$nulls":10},2,1]
[1,1,{"$nulls":10},1,1]
[3,2,{"$nulls":10},3,2]
[2,2,{"$nulls":10},2,2]
[1,1,{"$nulls":10},1,1]
[2,1,{"$nulls":10},2,1]
[2,1,{"$nulls":10},2,1]
[3,2,{"$nulls":10},3,2]
[1,1,{"$nulls":10},1,1]
[3,2,{"$nulls":10},3,2]
[1,1,{"$nulls":10},1,1]
[3,2,{"$nulls":10},3,2]
[2,1,{"$nulls":10},2,1]
[1,2,{"$nulls":10},1,2]
[1,2,{"$nulls":10},1,2]
[3,2,{"$nulls":10},3,2]
[3,3,{"$nulls":10},3,3]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[1,2,{"$nulls":10},1,2]
[3,3,{"$nulls":10},3,3]
[2,2,{"$nulls":10},2,2]
[2,1,{"$nulls":10},2,1]
[2,2,{"$nulls":10},2,2]
[3,2,{"$nulls":10},3,2]
[1,1,{"$nulls":10},1,1]
[3,1,{"$nulls":10},3,1]
[2,3,{"$nulls":10},2,3]
[3,2,{"$nulls":10},3,2]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[3,2,{"$nulls":10},3,2]
[3,2,{"$nulls":10},3,2]
[2,1,{"$nulls":10},2,1]
[2,2,{"$nulls":10},2,2]
[1,2,{"$nulls":10},1,2]
[2,2,{"$nulls":10},2,2]
[3,3,{"$nulls":10},3,3]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[3,2,{"$nulls":10},3,2]
[2,2,{"$nulls":10},2,2]
[1,3,{"$nulls":10},1,3]
[3,1,{"$nulls":10},3,1]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[2,1,{"$nulls":10},2,1]
[3,2,{"$nulls":10},3,2]
[2,1,{"$nulls":10},2,1]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[2,2,{"$nulls":10},2,2]
[3,2,{"$nulls":10},3,2]
[2,2,{"$nulls":10},2,2]
[1,1,{"$nulls":10},1,1]
[1,2,{"$nulls":10},1,2]
[1,1,{"$nulls":10},1,1]
[1,3,{"$nulls":10},1,3]
[2,2,{"$nulls":10},2,2]
[1,1,{"$nulls":10},1,1]
[2,1,{"$nulls":10},2,1]
[2,1,{"$nulls":10},2,1]
[3,2,{"$nulls":10},3,2]
[2,2,{"$nulls":10},2,2]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[3,2,{"$nulls":10},3,2]
[2,2,{"$nulls":10},2,2]
[3,2,{"$nulls":10},3,2]
[3,3,{"$nulls":10},3,3]
[2,1,{"$nulls":10},2,1]
[3,1,{"$nulls":10},3,1]
[1,1,{"$nulls":10},1,1]
[3,2,{"$nulls":10},3,2]
[1,2,{"$nulls":10},1,2]
[1,1,{"$nulls":10},1,1]
[2,2,{"$nulls":10},2,2]
[1,1,{"$nulls":10},1,1]
[1,2,{"$nulls":10},1,2]
[2,2,{"$nulls":10},2,2]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[1,1,{"$nulls":10},1,1]
[1,2,{"$nulls":10},1,2]
[1,3,{"$nulls":10},1,3]
[1,1,{"$nulls":10},1,1]
[3,2,{"$nulls":10},3,2]
[1,1,{"$nulls":10},1,1]
[2,1,{"$nulls":10},2,1]
[1,1,{"$nulls":10},1,1]
[3,1,{"$nulls":10},3,1]
[1,2,{"$nulls":10},1,2]
[3,2,{"$nulls":10},3,2]
[2,1,{"$nulls":10},2,1]
[2,2,{"$nulls":10},2,2]
[2,2,{"$nulls":10},2,2]
[2,2,{"$nulls":10},2,2]
[1,3,{"$nulls":10},1,3]
[1,2,{"$nulls":10},1,2]
[1,1,{"$nulls":10},1,1]
[3,1,{"$nulls":10},3,1]
[1,2,{"$nulls":10},1,2]
[2,1,{"$nulls":10},2,1]
[3,2,{"$nulls":10},3,2]
[1,1,{"$nulls":10},1,1]
[3,2,{"$nulls":10},3,2]
[1,2,{"$nulls":10},1,2]
[2,2,{"$nulls":10},2,2]
[3,3,{"$nulls":10},3,3]
[1,1,{"$nulls":10},1,1]
[3,1,{"$nulls":10},3,1]
[2,2,{"$nulls":10},2,2]
[3,2,{"$nulls":10},3,2]
[2,1,{"$nulls":10},2,1]
[1,1,{"$nulls":10},1,1]
[1,2,{"$nulls":10},1,2]
[1,1,{"$nulls":10},1,1]
[2,3,{"$nulls":10},2,3]
[2,2,{"$nulls":10},2,2]
[2,1,{"$nulls":10},2,1]
[2,1,{"$nulls":10},2,1]
[3,2,{"$nulls":10},3,2]
[2,1,{"$nulls":10},2,1]
[3,3,{"$nulls":10},3,3]
[2,1,{"$nulls":10},2,1]
[2,1,{"$nulls":10},2,1]
[1,1,{"$nulls":10},1,1]
[1,2,{"$nulls":10},1,2]

{"sheet":"Uebung 3","index":4,"n_rows":81,"n_cols":8,"rows_kept":81}
["Geschlecht (1 Männer; 2 Frauen)","Alter (1: < 20; 2: 21 - 35; 3: 36 - 50; 4: 51 - 65; 5 > 66)","Einstellung (1 positive; 2 negative)","Wohnort (1 Land; 2 Stadt; 3 Agglomeration)",{"$nulls":3},"Lassen sich Gruppen herausfinden, "]
[1,5,2,1,{"$nulls":3},"die eine unterschiedliche Einstellung zum"]
[2,5,2,1,{"$nulls":3},"Produkt haben? "]
[1,4,2,1,{"$nulls":3},"(Alpha jeweils 0.05)"]
[2,4,1,1]
[2,3,2,1]
[2,2,2,3]
[2,5,2,3]
[1,1,2,1]
[1,1,1,3]
[1,2,2,3]
[2,2,2,3]
[1,1,2,3]
[2,2,1,2]
[1,3,2,2]
[1,3,2,2]
[1,4,1,2]
[1,5,2,2]
[1,1,2,3]
[1,3,1,2]
[1,2,2,3]
[1,3,2,3]
[2,2,2,2]
[1,3,2,3]
[2,4,2,3]
[2,5,2,2]
[2,3,1,2]
[2,4,1,3]
[2,2,2,2]
[2,5,2,2]
[1,1,2,3]
[1,3,2,3]
[1,3,1,3]
[2,3,2,2]
[1,4,1,2]
[2,5,2,1]
[1,5,2,1]
[2,3,2,2]
[1,3,2,2]
[1,2,2,1]
[1,2,1,1]
[1,1,1,3]
[1,5,2,2]
[2,4,1,3]
[1,1,2,2]
[1,5,2,3]
[1,2,2,3]
[1,3,2,1]
[2,2,2,1]
[2,4,2,1]
[1,3,2,2]
[2,5,2,1]
[2,1,2,1]
[2,2,1,1]
[2,3,2,1]
[1,4,1,1]
[2,2,2,2]
[1,1,2,1]
[2,2,2,2]
[2,3,2,2]
[2,2,1,2]
[2,3,2,2]
[1,2,2,2]
[2,3,2,2]
[1,1,2,2]
[2,1,2,1]
[1,5,2,1]
[2,5,2,1]
[1,5,2,1]
[2,4,2,2]
[1,5,2,3]
[1,4,2,3]
[1,5,2,3]
[1,4,2,2]
[2,5,1,3]
[1,4,2,2]
[2,5,2,3]
[1,3,1,2]
[2,4,2,3]
[1,5,1,2]
[2,4,2,3]

{"sheet":"Uebung 3 (2)","index":5,"n_rows":195,"n_cols":16,"rows_kept":195}
["Geschlecht (1 Männer; 2 Frauen)","Alter (1: < 20; 2: 21 - 35; 3: 36 - 50; 4: 51 - 65; 5 > 66)","Einstellung (1 positive; 2 negative)","Wohnort (1 Land; 2 Stadt; 3 Agglomeration)",{"$nulls":3},"Lassen sich Gruppen herausfinden, ",{"$nulls":4},"Geschlecht","Alter","Einstellung","Wohnort"]
[1,5,2,1,{"$nulls":3},"die eine unterschiedliche Einstellung zum",{"$nulls":4},1,5,2,1]
[2,5,2,1,{"$nulls":3},"Produkt haben? ",{"$nulls":4},2,5,2,1]
[1,4,2,1,{"$nulls":8},1,4,2,1]
[2,4,1,1,{"$nulls":8},2,4,1,1]
[2,3,2,1,"Geschlecht * Einstellung",{"$nulls":7},2,3,2,1]
[2,2,2,3,{"$nulls":8},2,2,2,3]
[2,5,2,3,"H0: Es gibt keine geschlechtsspezifische Unterschiede in Bezug auf die Einstellung",{"$nulls":7},2,5,2,3]
[1,1,2,1,"HA. Esg gibt solche Unteschiede (Alpha = 0.05)",{"$nulls":7},1,1,2,1]
[1,1,1,3,{"$nulls":8},1,1,1,3]
[1,2,2,3,"beobachtete Häufigkeiten",{"$nulls":7},1,2,2,3]
[2,2,2,3,{"$nulls":3},"positiv","negativ",{"$nulls":3},2,2,2,3]
[1,1,2,3,{"$nulls":3},1,2,"Randsummen",null,null,1,1,2,3]
[2,2,1,2,"Geschlecht","Männer",1,{"$f":"SUM(IF(($A$2:$A$81=$G14)*($C$2:$C$81=H$13),1,0))","v":10},{"$f":"SUM(IF(($A$2:$A$81=$G14)*($C$2:$C$81=I$13),1,0))","v":33},{"$f":"SUM(H14:I14)","v":43},null,null,2,2,1,2]
[1,3,2,2,null,"Frauen",2,{"$f":"SUM(IF(($A$2:$A$81=$G15)*($C$2:$C$81=H$13),1,0))","v":8},{"$f":"SUM(IF(($A$2:$A$81=$G15)*($C$2:$C$81=I$13),1,0))","v":29},{"$f":"SUM(H15:I15)","v":37},null,null,1,3,2,2]
[1,3,2,2,null,null,"Randsummen",{"$f":"SUM(H14:H15)","v":18},{"$f":"SUM(I14:I15)","v":62},{"$f":"SUM(J14:J15)","v":80},null,null,1,3,2,2]
[1,4,1,2,{"$nulls":8},1,4,1,2]
[1,5,2,2,{"$nulls":8},1,5,2,2]
[1,1,2,3,null,"zweiseitiger exakter Test von Fischer",{"$nulls":6},1,1,2,3]
[1,3,1,2,{"$nulls":3},"Testwert 10",{"$nulls":4},1,3,1,2]
[1,2,2,3,{"$nulls":8},1,2,2,3]
[1,3,2,3,{"$nulls":3},"P(X >=10)=",{"$f":"1-_xlfn.HYPGEOM.DIST(9,43,18,80,1)","v":0.5388120675948735},{"$nulls":3},1,3,2,3]
[2,2,2,2,{"$nulls":3},"P(X <=10)=",{"$f":"_xlfn.HYPGEOM.DIST(H14,H16,J14,J16,1)","v":0.6695819043114175},{"$nulls":3},2,2,2,2]
[1,3,2,3,{"$nulls":8},1,3,2,3]
[2,4,2,3,null,null,"p-Wert",{"$f":"ROUNDDOWN(MIN(I22:I23)*2,0)","v":1},"(Befehl abrunden, weil p-Wert nicht grösser",{"$nulls":3},2,4,2,3]
[2,5,2,2,{"$nulls":4},"als 1 sein kann)",{"$nulls":3},2,5,2,2]
[2,3,1,2,null,null,"kiene signifikante Unterschiede zwischen Geschlechtern",{"$nulls":5},2,3,1,2]
[2,4,1,3,{"$nulls":8},2,4,1,3]
[2,2,2,2,null,"Quotenverhältnis (OR):",null,{"$f":"10*29/(8*33)","v":1.0984848484848484},"(kaum von 1 verschieden)",{"$nulls":3},2,2,2,2]
[2,5,2,2,null,"ln(OR)",null,{"$f":"LN(H29)","v":0.09393181983420347},{"$nulls":4},2,5,2,2]
[1,1,2,3,null,"s(ln(OR)",null,{"$f":"SQRT(1/H14+1/I14+1/H15+1/I15)","v":0.5383175539806593},{"$nulls":4},1,1,2,3]
[1,3,2,3,null,"untere Grenze 0.95-VI für OR",null,{"$f":"EXP(H30-1.96*H31)","v":0.38244493916685995},{"$nulls":4},1,3,2,3]
[1,3,1,3,null,"obere Grenze 0.95-VI für OR",null,{"$f":"EXP(H30+1.96*H31)","v":3.1551442803229595},{"$nulls":4},1,3,1,3]
[2,3,2,2,{"$nulls":3},"VI enthält 1, also nicht signifikante Abweichung",{"$nulls":4},2,3,2,2]
[1,4,1,2,{"$nulls":3},"der OR von 1.",{"$nulls":4},1,4,1,2]
[2,5,2,1,{"$nulls":8},2,5,2,1]
[1,5,2,1,null,"Mit R:",{"$nulls":6},1,5,2,1]
[2,3,2,2,null,"> einst=read.table(\"clipboard\",header=T)",{"$nulls":6},2,3,2,2]
[1,3,2,2,null,"> head(einst)",{"$nulls":6},1,3,2,2]
[1,2,2,1,null,"  Geschlecht Alter Einstellung Wohnort",{"$nulls":6},1,2,2,1]
[1,2,1,1,null,"1          1     5           2       1",{"$nulls":6},1,2,1,1]
[1,1,1,3,null,"2          2     5           2       1",{"$nulls":6},1,1,1,3]
[1,5,2,2,null,"3          1     4           2       1",{"$nulls":6},1,5,2,2]
[2,4,1,3,null,"4          2     4           1       1",{"$nulls":6},2,4,1,3]
[1,1,2,2,null,"5          2     3           2       1",{"$nulls":6},1,1,2,2]
[1,5,2,3,null,"6          2     2           2       3",{"$nulls":6},1,5,2,3]
[1,2,2,3,null,"> tabGeschl=table(einst$Geschlecht,einst$Einstellung)",{"$nulls":6},1,2,2,3]
[1,3,2,1,null,"> rownames(tabGeschl)=c(\"Männer\",\"Frauen\")",{"$nulls":6},1,3,2,1]
[2,2,2,1,null,"> colnames(tabGeschl)=c(\"positiv\",\"negativ\")",{"$nulls":6},2,2,2,1]
[2,4,2,1,null,"> tabGeschl",{"$nulls":6},2,4,2,1]
[1,3,2,2,null,"        ",{"$nulls":6},1,3,2,2]
[2,5,2,1,null,"         positiv negativ",{"$nulls":6},2,5,2,1]
[2,1,2,1,null,"  Männer      10      33",{"$nulls":6},2,1,2,1]
[2,2,1,1,null,"  Frauen       8      29",{"$nulls":6},2,2,1,1]
[2,3,2,1,null,"> fisher.test(tabGeschl)",{"$nulls":6},2,3,2,1]
[1,4,1,1,{"$nulls":8},1,4,1,1]
[2,2,2,2,null,"        Fisher's Exact Test for Count Data",{"$nulls":6},2,2,2,2]
[1,1,2,1,{"$nulls":8},1,1,2,1]
[2,2,2,2,null,"data:  tabGeschl",{"$nulls":6},2,2,2,2]
[2,3,2,2,null,"p-value = 1",{"$nulls":6},2,3,2,2]
[2,2,1,2,null,"alternative hypothesis: true odds ratio is not equal to 1",{"$nulls":6},2,2,1,2]
[2,3,2,2,null,"95 percent confidence interval:",{"$nulls":6},2,3,2,2]
[1,2,2,2,null," 0.3373753 3.6709607",{"$nulls":6},1,2,2,2]
[2,3,2,2,null,"sample estimates:",{"$nulls":6},2,3,2,2]
[1,1,2,2,null,"odds ratio ",{"$nulls":6},1,1,2,2]
[2,1,2,1,null,1.097192,{"$nulls":6},2,1,2,1]
[1,5,2,1,{"$nulls":8},1,5,2,1]
[2,5,2,1,null,"Die OR und die VIs werden in R etwas anders berechnet. Verwenden Sie",{"$nulls":6},2,5,2,1]
[1,5,2,1,null," jeweils die Variante des Programms, mit dem Sie rechnen.",{"$nulls":6},1,5,2,1]
[2,4,2,2,{"$nulls":8},2,4,2,2]
[1,5,2,3,{"$nulls":8},1,5,2,3]
[1,4,2,3,"Alter * Einstellung",null,null,"(hier wäre Testen von Gamma besser!!!!)",{"$nulls":4},1,4,2,3]
[1,5,2,3,{"$nulls":8},1,5,2,3]
[1,4,2,2,null,"H0: Es gibt keine alterspezifischen Unterschiede in Bezug auf die Einstellung",{"$nulls":6},1,4,2,2]
[2,5,1,3,null,"HA. Esg gibt solche Unteschiede (Alpha = 0.05)",{"$nulls":6},2,5,1,3]
[1,4,2,2,{"$nulls":8},1,4,2,2]
[2,5,2,3,{"$nulls":8},2,5,2,3]
[1,3,1,2,{"$nulls":8},1,3,1,2]
[2,4,2,3,"beobachtete Häufigkeiten",{"$nulls":7},2,4,2,3]
[1,5,1,2,null,null,"Alter",{"$nulls":5},1,5,1,2]
[2,4,2,3,null,null,"< 20","21 - 53","36 - 50","51 - 65",">66",null,2,4,2,3]
[{"$nulls":6},1,2,3,4,5,"Randsummen"]
[{"$nulls":4},"positiv",1,{"$f":"SUM(IF(($C$2:$C$81=$F83)*($B$2:$B$81=G$82),1,0))","v":2},{"$f":"SUM(IF(($C$2:$C$81=$F83)*($B$2:$B$81=H$82),1,0))","v":4},{"$f":"SUM(IF(($C$2:$C$81=$F83)*($B$2:$B$81=I$82),1,0))","v":4},{"$f":"SUM(IF(($C$2:$C$81=$F83)*($B$2:$B$81=J$82),1,0))","v":6},{"$f":"SUM(IF(($C$2:$C$81=$F83)*($B$2:$B$81=K$82),1,0))","v":2},{"$f":"SUM(G83:K83)","v":18}]
[{"$nulls":4},"negativ",2,{"$f":"SUM(IF(($C$2:$C$81=$F84)*($B$2:$B$81=G$82),1,0))","v":9},{"$f":"SUM(IF(($C$2:$C$81=$F84)*($B$2:$B$81=H$82),1,0))","v":12},{"$f":"SUM(IF(($C$2:$C$81=$F84)*($B$2:$B$81=I$82),1,0))","v":15},{"$f":"SUM(IF(($C$2:$C$81=$F84)*($B$2:$B$81=J$82),1,0))","v":9},{"$f":"SUM(IF(($C$2:$C$81=$F84)*($B$2:$B$81=K$82),1,0))","v":17},{"$f":"SUM(G84:K84)","v":62}]
[{"$nulls":5},"Randsummen",{"$f":"SUM(G83:G84)","v":11},16,19,15,19,80]
[]
[{"$nulls":4},"erwartete Häufigkeiten"]
[{"$nulls":6},{"$f":"(G$85*$L83/$L$85)","v":2.475},3.6,4.275,3.375,4.275]
[{"$nulls":6},8.525,12.4,14.725,11.625,14.725]
[]
[{"$nulls":5},"Achtung: in 5 von 10 Zellen sind erwarteten Häufigkeiten < 5; Chi-Quadrat-Test darf nicht"]
[{"$nulls":5}," angewendet werden."]
[]
[{"$nulls":5},"deshalb exakter Test von Fisher mit Excel - der auf verallgemeinerter hypergeometrischer Verteilung beruht"]
[{"$nulls":5},"> fisher.test(table(einst$Einstellung,einst$Alter))"]
[]
[{"$nulls":5},"        Fisher's Exact Test for Count Data"]
[]
[{"$nulls":5},"data:  table(einst$Einstellung, einst$Alter)"]
[{"$nulls":5},"p-value = 0.3761"]
[{"$nulls":5},"alternative hypothesis: two.sided"]
[{"$nulls":6},"Keine signfikante Unterschiede"]
[]
[]
[]
[{"$nulls":4},"Mit Gamma:"]
[{"$nulls":5},"gamma.test(einst$Einstellung,einst$Alter)"]
[]
[{"$nulls":5},"        Bivariate test of Gamma"]
[]
[{"$nulls":5},"data:  "]
[{"$nulls":5},"z = 0.32079, p-value = 0.7484"]
[{"$nulls":5},"alternative hypothesis: two.sided"]
[{"$nulls":5},"null values:"]
[{"$nulls":5},"[1] \"Gamma = 0\" \"\"         "]
[{"$nulls":5},"95 percent confidence interval:"]
[{"$nulls":5}," -0.2832510  0.3941157"]
[{"$nulls":5},"sample estimates:"]
[{"$nulls":5},"                  Gamma: standard error of Gamma: "]
[{"$nulls":5},"              0.05543237               0.17280079 "]
[]
[{"$nulls":5},"Auch hier keine signifikante Abweichung Gammas von 0."]
[]
[{"$nulls":5},"Mit der Bootstrap-Methode:"]
[{"$nulls":5},"> gamma.test(einst$Einstellung,einst$Alter,bootstrap =T)"]
[{"$nulls":5},"[1] Quantiles Bootstrap Method:"]
[{"$nulls":5},"      2.5%      97.5% "]
[{"$nulls":5},"-0.2286686  0.3319136 "]
[{"$nulls":5},"[1] Bootstrap Confidence Interval:"]
[{"$nulls":5},"      2.5%      97.5% "]
[{"$nulls":5},"-0.2210489  0.3395334 "]
[]
[]
[]
[{"$nulls":4},"Wohnhort * Einstellung"]
[]
[{"$nulls":4},"H0: Es gibt keine wohnortsspezifische Unterschiede bezüglich Einstelllung"]
[{"$nulls":4},"HA: Es gibt solche."]
[]
[{"$nulls":4},"beobachtete Häufigkeiten"]
[{"$nulls":6},"positiv","negativ"]
[{"$nulls":6},1,2,"Randsummen"]
[{"$nulls":4},"Land",1,{"$f":"SUM(IF(($D$2:$D$81=$F143)*($C$2:$C$81=G$142),1,0))","v":4},{"$f":"SUM(IF(($D$2:$D$81=$F143)*($C$2:$C$81=H$142),1,0))","v":19},{"$f":"SUM(G143:H143)","v":23}]
[{"$nulls":4},"Stadt",2,{"$f":"SUM(IF(($D$2:$D$81=$F144)*($C$2:$C$81=G$142),1,0))","v":8},{"$f":"SUM(IF(($D$2:$D$81=$F144)*($C$2:$C$81=H$142),1,0))","v":23},{"$f":"SUM(G144:H144)","v":31}]
[{"$nulls":4},"Aglo",3,{"$f":"SUM(IF(($D$2:$D$81=$F145)*($C$2:$C$81=G$142),1,0))","v":6},{"$f":"SUM(IF(($D$2:$D$81=$F145)*($C$2:$C$81=H$142),1,0))","v":20},{"$f":"SUM(G145:H145)","v":26}]
[{"$nulls":5},"Randsummen",{"$f":"SUM(G143:G145)","v":18},{"$f":"SUM(H143:H145)","v":62},{"$f":"SUM(G143:H145)","v":80}]
[]
[{"$nulls":4},"erwartete Häufigkeiten"]
[{"$nulls":6},{"$f":"(G$146*$I143/$I$146)","v":5.175},17.825]
[{"$nulls":6},6.975,24.025]
[{"$nulls":6},5.85,20.15]
[{"$nulls":8},{"$f":"SUM(G149:H151)","v":80}]
[]
[{"$nulls":4},"Summanden der Teststatistik"]
[{"$nulls":6},{"$f":"(G143-G149)^2/G149","v":0.26678743961352647},0.07745441795231427]
[{"$nulls":6},0.1506272401433693,0.04373048907388125]
[{"$nulls":6},3.8461538461538646E-3,1.1166253101736762E-3]
[{"$nulls":7},"Testwert",{"$f":"SUM(G155:H157)","v":0.5435623659394188}]
[{"$nulls":7},"p-Wert",{"$f":"1-_xlfn.CHISQ.DIST(I158,2,1)","v":0.762020986017225}]
[{"$nulls":6},"nicht singifikante Abweichungen"]
[]
[{"$nulls":4},"Mit R:"]
[{"$nulls":4},"> tabwohn=table(einst$Wohnort,einst$Einstellung)"]
[{"$nulls":4},"> "]
[{"$nulls":4},"> colnames(tabwohn)=c(\"positiv\",\"negativ\")"]
[{"$nulls":4},"> rownames(tabwohn)=c(\"Land\",\"Stadt\",\"Aglo\")"]
[{"$nulls":4},"> tabwohn"]
[{"$nulls":4},"       "]
[{"$nulls":4},"        positiv negativ"]
[{"$nulls":4},"  Land        4      19"]
[{"$nulls":4},"  Stadt       8      23"]
[{"$nulls":4},"  Aglo        6      20"]
[{"$nulls":4},"> "]
[{"$nulls":4},"> wohntest=chisq.test(tabwohn)"]
[{"$nulls":4},"> wohntest"]
[]
[{"$nulls":4},"        Pearson's Chi-squared test"]
[]
[{"$nulls":4},"data:  tabwohn"]
[{"$nulls":4},"X-squared = 0.54356, df = 2, p-value = 0.762"]
[]
[{"$nulls":4},"> wohntest$residuals"]
[{"$nulls":4},"       "]
[{"$nulls":4},"            positiv     negativ"]
[{"$nulls":4},"  Land  -0.51651470  0.27830634"]
[{"$nulls":4},"  Stadt  0.38810725 -0.20911836"]
[{"$nulls":4},"  Aglo   0.06201737 -0.03341594"]
[{"$nulls":4},"> wohntest$stdres"]
[{"$nulls":4},"       "]
[{"$nulls":4},"            positiv     negativ"]
[{"$nulls":4},"  Land  -0.69508738  0.69508738"]
[{"$nulls":4},"  Stadt  0.56331052 -0.56331052"]
[{"$nulls":4},"  Aglo   0.08574535 -0.08574535"]
[]
[{"$nulls":5},"keine Zellen mit signifikanten Abweichungen"]

{"sheet":"Uebung 4","index":6,"n_rows":481,"n_cols":4,"rows_kept":481}
["Alter (<=30, 30- 40, 40 - 60, 60 - 100)","Einstellung (dafür 1, eher dafür 2, weiss nicht 3, eher dagegen 4, dagegen 5)"]
[1,1]
[1,1,null,"Gibt es Unterschiede bezüglich der 4 Kategorien Alter-Geschlecht?"]
[1,1,null,"Bemerkung: Es wäre besser, die Daten in drei Variablen zu"]
[1,1,null,"erheben (Alter, Geschlecht und Einstellung)."]
[1,1,null,"Es gibt multivariate Verfahren, um drei Variablen zusammen zu  analysieren "]
[1,1,null,"analysieren."]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
[1,1]
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[1,3]
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[1,3]
[1,3]
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[1,3]
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[1,3]
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[1,3]
[1,3]
[1,4]
[1,4]
[1,4]
[1,4]
[1,4]
[1,4]
[1,4]
[1,4]
[1,4]
[1,4]
[1,5]
[1,5]
[1,5]
[1,5]
[1,5]
[2,1]
[2,1]
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[2,1]
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[2,1]
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[2,1]
[2,1]
[2,1]
[2,1]
[2,2]
[2,2]
[2,2]
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[2,2]
[2,2]
[2,2]
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[2,2]
[2,2]
[2,2]
[2,2]
[2,2]
[2,2]
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[2,2]
[2,3]
[2,3]
[2,3]
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[2,3]
[2,3]
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[2,3]
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[2,4]
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[2,5]
[2,5]
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[2,5]
[2,5]
[3,1]
[3,1]
[3,1]
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[3,1]
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[3,1]
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[3,1]
[3,1]
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[3,1]
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[3,1]
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[3,1]
[3,1]
[3,1]
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[3,1]
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[3,1]
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[3,1]
[3,1]
[3,1]
[3,2]
[3,2]
[3,2]
[3,2]
[3,2]
[3,2]
[3,2]
[3,2]
[3,2]
[3,2]
[3,2]
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[3,5]
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[4,1]
[4,1]
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[4,5]

{"sheet":"Uebung 4 (2)","index":7,"n_rows":481,"n_cols":15,"rows_kept":481}
["Alter (<=30, 30- 40, 40 - 60, 60 - 100)","Einstellung (dafür 1, eher dafür 2, weiss nicht 3, eher dagegen 4, dagegen 5)",{"$nulls":11},"Alter ","Einstellung"]
[1,1,{"$nulls":11},1,1]
[1,1,null,"Gibt es Unterschiede bezüglich der 4 Kategorien Alter-Geschlecht?",{"$nulls":9},1,1]
[1,1,null,"Bemerkung: Es wäre besser, die Daten in drei Variablen zu",{"$nulls":9},1,1]
[1,1,null,"erheben (Alter, Geschlecht und Einstellung).",{"$nulls":9},1,1]
[1,1,null,"Es gibt multivariate Verfahren, um drei Variablen zusammen zu  analysieren ",{"$nulls":9},1,1]
[1,1,null,"analysieren.",{"$nulls":9},1,1]
[1,1,{"$nulls":11},1,1]
[1,1,null,"H0: Es gibt keine Unterschiede zwischen beobachteten und erwarteten Häufigkeiten",{"$nulls":9},1,1]
[1,1,null,"HA: Esg ibt solche Unterschiede (Alphha = 0.05)",{"$nulls":9},1,1]
[1,1,{"$nulls":11},1,1]
[1,1,{"$nulls":11},1,1]
[1,1,null,"beobachtete Häufigkeiten",{"$nulls":9},1,1]
[1,1,{"$nulls":4},"<=30","30 - 40","40 - 60","60 - 100",{"$nulls":3},1,1]
[1,1,{"$nulls":4},1,2,3,4,"Randsummen",null,null,1,1]
[1,1,null,"  dafür ",null,1,{"$f":"SUM(IF(($B$2:$B$481=$F16)*($A$2:$A$481=G$15),1,0))","v":50},{"$f":"SUM(IF(($B$2:$B$481=$F16)*($A$2:$A$481=H$15),1,0))","v":40},{"$f":"SUM(IF(($B$2:$B$481=$F16)*($A$2:$A$481=I$15),1,0))","v":60},{"$f":"SUM(IF(($B$2:$B$481=$F16)*($A$2:$A$481=J$15),1,0))","v":50},{"$f":"SUM(G16:J16)","v":200},null,null,1,1]
[1,1,null,"  eher dafür",null,2,{"$f":"SUM(IF(($B$2:$B$481=$F17)*($A$2:$A$481=G$15),1,0))","v":30},{"$f":"SUM(IF(($B$2:$B$481=$F17)*($A$2:$A$481=H$15),1,0))","v":30},{"$f":"SUM(IF(($B$2:$B$481=$F17)*($A$2:$A$481=I$15),1,0))","v":40},{"$f":"SUM(IF(($B$2:$B$481=$F17)*($A$2:$A$481=J$15),1,0))","v":40},140,null,null,1,1]
[1,1,null,"  weiss nicht ",null,3,{"$f":"SUM(IF(($B$2:$B$481=$F18)*($A$2:$A$481=G$15),1,0))","v":20},{"$f":"SUM(IF(($B$2:$B$481=$F18)*($A$2:$A$481=H$15),1,0))","v":30},{"$f":"SUM(IF(($B$2:$B$481=$F18)*($A$2:$A$481=I$15),1,0))","v":10},{"$f":"SUM(IF(($B$2:$B$481=$F18)*($A$2:$A$481=J$15),1,0))","v":5},65,null,null,1,1]
[1,1,null,"  eher dagegen",null,4,{"$f":"SUM(IF(($B$2:$B$481=$F19)*($A$2:$A$481=G$15),1,0))","v":10},{"$f":"SUM(IF(($B$2:$B$481=$F19)*($A$2:$A$481=H$15),1,0))","v":20},{"$f":"SUM(IF(($B$2:$B$481=$F19)*($A$2:$A$481=I$15),1,0))","v":5},{"$f":"SUM(IF(($B$2:$B$481=$F19)*($A$2:$A$481=J$15),1,0))","v":10},45,null,null,1,1]
[1,1,null,"  dagegen ",null,5,{"$f":"SUM(IF(($B$2:$B$481=$F20)*($A$2:$A$481=G$15),1,0))","v":5},{"$f":"SUM(IF(($B$2:$B$481=$F20)*($A$2:$A$481=H$15),1,0))","v":10},{"$f":"SUM(IF(($B$2:$B$481=$F20)*($A$2:$A$481=I$15),1,0))","v":5},{"$f":"SUM(IF(($B$2:$B$481=$F20)*($A$2:$A$481=J$15),1,0))","v":10},30,null,null,1,1]
[1,1,{"$nulls":3},"Randsummen",{"$f":"SUM(G16:G20)","v":115},{"$f":"SUM(H16:H20)","v":130},{"$f":"SUM(I16:I20)","v":120},{"$f":"SUM(J16:J20)","v":115},480,null,null,1,1]
[1,1,{"$nulls":11},1,1]
[1,1,{"$nulls":11},1,1]
[1,1,null,"erwartete Häufigkeiten",null,null,{"$f":"G$21*$K16/$K$21","v":47.916666666666664},54.166666666666664,50,47.916666666666664,{"$f":"SUM(G24:J24)","v":199.99999999999997},null,null,1,1]
[1,1,{"$nulls":4},33.541666666666664,37.916666666666664,35,33.541666666666664,{"$f":"SUM(G25:J25)","v":140},null,null,1,1]
[1,1,{"$nulls":4},15.572916666666666,17.604166666666668,16.25,15.572916666666666,{"$f":"SUM(G26:J26)","v":65},null,null,1,1]
[1,1,{"$nulls":4},10.78125,12.1875,11.25,10.78125,{"$f":"SUM(G27:J27)","v":45},null,null,1,1]
[1,1,{"$nulls":4},7.1875,8.125,7.5,7.1875,{"$f":"SUM(G28:J28)","v":30},null,null,1,1]
[1,1,{"$nulls":3},"Randsummen",{"$f":"SUM(G24:G28)","v":115},{"$f":"SUM(H24:H28)","v":130},{"$f":"SUM(I24:I28)","v":120},{"$f":"SUM(J24:J28)","v":115},{"$f":"SUM(K24:K28)","v":480},null,null,1,1]
[1,1,{"$nulls":11},1,1]
[1,1,{"$nulls":11},1,1]
[1,1,null,"Summanden der Teststatistik",null,null,{"$f":"(G16-G24)^2/G24","v":0.09057971014492774},3.705128205128204,2,0.09057971014492774,{"$nulls":3},1,1]
[1,1,{"$nulls":4},0.37396480331262894,1.652930402930402,0.7142857142857143,1.2435300207039348,{"$nulls":3},1,1]
[1,1,{"$nulls":4},1.258535395763657,8.72842702169625,2.4038461538461537,7.178267837235229,{"$nulls":3},1,1]
[1,1,{"$nulls":4},0.05661231884057971,5.00801282051282,3.4722222222222223,0.05661231884057971,{"$nulls":3},1,1]
[1,1,{"$nulls":4},0.6657608695652174,0.4326923076923077,0.8333333333333334,1.1005434782608696,{"$nulls":3},1,1]
[1,1,{"$nulls":7},"Testwert",{"$f":"SUM(G32:J36)","v":41.06586464445996},null,null,1,1]
[1,1,{"$nulls":7},"p-Wert",{"$f":"1-_xlfn.CHISQ.DIST(K37,12,1)","v":4.7775580019226993E-5},null,null,1,1]
[1,1,{"$nulls":5},"signifikante Abweichung der Häufigkiten",{"$nulls":5},1,1]
[1,1,{"$nulls":11},1,1]
[1,1,{"$nulls":11},1,1]
[1,1,null,"Analyse mit Residuen s. folgende R-Ergebnisse:",{"$nulls":9},1,1]
[1,1,{"$nulls":11},1,1]
[1,1,{"$nulls":11},1,1]
[1,1,{"$nulls":11},1,1]
[1,1,{"$nulls":11},1,1]
[1,1,null,"Mit R:",{"$nulls":9},1,1]
[1,1,null,"> altein=read.table(\"clipboard\",header=T)",{"$nulls":9},1,1]
[1,1,null,"> head(altein)",{"$nulls":9},1,1]
[1,1,null,"  Alter Einstellung",{"$nulls":9},1,1]
[1,1,null,"1     1           1",{"$nulls":9},1,1]
[1,2,null,"2     1           1",{"$nulls":9},1,2]
[1,2,null,"3     1           1",{"$nulls":9},1,2]
[1,2,null,"4     1           1",{"$nulls":9},1,2]
[1,2,null,"5     1           1",{"$nulls":9},1,2]
[1,2,null,"6     1           1",{"$nulls":9},1,2]
[1,2,null,"> tabAE=table(altein$Einstellung,altein$Alter)",{"$nulls":9},1,2]
[1,2,null,"> colnames(tabAE)=c(\"<= 30\",\"30-40\",\"40-60\", \"60-100\")",{"$nulls":9},1,2]
[1,2,null,"> rownames(tabAE)=c(\"dafür\",\"eher dafür\", \"weiss nicht\",\"eher dagegen\", \"dagegen\")",{"$nulls":9},1,2]
[1,2,null,"> tabAE",{"$nulls":9},1,2]
[1,2,null,"              ",{"$nulls":9},1,2]
[1,2,null,"               <= 30 30-40 40-60 60-100",{"$nulls":9},1,2]
[1,2,null,"  dafür           50    40    60     50",{"$nulls":9},1,2]
[1,2,null,"  eher dafür      30    30    40     40",{"$nulls":9},1,2]
[1,2,null,"  weiss nicht     20    30    10      5",{"$nulls":9},1,2]
[1,2,null,"  eher dagegen    10    20     5     10",{"$nulls":9},1,2]
[1,2,null,"  dagegen          5    10     5     10",{"$nulls":9},1,2]
[1,2,null,"> testAE=chisq.test(tabAE)",{"$nulls":9},1,2]
[1,2,null,"> testAE",{"$nulls":9},1,2]
[1,2,{"$nulls":11},1,2]
[1,2,null,"        Pearson's Chi-squared test",{"$nulls":9},1,2]
[1,2,{"$nulls":11},1,2]
[1,2,null,"data:  tabAE",{"$nulls":9},1,2]
[1,2,null,"X-squared = 41.066, df = 12, p-value = 4.778e-05",{"$nulls":9},1,2]
[1,2,{"$nulls":11},1,2]
[1,2,null,"> testAE$residuals",{"$nulls":9},1,2]
[1,2,null,"              ",{"$nulls":9},1,2]
[1,2,null,"                    <= 30      30-40      40-60     60-100",{"$nulls":9},1,2]
[1,2,null,"  dafür         0.3009646 -1.9248710  1.4142136  0.3009646",{"$nulls":9},1,2]
[1,2,null,"  eher dafür   -0.6115266 -1.2856634  0.8451543  1.1151368",{"$nulls":9},1,2]
[1,2,null,"  weiss nicht   1.1218446  2.9543911 -1.5504342 -2.6792290",{"$nulls":9},1,2]
[1,3,null,"  eher dagegen -0.2379334  2.2378590 -1.8633900 -0.2379334",{"$nulls":9},1,3]
[1,3,null,"  dagegen      -0.8159417  0.6577935 -0.9128709  1.0490679",{"$nulls":9},1,3]
[1,3,null,"> testAE$stdres",{"$nulls":9},1,3]
[1,3,null,"              ",{"$nulls":9},1,3]
[1,3,null,"                    <= 30      30-40      40-60     60-100",{"$nulls":9},1,3]
[1,3,null,"  dafür         0.4518885 -2.9514119  2.1380899  0.4518885",{"$nulls":9},1,3]
[1,3,null,"  eher dafür   -0.8332412 -1.7889370  1.1595421  1.5194397",{"$nulls":9},1,3]
[1,3,null,"  weiss nicht   1.3835774  3.7209271 -1.9253925 -3.3043085",{"$nulls":9},1,3]
[1,3,null,"  eher dagegen -0.2866194  2.7529309 -2.2602117 -0.2866194",{"$nulls":9},1,3]
[1,3,null,"  dagegen      -0.9663794  0.7955923 -1.0886621  1.2424878",{"$nulls":9},1,3]
[1,3,{"$nulls":11},1,3]
[1,3,{"$nulls":11},1,3]
[1,3,null,"Es gibt signifikante Abweichungen in (1,2), (1,3), (3,2), (3,4), (4,2), (4,3)",{"$nulls":9},1,3]
[1,3,{"$nulls":11},1,3]
[1,3,{"$nulls":11},1,3]
[1,3,{"$nulls":11},1,3]
[1,3,{"$nulls":11},1,3]
[1,3,{"$nulls":11},1,3]
[1,3,{"$nulls":11},1,3]
[1,3,{"$nulls":11},1,3]
[1,4,{"$nulls":11},1,4]
[1,4,{"$nulls":11},1,4]
[1,4,{"$nulls":11},1,4]
[1,4,{"$nulls":11},1,4]
[1,4,{"$nulls":11},1,4]
[1,4,{"$nulls":11},1,4]
[1,4,{"$nulls":11},1,4]
[1,4,{"$nulls":11},1,4]
[1,4,{"$nulls":11},1,4]
[1,4,{"$nulls":11},1,4]
[1,5,{"$nulls":11},1,5]
[1,5,{"$nulls":11},1,5]
[1,5,{"$nulls":11},1,5]
[1,5,{"$nulls":11},1,5]
[1,5,{"$nulls":11},1,5]
[2,1,{"$nulls":11},2,1]
[2,1,{"$nulls":11},2,1]
[2,1,{"$nulls":11},2,1]
[2,1,{"$nulls":11},2,1]
[2,1,{"$nulls":11},2,1]
[2,1,{"$nulls":11},2,1]
[2,1,{"$nulls":11},2,1]
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{"sheet":"Uebung 5","index":8,"n_rows":89,"n_cols":14,"rows_kept":89}
["Alter (1 < 30; 2 31 - 50; 3 > 51)","Wohnort (1 Stadt; 2 Aglo; 3 Land)",null,null,"Passt die Stichprobe zur folgenden Populationsverteilung?",{"$nulls":6},"Alter"]
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[1,1,{"$nulls":7},"Wohnort","Aglo",0.2,0.03,0.235]
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{"sheet":"FisherBeispiel","index":9,"n_rows":79,"n_cols":6,"rows_kept":79}
[null,null,"Rauchverhalten"]
[null,null,"Raucher","Nichtraucher","Summen"]
["Geschlecht","Männer",12,34,{"$f":"SUM(C3:D3)","v":46}]
[null,"Frauen",11,43,{"$f":"SUM(C4:D4)","v":54}]
[null,"Summen",{"$f":"SUM(C3:C4)","v":23},{"$f":"SUM(D3:D4)","v":77},{"$f":"SUM(C5:D5)","v":100}]
[]
["zweiseitiger Test:"]
["erste Art: ","2*min(P(X<=12),P(X >=12))",null,null,"X hpergeometrisch verteilt."]
["P(X >=12)",{"$f":"1-_xlfn.HYPGEOM.DIST(11,23,46,100,1)","v":0.3297465046637198},"=1-HYPGEOM.VERT(11;23;46;100;1)"]
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["p-Wert",{"$f":"2*B9","v":0.6594930093274396}]
[]
["zweite Art:"]
["x","P(X=x)","P(X=x) < P(X = 12)"]
[0,{"$f":"_xlfn.HYPGEOM.DIST(A15,23,46,100,0)","v":4.3672558946068775E-8},{"$f":"IF(B15<=$B$27,B15,0)","v":4.3672558946068775E-8},{"$f":"SUM(C15:C49)","v":0.6342973735462956},"P-Wert"]
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[10,0.1816716273350661,0]
[11,0.18403099911863827,0]
[12,0.14979267370121713,0.14979267370121713]
[13,0.09794136357387269,0.09794136357387269]
[14,0.05130261901488575,0.05130261901488575]
[15,0.021413267067082752,0.021413267067082752]
[16,0.007061822117867721,0.007061822117867721]
[17,1.8173806920983085E-3,1.8173806920983085E-3]
[18,3.5853088483571915E-4,3.5853088483571915E-4]
[19,5.2836130396843273E-5,5.2836130396843273E-5]
[20,5.5944138067245465E-6,5.5944138067245465E-6]
[21,3.9960098619461274E-7,3.9960098619461274E-7]
[22,1.7135548293079342E-8,1.7135548293079342E-8]
[23,3.311217061464624e-10,3.311217061464624e-10]
[24,0,0]
[25,0,0]
[26,0,0]
[27,0,0]
[28,0,0]
[29,0,0]
[30,0,0]
[31,0,0]
[32,0,0]
[33,0,0]
[34,0,0]
[{"$nulls":4},"Variante"]
["3. Art","Quotenverhältnis (OR):",null,{"$f":"12*43/(11*34)","v":1.3796791443850267},{"$f":"12.5*43.5/(11.5*34.5)","v":1.3705103969754253}]
[null,"ln(OR)",null,{"$f":"LN(D51)","v":0.3218509680670308},{"$f":"LN(E51)","v":0.31518322299637536},"Teststatistik, näherungsweise normalverteilt (E(ln(=R))=0"]
[null,"Varianz(ln(OR))",null,{"$f":"1/12+1/34+1/11+1/43","v":0.22691000290179497},{"$f":"1/12.5+1/34.5+1/11.5+1/43.5","v":0.21893053473263369}]
[null,"Stabw(Ln(OR))",null,{"$f":"SQRT(E53)","v":0.46790013328982255},{"$f":"SQRT(E53)","v":0.46790013328982255}]
[null,"0.95-VI"]
[null,"untere Grenze",null,{"$f":"EXP(D52-1.96*D54)","v":0.5514339050907306},{"$f":"EXP(E52-1.96*E54)","v":0.5477693152406603},"R ist konservativer!!!!"]
[null,"obere Grenze",null,{"$f":"EXP(D52+1.96*D54)","v":3.451935987029675},{"$f":"EXP(E52+1.96*E54)","v":3.4289959221109605}]
[]
[null,"1 liegt im VI: also nicht signifikante Abweichung der OR von 1"]
[]
[]
["Mit R:"]
["> m=matrix(c(12,34,11,43),byrow=T,ncol=2)"]
["> m"]
["     [,1] [,2]"]
["[1,]   12   34"]
["[2,]   11   43"]
["> fisher.test(m)"]
[]
["        Fisher's Exact Test for Count Data"]
[]
["data:  m"]
["p-value = 0.6343"]
["alternative hypothesis: true odds ratio is not equal to 1"]
["95 percent confidence interval:"]
[" 0.4877661 3.9167187"]
["sample estimates:"]
["odds ratio "]
[1.375193]

{"sheet":"Uebung 5 (2)","index":10,"n_rows":117,"n_cols":17,"rows_kept":117}
["Alter (1 < 30; 2 31 - 50; 3 > 51)","Wohnort (1 Stadt; 2 Aglo; 3 Land)",null,null,"Passt die Stichprobe zur folgenden Populationsverteilung?",{"$nulls":10},"Alter","Wohnort"]
[2,1,{"$nulls":7},"Anteile in Grundgesamtheit",{"$nulls":5},2,1]
[1,1,{"$nulls":9},"Alter",{"$nulls":3},1,1]
[1,1,null,"H0: die Stichprobe passt zur Populationsverteilung (weicht nicht ab)",{"$nulls":7},"<= 30","30 - 50","50 - 100",null,1,1]
[3,1,null,"HA. Die Stichprobe passt nicht (weicht ab)",{"$nulls":6},"Stadt",0.05,0.15,0.2,null,3,1]
[1,2,null,"(Alpha = 0.05)",{"$nulls":5},"Wohnort","Aglo",0.2,0.03,0.235,null,1,2]
[3,2,{"$nulls":8},"Land",0.1,0.025,0.01,null,3,2]
[3,1,{"$nulls":13},3,1]
[2,2,{"$nulls":13},2,2]
[1,3,{"$nulls":13},1,3]
[1,2,{"$nulls":13},1,2]
[2,2,null,"Beobachtete Häufigkeiten",{"$nulls":11},2,2]
[1,2,{"$nulls":13},1,2]
[1,3,{"$nulls":3},"<= 30","30 - 50","50 - 100",{"$nulls":7},1,3]
[3,1,{"$nulls":3},1,2,3,"Randsummen",{"$nulls":6},3,1]
[3,2,null,"Stadt",1,{"$f":"SUM(IF(($B$2:$B$89=$E16)*($A$2:$A$89=F$15),1,0))","v":5},{"$f":"SUM(IF(($B$2:$B$89=$E16)*($A$2:$A$89=G$15),1,0))","v":6},{"$f":"SUM(IF(($B$2:$B$89=$E16)*($A$2:$A$89=H$15),1,0))","v":18},{"$f":"SUM(F16:H16)","v":29},{"$nulls":6},3,2]
[3,2,null,"Aglo",2,{"$f":"SUM(IF(($B$2:$B$89=$E17)*($A$2:$A$89=F$15),1,0))","v":9},{"$f":"SUM(IF(($B$2:$B$89=$E17)*($A$2:$A$89=G$15),1,0))","v":2},{"$f":"SUM(IF(($B$2:$B$89=$E17)*($A$2:$A$89=H$15),1,0))","v":16},{"$f":"SUM(F17:H17)","v":27},{"$nulls":6},3,2]
[3,1,null,"Land",3,{"$f":"SUM(IF(($B$2:$B$89=$E18)*($A$2:$A$89=F$15),1,0))","v":12},{"$f":"SUM(IF(($B$2:$B$89=$E18)*($A$2:$A$89=G$15),1,0))","v":5},{"$f":"SUM(IF(($B$2:$B$89=$E18)*($A$2:$A$89=H$15),1,0))","v":15},{"$f":"SUM(F18:H18)","v":32},{"$nulls":6},3,1]
[3,3,null,null,"Randsummen",{"$f":"SUM(F16:F18)","v":26},{"$f":"SUM(G16:G18)","v":13},{"$f":"SUM(H16:H18)","v":49},{"$f":"SUM(F16:H18)","v":88},{"$nulls":6},3,3]
[1,3,{"$nulls":13},1,3]
[1,3,{"$nulls":13},1,3]
[1,3,{"$nulls":13},1,3]
[1,1,{"$nulls":13},1,1]
[3,3,null,"erwartete Häufigkeiten",{"$nulls":11},3,3]
[3,1,{"$nulls":13},3,1]
[3,1,{"$nulls":3},"<= 30","30 - 50","50 - 100",{"$nulls":7},3,1]
[3,2,{"$nulls":3},1,2,3,"Randsummen",{"$nulls":6},3,2]
[3,2,null,"Stadt",1,{"$f":"L5*$I$19","v":4.4},13.2,17.6,{"$f":"SUM(F28:H28)","v":35.2},{"$nulls":6},3,2]
[3,2,null,"Aglo",2,17.6,2.6399999999999997,20.68,{"$f":"SUM(F29:H29)","v":40.92},{"$nulls":6},3,2]
[3,1,null,"Land",3,8.8,2.2,0.88,{"$f":"SUM(F30:H30)","v":11.88},{"$nulls":6},3,1]
[3,2,null,null,"Randsummen",{"$f":"SUM(F28:F30)","v":30.8},{"$f":"SUM(G28:G30)","v":18.04},{"$f":"SUM(H28:H30)","v":39.160000000000004},{"$f":"SUM(F28:H30)","v":88},{"$nulls":6},3,2]
[3,3,{"$nulls":13},3,3]
[3,2,null,null,"Achtung: Randsummen stimmen hier nicht überein!!!!! (Bei Vergleich mit vorgegebener (bivariater) Häufigkeitsverteilung der Fall)",{"$nulls":10},3,2]
[3,3,null,"Es hat vier erwartete Häufigkeiten unter 5, was ",{"$nulls":11},3,3]
[2,3,null,{"$f":"4/9*100","v":44.44444444444444},"% ausmacht. Deshalb sollt man eine Monte-Carlo-Analyse mit R vornehmen.",{"$nulls":10},2,3]
[2,3,{"$nulls":13},2,3]
[2,1,null,"(s. unten)",{"$nulls":11},2,1]
[1,2,{"$nulls":13},1,2]
[3,2,{"$nulls":13},3,2]
[1,1,{"$nulls":13},1,1]
[1,3,{"$nulls":13},1,3]
[1,2,{"$nulls":13},1,2]
[3,3,{"$nulls":13},3,3]
[2,1,{"$nulls":13},2,1]
[3,3,{"$nulls":13},3,3]
[2,3,null,"Mit R:",{"$nulls":11},2,3]
[3,3,null,"> wohnalt=read.table(\"clipboard\",header=T)",{"$nulls":11},3,3]
[3,1,null,"> head(wohnalt)",{"$nulls":11},3,1]
[3,3,null,"  Alter Wohnort",{"$nulls":11},3,3]
[3,2,null,"1     2       1",{"$nulls":11},3,2]
[3,1,null,"2     1       1",{"$nulls":11},3,1]
[3,1,null,"3     1       1",{"$nulls":11},3,1]
[1,2,null,"4     3       1",{"$nulls":11},1,2]
[2,1,null,"5     1       2",{"$nulls":11},2,1]
[3,3,null,"6     3       2",{"$nulls":11},3,3]
[1,3,null,"> tabWA=table(wohnalt$Wohnort,wohnalt$Alter)",{"$nulls":11},1,3]
[3,1,null,"> rownames(tabWA)=c(\"Stadt\",\"Aglo\",\"Land\")",{"$nulls":11},3,1]
[3,2,null,"> colnames(tabWA)=c(\"<= 30\",\"30 - 50\",\"50 - 100\")",{"$nulls":11},3,2]
[3,3,null,"> tabWA",{"$nulls":11},3,3]
[3,1,null,"       ",{"$nulls":11},3,1]
[1,3,null,"        <= 30 30 - 50 50 - 100",{"$nulls":11},1,3]
[2,1,null,"  Stadt     5       6       18",{"$nulls":11},2,1]
[3,3,null,"  Aglo      9       2       16",{"$nulls":11},3,3]
[3,2,null,"  Land     12       5       15",{"$nulls":11},3,2]
[1,2,null,"> beobH=c(tabWA[1,],tabWA[2,],tabWA[3,])",{"$nulls":4},"# Tabelle in Vektor umwandeln, Zeilenweises Einlesen der Häufigkeiten der Tabelle tabWA",{"$nulls":6},1,2]
[3,3,null,"> anteile=c(0.05,       0.15,   0.2,",{"$nulls":11},3,3]
[3,3,null,"+           0.2,        0.03,   0.235,",{"$nulls":11},3,3]
[3,2,null,"+           0.1 ,0.025, 0.01)",{"$nulls":11},3,2]
[2,3,null,"> WAtest=chisq.test(beobH,p=anteile)",{"$nulls":11},2,3]
[1,2,null,"Warning message:",{"$nulls":11},1,2]
[1,3,null,"In chisq.test(beobH, p = anteile) :",{"$nulls":11},1,3]
[3,1,null,"  Chi-Quadrat-Approximation kann inkorrekt sein",{"$nulls":11},3,1]
[3,2,{"$nulls":13},3,2]
[3,1,null,"Die rote Fehlermeldung rührt daher, dass es zu viele erwartete Häufigkeiten unter 5 hat.",{"$nulls":11},3,1]
[1,1,{"$nulls":13},1,1]
[1,3,null,"Das kann man mit R überprüfen:",{"$nulls":11},1,3]
[1,2,null,"> WAtest$expected",{"$nulls":11},1,2]
[3,2,null,"   <= 30  30 - 50 50 - 100    <= 30  30 - 50 50 - 100    <= 30  30 - 50 50 - 100 ",{"$nulls":11},3,2]
[3,2,null,"    4.40    13.20    17.60    17.60     2.64    20.68     8.80     2.20     0.88 ",{"$nulls":11},3,2]
[1,3,{"$nulls":13},1,3]
[3,1,{"$nulls":13},3,1]
[3,3,null,"Mit ",{"$nulls":11},3,3]
[3,1,null,"> chisq.test(beobH,p=anteile,simulate.p.value = T)",{"$nulls":11},3,1]
[3,1,{"$nulls":13},3,1]
[2,3,null,"        Chi-squared test for given probabilities with simulated p-value (based on",{"$nulls":11},2,3]
[1,3,null,"        2000 replicates)",{"$nulls":11},1,3]
[2,1,{"$nulls":13},2,1]
[3,3,null,"data:  beobH",{"$nulls":11},3,3]
[3,1,null,"X-squared = 240.72, df = NA, p-value = 0.0004998",{"$nulls":11},3,1]
[]
[]
[{"$nulls":3},"Es gibt also singifikante Abweichungen"]
[]
[]
[{"$nulls":3},"Residuenanalyse"]
[{"$nulls":3},"> WA1test=chisq.test(beobH,p=anteile,simulate.p.value = T)"]
[{"$nulls":3},"> WA1test$residuals"]
[{"$nulls":3},"      <= 30     30 - 50    50 - 100       <= 30     30 - 50    50 - 100       <= 30 "]
[{"$nulls":3}," 0.28603878 -1.98173478  0.09534626 -2.04994457 -0.39389277 -1.02913082  1.07871978 "]
[{"$nulls":3},"    30 - 50    50 - 100 "]
[{"$nulls":3}," 1.88775961 15.05197057 "]
[{"$nulls":3},"> WA1test$stdres"]
[{"$nulls":3},"     <= 30    30 - 50   50 - 100      <= 30    30 - 50   50 - 100      <= 30 "]
[{"$nulls":3}," 0.2934696 -2.1494932  0.1066004 -2.2919077 -0.3999375 -1.1766299  1.1370705 "]
[{"$nulls":3},"   30 - 50   50 - 100 "]
[{"$nulls":3}," 1.9118085 15.1277996 "]
[]
[{"$nulls":3},"> matrix(WA1test$stdres,ncol=3,byrow=T)"]
[{"$nulls":3},"           [,1]       [,2]       [,3]"]
[{"$nulls":3},"[1,]  0.2934696 -2.1494932  0.1066004"]
[{"$nulls":3},"[2,] -2.2919077 -0.3999375 -1.1766299"]
[{"$nulls":3},"[3,]  1.1370705  1.9118085 15.1277996"]
[]
[{"$nulls":3},"signifikante Abweichungen in (1,2), (2,1) und (3,3)"]
[]
[]
[{"$nulls":3},"Schlussfolgerung: Die Stichprobe kann nicht als Zufallsstichprobe aus der Grundgesamtheit betrachtet werden."]