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O Aplia Student Question x C O courses aplia.com/af/servlet/quiz?quiz action takeQuiz&quiz; probGuida 01 70080000&ctx; thomas myers1-00038 00000036c7fa Set None Law Level High-Level Set Total 101 110 92 93 124 B 93 102 112 307 B 92 109 C 92 104 112 P 308 125 C 107 D 95 106 115 316 91 P-323 D 122 110 372 T-413 14,7SSRS 1,249 The between-treatments variance is The between-treatments variance is The between-subjects variance is The between-subjects variance is (Hint: Since this is a matched-subjects design, the between-subjects variance describes variance due to the differences between the sets of matched subjects. It can be calculated by computing Msbetween sutrects ssbetaren subyects/dfbetween subwects The error variance is The error variance is O Type here to searchExplanation / Answer
Outcome A:
T1 = 398, T2 = 406, T3 = 404
G = 1208
CM, the correction for the mean = (1208)^2/12 = 121605.3
SST = Sum of Square of treatments/Number of subjects - CM
= 398^2/4 + 406^2/4 + 404^2/4 - 121605.3 = 8.7
MST = SST/k-1 = 8.7/(3-1) = 4.35
SSSubjects = Sum of Square of Subjects/Number of treatments - CM
= 294^2/3 + 279^2/3 + 312^2/3 + 323^2/3 - 121605.3 = 378.0333
MSSubjects = SSSubjects/n-1 = 378.0333/(4-1) = 126.01
Between treatments variance = 4.35
Between Subjects variance = 126.01
SStotal = (77^2 + 93^2 + 124^2 + 92^2 + 78^2 + 109^2 + 107^2 + 125^2 + 80^2 + 122^2 + 110^2 + 91^2) - 121605.3
3516.7
SSE = SStotal - SST = 3516.7 - 8.7 = 3508
MSE = SSE/N-k = 3508/(12-3) = 389.78
Error Variance = 389.78
Outcome B:
T1 = 372, T2 = 413, T3 = 449
G = 1234
CM, the correction for the mean = (1234)^2/12 = 126896.3
SST = Sum of Square of treatments/Number of subjects - CM
= 372^2/4 + 413^2/4 + 449^2/4 - 126896.3 = 742.2
MST = SST/k-1 = 742.2/(3-1) = 371.1
SSSubjects = Sum of Square of Subjects/Number of treatments - CM
= 303^2/3 + 307^2/3 + 308^2/3 + 316^2/3 - 126896.3 = 29.7
MSSubjects = SSSubjects/n-1 = 378.0333/(4-1) = 9.9
Between treatments variance = 371.1
Between Subjects variance = 9.9
SStotal = (92^2 + 101^2 + 110^2 + 93^2 + 102^2 + 112^2 + 92^2 + 104^2 + 112^2 + 95^2 + 106^2 + 115^2) - 126896.3
775.7
SSE = SStotal - SST = 775.7 - 742.2 = 33.5
MSE = SSE/N-k = 33.5/(12-3) = 3.72
Error Variance = 3.72
Outcome A appears to have smaller between-treatments variance than (as) outcome B.
Outcome A appears to have greater between-subjects variance than (as) outcome B.
F for outcome A = MST/MSE = 4.35/389.78 = 0.01
F for outcome B = MST/MSE = 371.1/3.72 = 99.75
Outcome A has smaller F-ratio than (as) outcome B.
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