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Chapter 11: Multifactor Analysis of Variance32.a. SinceE( MSABC )E( MSE)σ=2+ Lσσ22ABC= 12if = 02σ and > 1 if > 0ABCσ ,MSABC is the appropriate F ratio for testing :2MSCH0σABC= 0 . Similarly, isMSEMSE2 MSABH0: σC= ; is the F ratio for testing H0 : allMSABCthe F ratio for testing 0ABCABγijMSA= 0 ; and is the F ratio for testing H : allMSAC0 i= 0α .b.Source Df SS MS f F .01MSAA 1 14,318.24 14,318.24 =19. 85MSACMSBB 3 9656.4 3218.80 = 6. 24MSBCMSCC 2 2270.22 1135.11 = 3. 15MSEMSABAB 3 3408.93 1136.31 = 2. 41MSABCMSACAC 2 1442.58 721.29 = 2. 00MSABCMSBCMSEMSABCMSEBC 6 3096.21 516.04 =1. 43ABC 6 2832.72 472.12 =1. 31Error 24 8655.60 360.65Total 4798.50At level .01, no H o ’s can be rejected, so there appear to be no interaction or main effectspresent.9.785.619.785.613.673.6733.Source Df SS MS fA 6 67.32 11.02B 6 51.06 8.51C 6 5.43 .91 .61Error 30 44.26 1.48Total 48 168.07Since .61 < F 2. 42 , treatment was not effective.. 05,6,30=332

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