chapter 1

Chapter 11: Multifactor Analysis of Variance51.Source Df SS MS fA 1 322.667 322.667 980.38B 3 35.623 11.874 36.08AB 3 8.557 2.852 8.67Error 16 5.266 .329Total 23 372.113We first test the null hypothesis of no interactions ( : 0H γ for all I, j). H o will be0 ij=MSABrejected at level .05 if f AB = ≥ F. 05,3,16 = 3. 24 . Because 8.67≥ 3. 24 , H o isMSErejected. Because we have concluded that interaction is present, tests for main effects are notappropriate.52. Let Xij= the amount of clover accumulation when the i th sowing rate is used in the j th plot =µ + α + β + e . H α = α = α = α 0 will be rejected iffiMSTrMSEjij0:1 2 3 4== ≥ Fα, I−1,(I−1)(J −1)= F.05,3,9=3.86Source Df SS MS fTreatment 3 3,141,153.5 1,040,751.17 2.28Block 3 19,470,550.0Error 9 4,141,165.5 460,129.50Total 15 26,752,869.0Because 2 .28 < 3. 86 , H o is not rejected. Expected accumulation does not appear to dependon sowing rate.344