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38 3 Treatment structureThere is a box controlling theprinting of contrasts in the Displaysection of the ANOVA options menu(obtained as usual by clicking on theOptions button in the main Analysisof Variance menu). In Figure 3.9, wehave checked this together with theAOV Table and F-probabilities boxes.These request the output below.Figure 3.9Analysis of varianceVariate: yieldSource of variation d.f. s.s. m.s. v.r. F pr.block stratum 2 0.30850 0.15425 3.44block.*Units* stratumN 2 4.59223 2.29611 51.22
3.2 Fitting contrasts 39S 0 10 20 40-0.35 -0.18 0.21 0.32Notice that, in the analysis-of-variance table, the line for the main effect N is nowaccompanied by a line entitled "0 versus 180 and 230" giving the degrees offreedom, sum of squares and so on for that comparison. In addition the N.S interactionis accompanied by a line "0 versus 180 and 230.S" which represents theinteraction between the comparison and the factor S (that is, it measures how the size ofthe comparison varies according to the level of S).The section headed "Tables of contrasts" then shows the estimate of thecontrast, 0.754, with standard error 0.0749. The "ss. div" value is analogous to thereplication of a table of means or effects: it is the divisor used in calculating the estimatedvalues of the contrasts. This is useful mainly where there is a range of e.s.e.'s for a tableof contrasts: the contrasts with the smallest values of the ss. div. are those with the largeste.s.e., and vice versa. (The ss. div. of each estimated contrast is in fact the sum of squaresof the values of the coefficients used to calculate it, weighted according to thereplication.) The N.S contrasts table shows how the overall value of the contrast variesaccording to the level of S. So, at level 0 of S, the estimated contrast is 0.7540.35.When a factor like sulphur (or nitrogen) has quantitative levels, you might want toinvestigate whether the yield increases linearly with the amount of sulphur (or nitrogen);you could also include a quadratic term to check for curvature in the response.Put the cursor into the Treatment 2box of the Analysis of Variance menu,and click on the Contrasts button toproduce the Anova Contrasts menuagain. To fit polynomial contrasts ofsulphur, we select Polynomial withinthe Contrast Type box in the ANOVAContrasts menu, set the ContrastFactor to S, and (for a quadraticpolynomial) set the Number ofContrasts to 2; see Figure 3.10. Afterwe click on OK, the Treatment 2 boxof the Analysis of Variance menu willFigure 3.10contain the function POL(S;2). If we change the setting of the Treatment 1 box back toN, and then click on Run, we obtain the output below.Analysis of varianceVariate: yieldSource of variation d.f. s.s. m.s. v.r. F pr.block stratum 2 0.30850 0.15425 3.44
Page 1 and 2: Anova and Design
Page 4 and 5: ContentsIntroduction 11 From t-test
Page 6 and 7: 1 From t-test to one-way anovaIn th
Page 8 and 9: 4 1 From t-test to one-way anovaIf
Page 10 and 11: 6 1 From t-test to one-way anovaWe
Page 12 and 13: 8 1 From t-test to one-way anova1.2
Page 14 and 15: 10 1 From t-test to one-way anovawi
Page 16 and 17: 12 1 From t-test to one-way anovaAl
Page 18 and 19: 14 1 From t-test to one-way anovaYo
Page 20 and 21: 16 1 From t-test to one-way anovaFi
Page 22 and 23: 18 1 From t-test to one-way anovaTa
Page 24 and 25: 20 1 From t-test to one-way anovaTh
Page 26 and 27: 2 Blocking structuresThe blocking s
Page 28 and 29: 24 2 Blocking structuresBlock 1D4.6
Page 30 and 31: 26 2 Blocking structuresNow we repe
Page 32 and 33: 28 2 Blocking structureswould give
Page 34 and 35: 30 2 Blocking structuresAnalysis of
Page 36 and 37: 3 Treatment structureSo far we have
Page 38 and 39: 34 3 Treatment structureTables of m
Page 40 and 41: 36 3 Treatment structureFigure 3.3
Page 44 and 45: 40 3 Treatment structureblock.*Unit
Page 46 and 47: 42 3 Treatment structureTables of c
Page 48 and 49: 44 3 Treatment structureN * Swas us
Page 50 and 51: 46 3 Treatment structureFumigant Am
Page 52 and 53: 48 3 Treatment structureFumigated S
Page 54 and 55: 50 3 Treatment structureCovariate 1
Page 56 and 57: 4 Checking the assumptionsIn this c
Page 58 and 59: 54 4 Checking the assumptions4.2 No
Page 60 and 61: 56 4 Checking the assumptions4.5 Tr
Page 62 and 63: 58 4 Checking the assumptionsFigure
Page 64 and 65: 60 4 Checking the assumptionsThe pr
Page 66 and 67: 62 4 Checking the assumptionsTotal
Page 68 and 69: 64 4 Checking the assumptionsMessag
Page 70 and 71: 66 5 Designs with several error ter
Page 78 and 79: 74 6 Design and sample size6.1 Desi
Page 80 and 81: 76 6 Design and sample sizeClicking
Page 82 and 83: 78 6 Design and sample sizeFigure 6
Page 84 and 85: 80 6 Design and sample sizeFigure 6
Page 86 and 87: 82 7 Balance and non-orthogonality7
Page 88 and 89: 84 7 Balance and non-orthogonalityA
Page 90 and 91: 86 7 Balance and non-orthogonalityT
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88 7 Balance and non-orthogonalityF
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90 7 Balance and non-orthogonalityf
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92 7 Balance and non-orthogonality7
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94 7 Balance and non-orthogonalityM
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96 7 Balance and non-orthogonalityM
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8 REML analysis of unbalanced desig
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100 8 REML analysis of unbalanced d
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9 Commands for analysis of variance
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116 9 Commands for analysis of vari
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118 9 Commands for analysis of vari
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IndexA2DISPLAY procedure 117A2WAY p
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122 IndexTransformation 56logarithm
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