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90 7 Balance and non-orthogonalityfoster mother. It was impossible to balance the numbers of litters over the two factors,and so the design is unbalanced.The One- and two-way Analysis ofVariance menu (Figure 7.6)automatically detects that a design isunbalanced, and calculates theanalysis instead by using theGenStat regression commands.The analysis-of-variance table ismodified so that it shows the effectof fitting each of the factors eitherbefore or after the other one. So theline "mother ignoring litter"fits the effect of mother first. Thealternative line " motherFigure 7.6elimining litter" fits the effect of mother after fitting the litter effect. So itlooks to see if there are any effects of the foster mother that cannot be explained by thegenotype of the litter itself. (Remember, though, that interactions are always fitted aftertheir main effects.)Notice that the means are now predicted means (from the GenStat PREDICT directive).These are accompanied by a summary of the standard errors of difference over the pairof means within the table. You can print s.e.d.'s for every possible comparison of pairsof means within the table, by using the Unbalanced ANOVA menu, as shown in Section 7.6.Analysis of varianceSource d.f. s.s. m.s. v.r. F pr.mother ignoring litter 3 771.61 257.20 4.74 0.006mother eliminating litter 3 775.08 258.36 4.76 0.006litter ignoring mother 3 60.16 20.05 0.37 0.775litter eliminating mother 3 63.63 21.21 0.39 0.760mother.litter 9 824.07 91.56 1.69 0.120Residual 45 2440.82 54.24Total 60 4100.13 68.34Predictions from regression modelResponse variate: littwtPredictionmotherA 54.79B 58.08I 53.60J 48.34Minimum standard error of difference 2.641Average standard error of difference 2.753
Maximum standard error of difference 2.8637.5 Practical 91Predictions from regression modelResponse variate: littwtPredictionlitterA 54.97B 53.07I 52.82J 53.50Minimum standard error of difference 2.659Average standard error of difference 2.755Maximum standard error of difference 2.848Predictions from regression modelResponse variate: littwtPredictionlitter A B I JmotherA 63.68 52.32 47.10 54.35B 52.40 60.64 64.37 56.10I 54.13 53.92 51.60 54.53J 48.96 45.90 49.43 49.06Minimum standard error of difference 4.658Average standard error of difference 5.499Maximum standard error of difference 6.7237.5 PracticalSpreadsheet file Unbalanced2way.gsh(Figure 7.7) contains results from an experimentwith two factors A and B. Analyse the responsevariate Y using the One- and two-way Analysis ofVariance menu.Figure 7.7
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Anova and Design
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ContentsIntroduction 11 From t-test
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1 From t-test to one-way anovaIn th
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4 1 From t-test to one-way anovaIf
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6 1 From t-test to one-way anovaWe
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8 1 From t-test to one-way anova1.2
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10 1 From t-test to one-way anovawi
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12 1 From t-test to one-way anovaAl
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14 1 From t-test to one-way anovaYo
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16 1 From t-test to one-way anovaFi
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18 1 From t-test to one-way anovaTa
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20 1 From t-test to one-way anovaTh
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2 Blocking structuresThe blocking s
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24 2 Blocking structuresBlock 1D4.6
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26 2 Blocking structuresNow we repe
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28 2 Blocking structureswould give
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30 2 Blocking structuresAnalysis of
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3 Treatment structureSo far we have
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34 3 Treatment structureTables of m
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36 3 Treatment structureFigure 3.3
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38 3 Treatment structureThere is a
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
Page 92 and 93: 88 7 Balance and non-orthogonalityF
Page 96 and 97: 92 7 Balance and non-orthogonality7
Page 98 and 99: 94 7 Balance and non-orthogonalityM
Page 100 and 101: 96 7 Balance and non-orthogonalityM
Page 102 and 103: 8 REML analysis of unbalanced desig
Page 104 and 105: 100 8 REML analysis of unbalanced d
Page 118 and 119: 9 Commands for analysis of variance
Page 120 and 121: 116 9 Commands for analysis of vari
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Page 124 and 125: IndexA2DISPLAY procedure 117A2WAY p
Page 126: 122 IndexTransformation 56logarithm
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