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112 8 REML analysis of unbalanced designs8.5 Analysis of variance by ANOVA, regression or REMLIn the earlier chapters of this Guide,you have seen that, if your design isbalanced you can produce an analysisif variance using the Analysis ofVariance menu (Figure 1.8), or youmay be able to use the One- and TwowayAnalysis of Variance menu (Figure1.14) if you have no more than twotreatment factors. GenStat will tellyou if the design is unbalanced.Figure 8.8Then, if it has only one error term you can use the Unbalanced ANOVA menu (Figure 7.9),or if it has several you can use the Linear Mixed Models menu (Figure 8.1). A smallcomplication is that you might want to use the Unbalanced ANOVA menu rather than theLinear Mixed Models menu, even when there several error terms, if the additional errorterms contain very little information about the treatments (and this was why we did notuse the Linear Mixed Models menu in Section 7.6).So you could define a set of rulesto decide how to analyse acomplicated design. However, youmight prefer GenStat to do this foryou and, in fact, it will do so if youuse the menu for Analysis of varianceby ANOVA, regression or REML. Figure8.9 shows the use of the menu toanalyse the production data inSection 7.6.Figure 8.9The Options menu (Figure 8.10)allows you to select only the types ofoutput that are available from all thepossible methods of analysis. Youcan also say how much information(i.e. efficiency) you are prepared tolose on any treatment term whendeciding to use whether to use theUnbalanced ANOVA menu (which usesregression) rather than the LinearMixed Models menu (which usesREML). The Information section willcontain details of the recommendedmethod, and the amount ofinformation that may have been lost.The output, below, confirms that it Figure 8.10was acceptable to use UnbalancedANOVA in Section 7.6: less than 1% of the information has been lost.
8.6 Practical 113Analysis of variance by ANOVA, REML or regressionInformation summaryDesign unbalanced with weights or more than 2 treatment factors, and no more than 0.801%of information on any contrast estimated between block terms; analyse by AUNBALANCED.Accumulated analysis of varianceChange d.f. s.s. m.s. v.r. F pr.+ day 1 914.0 914.0 3.67 0.061+ A 2 1706.8 853.4 3.42 0.041+ B 2 418.8 209.4 0.84 0.438+ C 1 1065.9 1065.9 4.28 0.044+ A.B 4 1166.0 291.5 1.17 0.336+ A.C 2 2456.7 1228.3 4.93 0.011+ B.C 2 284.4 142.2 0.57 0.569+ A.B.C 4 1397.4 349.4 1.40 0.248Residual 48 11960.4 249.2Total 66 21370.4 323.88.6 PracticalRe-analyse the data in Vartrial1.gsh using the menu for Analysis of variance byANOVA, regression or REML.
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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
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40 3 Treatment structureblock.*Unit
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42 3 Treatment structureTables of c
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44 3 Treatment structureN * Swas us
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46 3 Treatment structureFumigant Am
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48 3 Treatment structureFumigated S
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50 3 Treatment structureCovariate 1
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4 Checking the assumptionsIn this c
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54 4 Checking the assumptions4.2 No
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56 4 Checking the assumptions4.5 Tr
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58 4 Checking the assumptionsFigure
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60 4 Checking the assumptionsThe pr
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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
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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
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Page 102 and 103: 8 REML analysis of unbalanced desig
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Page 118 and 119: 9 Commands for analysis of variance
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Page 124 and 125: IndexA2DISPLAY procedure 117A2WAY p
Page 126: 122 IndexTransformation 56logarithm
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