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24 2 Blocking structuresBlock 1D4.6A7.3C5.5B6.3UPBlock 2A6.6C5.4D4.1B5.9HIBlock 3B5.6D3.5C4.9A6.0LLThe treatment occurs exactly once in each block. So, provided the units within each blockgenuinely are similar, the allocation of treatments to units will be fair overall. Here theneed for blocking seems clear: the yields from plots at the top of the slope can reasonablybe expected to be larger than the yields from plots at the bottom of the slope.Other situations may require more thought, whileothers may be more under your own control. Forexample you might decide to run an industrialexperiment on several days, and use blocking toremove any systematic differences between days.You do not need to know exactly what thesedifferences might be (temperature? humidity?motivation of the workforce?), merely that they arelikely to occur and be greater than those thatoccur within a day. As we shall see later, theanalysis will show whether you have selected thecriteria for blocking successfully.The easiest situation is when the grouping is aninnate characteristic of the experimental units.Spreadsheet file Ratlitters.gsh contains data fromanother rat-feeding experiment (John & Quenouille,1977, Experiments Design and Analysis, page 32).This has eight litters, each with five rats. Rats fromthe same litter can reasonably be assumed to beFigure 2.1more similar than rats from different litters. So the experiment was set up with littersacting as blocks i.e. the five diets (A-E) were allocated at random to the five rats withineach litter.
The advantage of the blocking canbe demonstrated by comparing theanalysis taking blocks into accountwith the analysis ignoring blocks.First we analyse the experimentignoring blocks, and analyse thedata as if the experiment werecompletely randomized (Figure 2.2).2.2 Randomized block designs 25Figure 2.2Analysis of varianceVariate: GainSource of variation d.f. s.s. m.s. v.r. F pr.Diet 4 346.9 86.7 0.42 0.794Residual 35 7237.2 206.8Total 39 7584.1Tables of meansVariate: GainGrand mean 65.3Diet A B C D E62.6 65.4 64.2 63.3 70.9Standard errors of differences of meansTable Dietrep. 8d.f. 35s.e.d. 7.19
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 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 42 and 43: 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
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74 6 Design and sample size6.1 Desi
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76 6 Design and sample sizeClicking
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78 6 Design and sample sizeFigure 6
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80 6 Design and sample sizeFigure 6
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82 7 Balance and non-orthogonality7
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84 7 Balance and non-orthogonalityA
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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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