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62 4 Checking the assumptionsTotal 47 25.6721Tables of meansVariate: Absolute residualsGrand mean 0.682Type 1 2 3 40.584 0.594 1.259 0.291Standard errors of differences of meansTable Typerep. 12d.f. 33s.e.d. 0.1711Levene tests for stability of varianceTest t-statistic d.f.pr.Small vs. large responses 2.285 12.7030.040Intermediate v.s. small & large responses 1.906 16.7620.074Shapiro-Wilk test for NormalityData variate: ResidualsTest statistic W: 0.9351Probability: 0.011Message: evidence of non-homogeneity of residual variance for Type andHaul.Message: the Shapiro-Wilk test shows evidence of non-Normality.The output shows that the type-3 plankton numbers are more variable than the othertypes. (This is not surprising as many more of this type of plankton have been recordedin the experiment than the other types.)If we repeat the analysis with the log-transformed numbers, there is no evidence thatthe assumptions are broken, and no warnings are given.
4.6 Practical 634.7 PracticalAn experiment was conducted to assess the percentage of alcohol by volume of five typesof wine labelled A to E. Three bottles of each type were tested in the laboratory in arandom order, as listed below and stored in file Wine.gsh.E 4.931D 7.263A 4.857C 3.361B 6.871E 4.141C 3.164B 3.012A 5.668D 12.185B 4.223E 3.323A 4.668C 2.686D 7.776Analyse the experiment and plot a graph of the residuals against the fitted values.Transform the data using a logit transformation, re-analyse the data and plot anothergraph of residuals against fitted values.4.8 Permutation and exact testsIf the distributional assumptions for the analysis of variance are not satisfied, you mightuse a permutation test an alternative way to assess the significance of the terms in theanalysis. You still need the model to be additive for the results to be meaningful, butthere is no longer any need for the residuals to follow Normal distributions with equalvariances.Clicking on the Permutation Testbutton in the ANOVA Further Outputmenu (Figure 1.10) produces themenu in Figure 4.17. This asksGenStat to make 4999 randompermutations of the values of theresponse variate (see the Number ofpermutations box), and repeat theanalysis with each one. The Seedbox specifies the seed to use for therandom-number generator that isFigure 4.17used to construct the permutations. The value 0 initializes the seed automatically (andprints the value in the output) if this is the first use of the generator in this run of GenStat;otherwise the seed is chosen to continue the existing sequence.The probability for each treatment term is now determined from its distribution overthe randomly permuted data sets. The output below prints a probability value
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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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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 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 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 94 and 95: 90 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
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112 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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