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18 1 From t-test to one-way anovaTables of contrastsVariate: weightdiet contrastsLin 0.54, s.e. 0.112, ss.div. 40.0Quad -0.111, s.e. 0.0951, ss.div. 56.0Deviations, e.s.e. 0.356, ss.div. 4.00diet a b c d e0.11 -0.26 0.11 0.11 -0.07Equation of the polynomial for diet80.46 + 0.98 * diet - 0.11 * diet**2The orthogonal polynomials cannot be printed from the menu, but they can be saved bythe AKEEP directive, and printed by the PRINT directive; see Chapter 9 for more details.1.7 PracticalSpreadsheet Octane.gsh contains data from anexperiment to study the effect of different additives on theoctane level of gasoline (P.W.M. John, Statistical Designand Analysis of Experiments, page 46). There were 5 typesof gasoline (A-E), and 4 observations on each. Use analysisof variance to assess whether there are differences in octanelevel between the gasolines.Suppose that gasolines A-E contain 0, 1, 2, 3 and 4cc/gallon of additive, respectively (but are otherwiseidentical). Estimate the linear and quadratic effects of theadditive.Figure 1.17
1.8 Multiple comparisons1.8 Multiple comparisons 19Multiple-comparison tests are designed to take account of the fact that there may be manypossible comparisons between pairs of treatment means in an analysis of variance (witht treatments there are t × (t1) / 2). So, some researchers feel that their significance levelsshould be adjusted to take account of all the tests that they might make and this can beachieved by use of a multiple-comparison test. Conversely, it has been pointed out thatmultiple-comparisons are unnecessary if you have only a small number of comparisonsto make either because there are few treatments, or because you should have identifiedbeforehand the comparisons that you feel are likely to be of interest. Also, they areinappropriate if the treatments have any sort of structure. For example, the levels of atreatment factor may represent different amounts of a substance like a fertiliser or a drug.It would then be more sensible to assess the treatment effect over all its levels by fittingsome sort of trend (like the polynomial contrasts that we fitted in Section 1.6), andillogical to assume that only some of the amounts might have an effect.Figure 1.18However, GenStat does have menusif you do need to use multiplecomparisontests. Because someorganisations may want todiscourage their use, these can beenabled and disabled through the Figure 1.19Options menu. You open the menuby clicking on the Options option of the Tools menu on the menu bar (Figure 1.18). In themenu (Figure 1.19), you need to select the Menus tab, and check the box Show MultipleComparisons on ANOVA menu.
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 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 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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68 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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