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58 4 Checking the assumptionsFigure 4.8 Figure 4.9Figure 4.8 shows the residual plot from the untransformed analysis, and Figure 4.9 showsthe residual plot from the analysis of the log-transformed numbers. The output from thetransformed is shown below. The untransformed fitted-value plot shows clear evidencethat the variance is increasing with the size of the number which is corrected in thetransformed analysis.Analysis of varianceVariate: Log10numberSource of variation d.f. s.s. m.s. v.r. F pr.Haul stratum 11 0.337442 0.030677 4.41Haul.*Units* stratumType 3 20.169765 6.723255 965.74
s.e.d. 0.03414.5 Transformations 59If you are analysing transformed data, it isimportant to remember that the statisticalproperties of the analysis apply only on thetransformed scale. So, for example,comparisons between means must be assessedon the transformed scale (i.e. using the tables ofmeans and s.e.d.'s, or l.s.d.'s, from the analysisof the transformed data). For interpretation,though, it is often helpful also to present thetables of means back-transformed to theoriginal scale. These values are often given inbrackets under the transformed values. To save Figure 4.10the means, you click on the Save button on theAnalysis of Variance menu, to open the ANOVA Save Options menu. Check the Means box,and then fill in an identifier for the table (here Meanlogplankton) to store the means.You can calculate the backtransformthe means by using theCalculate menu (accessible from theData menu on the menu bar); seeFigure 4.11. You can then displaythe tables by selecting the twotables, making a right-mouse click,and clicking on the Display line toopen the Display Data in OutputWindow menu (Figure 4.13).Figure 4.11Figure 4.12Figure 4.13
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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
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 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 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 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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108 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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