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76 6 Design and sample sizeClicking OK in Figure 6.3, pops ups the menu shownin Figure 6.4, which indicates the required number ofreplicates. You can then either click Apply to enter thatnumber automatically into the design menu (Figure6.1), click Cancel to close the menu with no actions, orclick Change to return to the Replications Required menu(Figure 6.4). The result here, of 4, matches what we had Figure 6.4hoped to find (and the value that we had already enteredinto the main menu!). So we can simple click Cancel.The Replication and SEDs boxes were checked in Figure 6.3, so GenStat prints a tablegiving the power (and the standard errors of differences) for up to 20 replicates, and areport of the required replication.PowerNumber of Residual Residual s.e.d. RESPONSE t-value Powerreplicates d.f. m.s. / s.e.d.2 5 0.5000 0.7071 2.121 2.015 0.5723 10 0.5000 0.5774 2.598 1.812 0.7804 15 0.5000 0.5000 3.000 1.753 0.8885 20 0.5000 0.4472 3.354 1.725 0.9446 25 0.5000 0.4082 3.674 1.708 0.9737 30 0.5000 0.3780 3.969 1.697 0.9878 35 0.5000 0.3536 4.243 1.690 0.9949 40 0.5000 0.3333 4.500 1.684 0.99710 45 0.5000 0.3162 4.743 1.679 0.99911 50 0.5000 0.3015 4.975 1.676 0.99912 55 0.5000 0.2887 5.196 1.673 1.00013 60 0.5000 0.2774 5.408 1.671 1.00014 65 0.5000 0.2673 5.612 1.669 1.00015 70 0.5000 0.2582 5.809 1.667 1.00016 75 0.5000 0.2500 6.000 1.665 1.00017 80 0.5000 0.2425 6.185 1.664 1.00018 85 0.5000 0.2357 6.364 1.663 1.00019 90 0.5000 0.2294 6.538 1.662 1.00020 95 0.5000 0.2236 6.708 1.661 1.000ReplicationTo detect a treatment difference of 1.500, at a significance level of 0.050,with a power of 0.800, using a one-sided test, requires a replication of 4.The Replications required button is available for any design where the replication can bemodified simply by altering the levels of one of the factors (for example split-plotdesigns, split-split-plot designs, criss-cross designs and so on), but not e.g. for Latinsquares where the replication cannot be changed without changing the number of levelsof the treatment factor.
6.1 Designing an experiment 77The Generate a Standard Design menu (Figure 6.1) will now be back as the activewindow. We have set our options and checked that the replication will be sufficient. Sowe now click on Run to generate the design, and the output below.Treatment combinations on each unit of the designLaboratory 1 2 3 4Subject1 1 1 3 1 3 2 1 12 3 2 2 1 1 1 1 23 2 1 3 2 1 2 3 14 1 2 1 1 2 2 3 25 2 2 1 2 3 1 2 16 3 1 2 2 2 1 2 2Treatment factors are listed in the order: Drug, Dose.Analysis of varianceSource of variationd.f.Laboratory stratum 3Laboratory.Subject stratumDrug 2Dose 1Drug.Dose 2Residual 15Total 23The Display design in spreadsheetbox was checked in the Generate aStandard Design menu in Figure 6.1.So the design factors are loaded intoa new spreadsheet as shown inFigure 6.5. GenStat's spreadsheetfacilities can now be used toredefine the factor levels or tospecify labels. To do this, you clickSpread on the menu bar, followed byFactor and then either Edit Levels orEdit Labels as required.Figure 6.5
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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
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
Page 78 and 79: 74 6 Design and sample size6.1 Desi
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
Page 118 and 119: 9 Commands for analysis of variance
Page 120 and 121: 116 9 Commands for analysis of vari
Page 122 and 123: 118 9 Commands for analysis of vari
Page 124 and 125: IndexA2DISPLAY procedure 117A2WAY p
Page 126: 122 IndexTransformation 56logarithm
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