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108 8 REML analysis of unbalanced designsreplicates 1 rows 4 columns 3 -1.665 approx. s.e. 0.623replicates 1 rows 5 columns 2 1.710 approx. s.e. 0.623Tables of meansVariate: yieldGrand mean 14.704variety 1 2 3 4 5 6 712.962 15.561 14.152 14.560 15.481 15.358 14.008variety 8 9 10 11 12 13 1414.428 12.968 11.928 13.222 14.835 16.176 13.187variety 15 16 17 18 19 20 2115.067 13.287 14.968 15.881 16.742 16.277 15.048variety 22 23 24 2516.430 13.283 15.464 16.344Standard errors of differences of meansTable varietyrep. 6d.f. 72s.e.d. 0.6363Notice that the analysis-of-variance table has three lines for variety. As each rowcontains a different set of varieties, the differences between the rows in each replicateenable us to obtain estimates of the variety effects (which appear in thereplicates.rows stratum). The same is true of the columns. The design is balancedbecause the various comparisons between varieties are all estimated with the sameefficiency in the replicates.rows stratum; the Information Summary indicates theefficiency is in fact 0.167. Similarly, they all have efficiency 0.167 in thereplicates.columns stratum, and efficiency 0.667 in thereplicates.rows.columns stratum. So, the possible information on variety is split(1/6 : 1/6 : 2/3 ) between the three strata.
8.3 Linear mixed models: a non-orthogonal design 109We can see the estimates obtainedin each stratum by checking theEffects box in the ANOVA FurtherOutput menu (Figure 8.7) and thenclicking Run, and you can verify thatthe standard table of means producedby ANOVA, above, is calculated usingthe estimated effects from the loweststratum (replicates.rows.columns): the mean 12.962 forvariety 1 is the grand mean 14.704plus the effect of variety 1 in thereplicates.rows.columnstable, namely 1.742.Figure 8.7Tables of effectsVariate: yieldreplicates.rows stratumvariety effects, e.s.e. *, rep. 6variety 1 2 3 4 5 6 7-5.614 1.296 0.604 -1.468 -3.522 2.790 -3.458variety 8 9 10 11 12 13 141.718 0.520 -3.814 -2.718 -2.544 1.020 1.236variety 15 16 17 18 19 20 210.582 5.598 3.786 3.480 3.902 3.530 -1.294variety 22 23 24 25-0.028 1.360 -3.058 -3.894replicates.columns stratumvariety effects, e.s.e. *, rep. 6variety 1 2 3 4 5 6 7-3.432 -2.588 0.812 -0.650 -1.450 -4.948 1.930variety 8 9 10 11 12 13 144.064 -3.010 -1.584 1.852 2.828 2.540 -0.752variety 15 16 17 18 19 20 21-3.536 -0.642 -2.494 0.740 -1.706 4.934 -2.924variety 22 23 24 25
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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
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26 2 Blocking structuresNow we repe
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28 2 Blocking structureswould give
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30 2 Blocking structuresAnalysis of
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3 Treatment structureSo far we have
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34 3 Treatment structureTables of m
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36 3 Treatment structureFigure 3.3
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38 3 Treatment structureThere is a
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40 3 Treatment structureblock.*Unit
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42 3 Treatment structureTables of c
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44 3 Treatment structureN * Swas us
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46 3 Treatment structureFumigant Am
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48 3 Treatment structureFumigated S
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50 3 Treatment structureCovariate 1
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4 Checking the assumptionsIn this c
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54 4 Checking the assumptions4.2 No
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56 4 Checking the assumptions4.5 Tr
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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
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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
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Page 98 and 99: 94 7 Balance and non-orthogonalityM
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Page 102 and 103: 8 REML analysis of unbalanced desig
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Page 118 and 119: 9 Commands for analysis of variance
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Page 124 and 125: IndexA2DISPLAY procedure 117A2WAY p
Page 126: 122 IndexTransformation 56logarithm
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