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96 7 Balance and non-orthogonalityMinimum standard error of difference 7.894Average standard error of difference 8.313Maximum standard error of difference 9.393Predictions from regression modelResponse variate: YPredictionC 1 2A1 125.9 100.92 101.7 100.73 104.6 105.9Minimum standard error of difference 6.454Average standard error of difference 6.778Maximum standard error of difference 7.103Predictions from regression modelResponse variate: YPredictionC 1 2B1 110.2 96.52 111.9 104.53 109.7 106.9Minimum standard error of difference 6.454Average standard error of difference 6.770Maximum standard error of difference 7.215Predictions from regression modelResponse variate: YPredictionC 1 2A B1 1 136.1 95.12 124.1 100.83 116.2 107.62 1 102.1 93.82 101.8 98.13 101.3 111.33 1 92.3 101.12 110.6 115.83 112.6 101.2
7.7 Practical 97Minimum standard error of difference 11.16Average standard error of difference 11.74Maximum standard error of difference 14.42Like the One- and two-way Analysis of Variance menu, the Unbalanced ANOVA menu usesthe PREDICT directive to form the predicted means, but it gives more control over theway in which they are formed. The first step (A) of the calculation forms the full table ofpredictions, classified by every factor in the model. The second step (B) averages the fulltable over the factors that do not occur in the table of means. The Factor combination formeans box specifies which cells of the full table are to be formed in Step A. The defaultsetting, estimable, fills in all the cells other than those that involve parameters that cannotbe estimated, for example because of aliasing. Alternatively, the setting present excludesthe cells for factor combinations that do not occur in the data. The Standardization methodbox then defines how the averaging is done in Step B. The default setting, marginal, formsa table of marginal weights for each factor, containing the proportion of observationswith each of its levels; the full table of weights is then formed from the product of themarginal tables. The setting equal weights all the combinations equally. Finally, thesetting observed uses the WEIGHTS option of PREDICT to weight each factor combinationaccording to its own individual replication in the data. The One- and two-way Analysis ofVariance menu, always uses the default settings.In an unbalanced design, there will usually be a different standard error for differencesbetween each pair of means. Here we have simply printed a summary giving theminimum, average and maximum standard errors for differences between pairs of means.The Options menu (Figure 7.11) allows you to print a symmetric matrix giving thestandard errors for differences between every possible pair of means, but this is omittedhere to save space. In the earlier designs in this chapter, the treatment combinations wereall equally replicated, and so the standard errors were the same for every pair of means.7.7 PracticalReanalyse the data in the Spreadsheet file Unbalanced2way.gsh, first analysed inSection 7.5, using the Unbalanced ANOVA menu. Print the standard errors of differencesfor all pairs of means. (Note, you do not have any Blocking or Nuisance terms.)
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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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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
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Page 62 and 63: 58 4 Checking the assumptionsFigure
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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
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Page 92 and 93: 88 7 Balance and non-orthogonalityF
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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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