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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.)