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90 7 Balance and non-orthogonalityfoster mother. It was impossible to balance the numbers of litters over the two factors,and so the design is unbalanced.The One- and two-way Analysis ofVariance menu (Figure 7.6)automatically detects that a design isunbalanced, and calculates theanalysis instead by using theGenStat regression commands.The analysis-of-variance table ismodified so that it shows the effectof fitting each of the factors eitherbefore or after the other one. So theline "mother ignoring litter"fits the effect of mother first. Thealternative line " motherFigure 7.6elimining litter" fits the effect of mother after fitting the litter effect. So itlooks to see if there are any effects of the foster mother that cannot be explained by thegenotype of the litter itself. (Remember, though, that interactions are always fitted aftertheir main effects.)Notice that the means are now predicted means (from the GenStat PREDICT directive).These are accompanied by a summary of the standard errors of difference over the pairof means within the table. You can print s.e.d.'s for every possible comparison of pairsof means within the table, by using the Unbalanced ANOVA menu, as shown in Section 7.6.Analysis of varianceSource d.f. s.s. m.s. v.r. F pr.mother ignoring litter 3 771.61 257.20 4.74 0.006mother eliminating litter 3 775.08 258.36 4.76 0.006litter ignoring mother 3 60.16 20.05 0.37 0.775litter eliminating mother 3 63.63 21.21 0.39 0.760mother.litter 9 824.07 91.56 1.69 0.120Residual 45 2440.82 54.24Total 60 4100.13 68.34Predictions from regression modelResponse variate: littwtPredictionmotherA 54.79B 58.08I 53.60J 48.34Minimum standard error of difference 2.641Average standard error of difference 2.753