Preface to First Edition - lib

ANALYSIS USING R 89always be the case and care is needed in dealing with unbalanced designs. Fora more complete discussion see Nelder (1977) and Aitkin (1978).Both ANOVA tables indicate that the main effect of mother’s genotype ishighly significant and that genotype B leads to the greatest litter weight andgenotype J to the smallest litter weight.We can investigate the effect of genotype B on litter weight in more detail bythe use of multiple comparison procedures (see Everitt, 1996, and Chapter 14).Such procedures allow a comparison of all pairs of levels of a factor whilstmaintaining the nominal significance level at its specified value and producingadjusted confidence intervals for mean differences. One such procedure is calledTukey honest significant differences suggested by Tukey (1953); see Hochbergand Tamhane (1987) also. Here, we are interested in simultaneous confidenceintervals for the weight differences between all four genotypes of the mother.First, an ANOVA model is fittedR> foster_aov foster_hsd foster_hsdTukey multiple comparisons of means95% family-wise confidence levelFit: aov(formula = weight ~ litgen * motgen, data = foster)$motgendiff lwr upr p adjB-A 3.330369 -3.859729 10.5204672 0.6078581I-A -1.895574 -8.841869 5.0507207 0.8853702J-A -6.566168 -13.627285 0.4949498 0.0767540I-B -5.225943 -12.416041 1.9641552 0.2266493J-B -9.896537 -17.197624 -2.5954489 0.0040509J-I -4.670593 -11.731711 2.3905240 0.3035490A convenient plot method exists for this object and we can get a graphicalrepresentation of the multiple confidence intervals as shown in Figure 5.5. Itappears that there is only evidence for a difference in the B and J genotypes.Note that the particular method implemented in TukeyHSD is applicable onlyto balanced and mildly unbalanced designs (which is the case here). Alternativeapproaches, applicable to unbalanced designs and more general researchquestions, will be introduced and discussed in Chapter 14.5.3.3 Water Hardness and MortalityThe water hardness and mortality data for 61 large towns in England andWales (see Table 3.3) was analysed in Chapter 3 and here we will extend theanalysis by an assessment of the differences of both hardness and mortality© 2010 by Taylor and Francis Group, LLC