Preface to First Edition - lib

ANALYSIS USING R 85being far more than for the low-protein diet. A smaller difference is seen forthe source factor with beef leading to a higher gain than cereal.To apply analysis of variance to the data we can use the aov function in Rand then the summary method to give us the usual analysis of variance table.The model formula specifies a two-way layout with interaction terms, wherethe first factor is source, and the second factor is type.R> wg_aov summary(wg_aov)Df Sum Sq Mean Sq F value Pr(>F)source 1 220.9 220.9 0.9879 0.32688type 1 1299.6 1299.6 5.8123 0.02114source:type 1 883.6 883.6 3.9518 0.05447Residuals 36 8049.4 223.6Figure 5.2R output of the ANOVA fit for the weightgain data.The resulting analysis of variance table in Figure 5.2 shows that the maineffect of type is highly significant confirming what was seen in Figure 5.1.The main effect of source is not significant. But interpretation of both thesemain effects is complicated by the type × source interaction which approachessignificance at the 5% level. To try to understand this interaction effect it willbe useful to plot the mean weight gain for low- and high-protein diets for eachlevel of source of protein, beef and cereal. The required R code is given withFigure 5.3. From the resulting plot we see that for low-protein diets, the useof cereal as the source of the protein leads to a greater weight gain than usingbeef. For high-protein diets the reverse is the case with the beef/high dietleading to the highest weight gain.The estimates of the intercept and the main and interaction effects can beextracted from the model fit byR> coef(wg_aov)(Intercept) sourceCereal typeLow100.0 -14.1 -20.8sourceCereal:typeLow18.8Note that the model was fitted with the restrictions γ 1 = 0 (corresponding toBeef) and β 1 = 0 (corresponding to High) because treatment contrasts wereused as default as can be seen fromR> options("contrasts")$contrastsunordered"contr.treatment"ordered"contr.poly"Thus, the coefficient for source of −14.1 can be interpreted as an estimate ofthe difference γ 2 − γ 1 . Alternatively, we can use the restriction ∑ i γ i = 0 by© 2010 by Taylor and Francis Group, LLC