Using R for Introductory Statistics : John Verzani

Analysis of variance 311Figure 11.4 Birth weight by smokinghistoryPerhaps the assumption of normality isn’t correct, but we ignore that. If the test is valid, itlooks like level 1 (smokes now) has a smaller mean. Is this due to sampling? We fit themodel as follows:> res=1m(wt factor(smoke), data=df)> summary(res)…Coefficients:Estimate Std. Error t value Pr(>|t|)(Intercept) 122.778 0.760 161.60 < 2e−16 ***factor (smoke) 1 -8.668 1.107 −7.83 1.1e-14 ***factor (smoke) 2 0.307 1.970 0.16 0.88factor (smoke) 3 1.659 1.904 0.87 0.38factor (smoke) 9 3.922 5.655 0.69 0.49--Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘’Residual standard error: 17.7 on 1231 degrees offreedomMultiple R-Squared: 0.0588, Adjusted R-squared:0.0557F-statistic: 19.2 on 4 and 1231 DF, p-value: 2.36e-15The marginal t-tests indicate that the level 1 of the smoke factor is important, whereas theothers may not contribute. That is, this is strong evidence that a mother’s smoking duringpregnancy decreases a baby’s birth weight. The treatment coding quantifies this in termsof differences from the reference level of never smoked. The estimate, −8.668, says thatthe birth weight of a baby whose mother smoked during her pregnancy is predicted to be8.688 grams less than that of a baby whose mother never smoked.