530 Inferences About Normal Linear ModelsAcura Ferrair Lotus Porsche Viper160165170175180SpeedFigure 9.4.1:Boxplot of car speeds cited in Example 9.4.1.P(Y =j). LetX 1 ,...,Xn 1 andY 1 ,...,Yn 2 be respective independent random
samples onXandY. The samples are recorded in a 2×kcontingency table of
countsOij,whereO 1 j=#{Xi=j}andO 2 j=#{Yi=j}. In Example 4.7.3,
based on this table, we discussed a test that the distributions ofXandY are the
same. Here we want to consider all the differencesp 1 j−p 2 jforj=1,...,k.Let
pˆij=Oij/ni.
(a)Determine the Bonferroni method for performing all these comparisons.(b)Determine the Fisher method for performing all these comparisons.9.4.4.Suppose the samples in Exercise 9.4.3 resulted in the contingency table:
1 2 3 4 5 6 7 8 9 10
x 20 31 56 18 45 55 47 78 56 81
y 36 41 65 15 38 78 18 72 59 85
To compute (in R) the confidence intervals below, use the commandprop.testas
in Example 4.2.5.
(a)Based on the Bonferroni procedure for all 10 comparisons, compute the con-
fidence interval forp 16 −p 26.(b)Based on the Fisher procedure for all 10 comparisons, compute the confidence
interval forp 16 −p 26.
9.4.5.Write an R function that computes the Fisher procedure of Exercise 9.4.3.
Validate it using the data of Exercise 9.4.4.