Rによる統計解析ハンドブック 第5章演習問題解答

This post is solutions of the chapter 5 of `A Handbook of Statistical Analyses Using R, Second Edition'.

このポストはRによる統計解析ハンドブック(第2版)の第5章の解答になります。

1

Estimated values are larger than actual ones for pair of beef and low or that of cereal and high. Otherwise these are lower than that. B, C, L, H in the below graph stand for Beef, Cereal, Low and High.

牛肉で低たんぱく質、穀物で高たんぱく質は推定値が大きめになり、それ以外は推定値が低めに出ている。グラフ中のB、C、LとHはそれぞれBeef、Cereal、LowとHighの頭文字をとったものであることに注意。

data("weightgain", package="HSAUR2")
resid <- weightgain$weightgain - aov(weightgain ~ source + type, data=weightgain)$fitted.values
plot(resid, type="n", main="residuals")
lab <- paste(abbreviate(weightgain[,1],minlength=1),
             abbreviate(weightgain[,2],minlength=1), sep="")
text(resid, label=lab)

2

The result of plot.design shows no effect on gender and learner. So I conducted anova only with race and school. Race is only affects absent days in conclusion. Note that if anova is conducted with all vatiable, f-value of learner is smaller than 1 and it should be pooled.

plot.designからgender、learnerは関係なさそうとなる。そこで、人種、学年のみを使って分散分析を行った。結論としては欠席日数に効いているのは人種であると言える。なお、全変数で分散分析をかけると、learnerのF値が1より小さくプーリングすべきと考えられる。

data("schooldays", package="HSAUR2")
plot.design(schooldays)
aov.res <- aov(absent ~ race * school,  data=schooldays)
anova(aov.res)
interaction.plot(schooldays$race, schooldays$school, schooldays$absent)

> anova(aov.res)
Analysis of Variance Table

Response: absent
             Df  Sum Sq Mean Sq F value    Pr(>F)    
race          1  2645.7 2645.65 12.4615 0.0005561 ***
school        3  1325.5  441.85  2.0812 0.1052455    
race:school   3  3738.2 1246.08  5.8693 0.0008221 ***
Residuals   146 30996.7  212.31                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

3

By executing below code, we find that the hypothesis of the uniformity of mean values are rejected between any two groups.

以下のコードを実行すると、任意の2グループ間で、平均値の同等性の仮定は棄却されることが分かる。

data("students", package="HSAUR2")
students.manova <- manova(cbind(low, high) ~ treatment, data=students)
summary(students.manova, test="Hotelling-Lawley") # p-value is very small!
summary.aov(students.manova)

summary(manova(cbind(low, high) ~ treatment, data=students, 
        subset = treatment %in% c("AA", "C")))
summary(manova(cbind(low, high) ~ treatment, data=students, 
        subset = treatment %in% c("C", "NC")))
summary(manova(cbind(low, high) ~ treatment, data=students, 
        subset = treatment %in% c("NC", "AA")))