一元配置実験
> x<-1:4 > y<-1:4+rnorm(4,mean=0,sd=0.1) > q<-aov(y~x) > anova(q) Analysis of Variance Table Response: y Df Sum Sq Mean Sq F value Pr(>F) x 1 5.3171 5.3171 12046 8.3e-05 *** Residuals 2 0.0009 0.0004 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > y<-1:4+rnorm(4,mean=0,sd=10) > q<-aov(y~x) > anova(q) Analysis of Variance Table Response: y Df Sum Sq Mean Sq F value Pr(>F) x 1 2.31 2.31 0.0173 0.9075 Residuals 2 267.52 133.76
データが４つ、自由度３、xの自由度が１、分散の自由度が２
2元配置実験
aa<-c(-5,-5,5,5) bb<-c(0,0,0,0) cc<-c(100,-100,-100,100) #aa<-c(4,4,1,1) #bb<-c(0,0,0,0) #cc<-c(14,0,0,0) a1<-aa+bb+cc+rnorm(4,sd=0.1) a2<-aa+bb+cc+rnorm(4,sd=0.1) a3<-aa+bb+cc+rnorm(4,sd=0.1) a4<-aa+bb+cc+rnorm(4,sd=0.1) a5<-aa+bb+cc+rnorm(4,sd=0.1) a=rep(c("1","1","2","2"),5) b=rep(c("1","2","1","2"),5) d<-data.frame(A=a,B=b,y=c(a1,a2,a3,a4,a5)) q<-aov(d$y~d$B+d$A) q2<-anova(q); print(q2) d<-data.frame(A=a,B=b,y=c(a1,a2,a3,a4,a5)) q<-aov(d$y~d$B*d$A) q2<-anova(q); print(q2)
結果
> source("anova123.R")
Analysis of Variance Table
Response: d$y
Df Sum Sq Mean Sq F value Pr(>F)
d$B 1 0 0 0.000 0.9989
d$A 1 506 506 0.043 0.8382
Residuals 17 199989 11764
Analysis of Variance Table
Response: d$y
Df Sum Sq Mean Sq F value Pr(>F)
d$B 1 0 0 2.4441e+00 0.1375
d$A 1 506 506 5.8320e+04 <2e-16 ***
d$B:d$A 1 199989 199989 2.3049e+07 <2e-16 ***
Residuals 16 0 0
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
主効果が交互作用に埋もれる例
