data(ToothGrowth)
summary(ToothGrowth)
##       len        supp         dose      
##  Min.   : 4.20   OJ:30   Min.   :0.500  
##  1st Qu.:13.07   VC:30   1st Qu.:0.500  
##  Median :19.25           Median :1.000  
##  Mean   :18.81           Mean   :1.167  
##  3rd Qu.:25.27           3rd Qu.:2.000  
##  Max.   :33.90           Max.   :2.000
VC<-subset(x = ToothGrowth,subset = supp=="VC")
OJ<-subset(x = ToothGrowth,subset = supp=="OJ")
VC05<-subset(x = VC,subset = VC$dose==0.5)
VC10<-subset(x = VC,subset = VC$dose==1.0)
VC20<-subset(x = VC,subset = VC$dose==2.0)
OJ05<-subset(x = OJ,subset = OJ$dose==0.5)
OJ10<-subset(x = OJ,subset = OJ$dose==1.0)
OJ20<-subset(x = OJ,subset = OJ$dose==2.0)
boxplot(VC05$len,VC10$len,VC20$len,
        OJ05$len,OJ10$len,OJ20$len,
        names=c("VC0.5","VC1.0","VC2.0",
                "OJ0.5","OJ1.0","OJ2.0"),
        xlab = "Group by Supp and Dose",ylab = "Len",main = "Len of ToothGrowth Grouped by Supp and Dose")

The figure shows that:

  1. Within the same supp, increasing dose tended to increase len.
  2. Within the same dose, OJ supp tended to increase more len than VC supp.

This analysis compared across different supp group, {VC,OJ}, with controlled dose.

t.test(VC05$len,OJ05$len)$p.value;t.test(VC10$len,OJ10$len)$p.value;t.test(VC20$len,OJ20$len)$p.value
## [1] 0.006358607
## [1] 0.001038376
## [1] 0.9638516

By using 5% level of significance with the null hypothesis that len of different supp (but the same dose) is equal, only at dose 2.0 which we cannot reject the null hypothesis (since p-value > 0.05). In other words, OJ0.5 and OJ1.0 increased more len than VC0.5 and VC1.0 respectively. But, OJ2.0 and VC2.0 tended to provide equal effect.