Part 2

Objectives:

1- Provide a basic summary of the data.

2- Use confidence intervals and/or hypothesis tests to compare tooth growth by supp and dose.

3- State your conclusions and the assumptions needed for your conclusions.

So, lets load and summarize the thooth growth data:

Data Summary

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
head(ToothGrowth)
##    len supp dose
## 1  4.2   VC  0.5
## 2 11.5   VC  0.5
## 3  7.3   VC  0.5
## 4  5.8   VC  0.5
## 5  6.4   VC  0.5
## 6 10.0   VC  0.5
plot <- ggplot(ToothGrowth, 
               aes(x=factor(dose),y=len,fill=factor(dose)))
plot + geom_boxplot(notch=F) + facet_grid(.~supp) +
     scale_x_discrete("Dosage") +   
     scale_y_continuous("Length of Teeth") +  
     ggtitle("Effect of Dosage and Supplement on Tooth Growth")

confidence intervals

supp.t1 <- t.test(len~supp, paired=F, var.equal=T, data=ToothGrowth)
supp.t2 <- t.test(len~supp, paired=F, var.equal=F, data=ToothGrowth)
supp.result <- data.frame("p-value"=c(supp.t1$p.value, supp.t2$p.value),
                          "Conf-Low"=c(supp.t1$conf[1],supp.t2$conf[1]),
                          "Conf-High"=c(supp.t1$conf[2],supp.t2$conf[2]),
                          row.names=c("Equal Var","Unequal Var"))
supp.result
##                p.value   Conf.Low Conf.High
## Equal Var   0.06039337 -0.1670064  7.567006
## Unequal Var 0.06063451 -0.1710156  7.571016

Conclusion :

The supplement (OJ) appears to provide better results than the supplementing with VC.

Part1 & 2 all on [github]https://github.com/aabodabash/BasicInferenceAnalysis.git