Now, the markdown file will show how to analyze the ToothGrowth data in the R datasets package. #Load the ToothGrowth data

library(datasets)

perform some basic exploratory data analyses

As we can see from dim function , the size about the data and there are 3 rows :

dim(ToothGrowth)
## [1] 60  3

let s check out more detail from the head:

head(ToothGrowth)

then use table function to see supp and dose :

table(ToothGrowth$supp)
## 
## OJ VC 
## 30 30
table(ToothGrowth$dose)
## 
## 0.5   1   2 
##  20  20  20

After viewing the info. up there , we will gather the basic detail from this data. To know more , #Provide a basic summary of the data. So, if we can seperate the data from “dose”, it will give us a better understanding of the data:

ggplot(ToothGrowth, aes(factor(dose), len, fill = factor(dose))) +
  geom_boxplot() +
  facet_grid(.~supp, labeller = as_labeller(c("OJ" = "Orange juice", "VC" = "Ascorbic Acid"))) +
  labs(title = "Tooth growth of 60 guinea pigs by dosage and\nby delivery method of vitamin C",
       x = "Dose in milligrams/day", 
       y = "Tooth Lengh") +
  scale_fill_discrete(name = "Dosage of\nvitamin C\nin mg/day")

g2 <- ggplot(ToothGrowth, aes(x = dose, y = len, dose = factor(supp)))
g2 <- g2 + geom_line(size = 1, aes(colour = supp)) + geom_point(size =10, pch = 21,  alpha = .5)
g2

str(ToothGrowth)
## 'data.frame':    60 obs. of  3 variables:
##  $ len : num  4.2 11.5 7.3 5.8 6.4 10 11.2 11.2 5.2 7 ...
##  $ supp: Factor w/ 2 levels "OJ","VC": 2 2 2 2 2 2 2 2 2 2 ...
##  $ dose: num  0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ...

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

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

State your conclusions and the assumptions

CONCLUSIONS:

-For lower dosages (0.5 and 1.0 mg), OJ provides more tooth growth than VC;

-For 2.0mg dosage tooth growth is teh same for both supplement methods;

-Higher dosages give more growth, indepedent of supplemetn method