The Effect of Vitamin C on Tooth Growth in Guinea Pigs

Overview

In this report we will do some exploratory analysis on the TootGrowth dataset in the R datasets package.

Description of the dataset

The response is the length of odontoblasts (teeth) in each of 10 guinea pigs at each of three dose levels of Vitamin C (0.5, 1, and 2 mg) with each of two delivery methods (orange juice or ascorbic acid).

A data frame with 60 observations on 3 variables.

[,1] len numeric Tooth length

[,2] supp factor Supplement type (VC or OJ).

[,3] dose numeric Dose in milligrams.

Basic data summary

library(ggplot2)
#import the dataset
data("ToothGrowth")
#show summary info
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

 ggplot(ToothGrowth, aes(x=dose, y=len, color=dose)) + 
   geom_point() +
   labs(title="Tooth Growth by Supplement Type and Dose") +
   xlab("Dose") +
   ylab("Length") + facet_wrap(~ supp, ncol=2)  +
   theme(plot.title = element_text(face="bold"))

Compare tooth growth by supp and dose

In order to compare tooth growth, we will do two-sample t-tests, (Orange Juice and Ascorbic Acid) at each dosage level (0.5mg, 1mg, 2mg).

t-test at 0.5mg

 t.test(len ~ supp, ToothGrowth[ToothGrowth$dose == .5, ])

## 
##  Welch Two Sample t-test
## 
## data:  len by supp
## t = 3.1697, df = 14.969, p-value = 0.006359
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  1.719057 8.780943
## sample estimates:
## mean in group OJ mean in group VC 
##            13.23             7.98

t-test at 1mg

 t.test(len ~ supp, ToothGrowth[ToothGrowth$dose == 1, ])

## 
##  Welch Two Sample t-test
## 
## data:  len by supp
## t = 4.0328, df = 15.358, p-value = 0.001038
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  2.802148 9.057852
## sample estimates:
## mean in group OJ mean in group VC 
##            22.70            16.77

t-test at 2mg

 t.test(len ~ supp, ToothGrowth[ToothGrowth$dose == 2, ])

## 
##  Welch Two Sample t-test
## 
## data:  len by supp
## t = -0.0461, df = 14.04, p-value = 0.9639
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -3.79807  3.63807
## sample estimates:
## mean in group OJ mean in group VC 
##            26.06            26.14

Conclusion

Based on the assumption that the data is representative of the population of guinea pigs and that the dosage and supplement were randomly assigned we can conclude that the vitamin c supplements have a positive effect on tooth growth for guinea pigs and that at 05.mg and 1mg dosages orange juice is more effective than ascorbic acid. For a dosage of 2mg we cannot conclude that orange juice is more effective than ascorbic acid.