Effect of Vitamin C on Tooth Growth in Guinea Pigs

Overview

We use ‘ToothGrowth’ dataset and perform exploratory analysis on it.
Then we use confidence intervals and hypothesis tests to compare tooth growth.

Exploratory Analysis:

library(datasets)
library(ggplot2)
head(ToothGrowth)

tail(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

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 ...

Plotting boxplot of toothlength per dosages & supplement:

data <- ToothGrowth
levels(data$supp) <- c("OrangeJuice", "AscorbicAcid")
g <- ggplot(data, aes(x = factor(dose), y = len))
g <- g + facet_grid(.~supp)
g <- g + geom_boxplot(aes(fill = supp))
g <- g + labs(title = "Tooth Length")
g <- g + labs(x = "Dose (mg/day)", y = "Tooth Length")
print(g)

We observe Orange juice shows better results for 0.5 and 1 mg/day dosages however 2 mg/day results are quite similar

Assumptions

We assume from here, ToothGrowth data follows normal distribution.

Hypothesis Tests

Testing three different hypothesis

For x = 0.5 mg/day

h0.5 <- t.test(len ~ supp, data = subset(data, dose == 0.5))
h0.5$conf.int

## [1] 1.719057 8.780943
## attr(,"conf.level")
## [1] 0.95

h0.5$p.value

## [1] 0.006358607

We reject null hypothesis as the p-value is smaller than significant level of 0.05. Therefore orange juice results in more tooth growth than absorbic acid.

For x = 1 mg/day

h1 <- t.test(len ~ supp, data = subset(data, dose == 1))
h1$conf.int

## [1] 2.802148 9.057852
## attr(,"conf.level")
## [1] 0.95

h1$p.value

## [1] 0.001038376

We again reject null hypothesis as the p-value is smaller than significant level of 0.05. Therefore orange juice results in more tooth growth than absorbic acid.

For x = 2 mg/day

h2 <- t.test(len ~ supp, data = subset(data, dose == 2))
h2$conf.int

## [1] -3.79807  3.63807
## attr(,"conf.level")
## [1] 0.95

h2$p.value

## [1] 0.9638516

Now, p-value is larger than the significance level of 0.05. therefore we cannot reject null hypothesis. Therefor orange juice and absorbic acid have same effect now.

Conclusions

We conducted three hypothesis tests. We inferred that Orange juice is better for tooth growth in guinea pigs in doses of 0.5 and 1 mg/day. however no difference between orange juice and absorbic acid for 2 mg/day dosage.