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Part 2

For the second part of the project, we are going to analyze the ToothGrowth data in the R datasets package.

2.1. Loading Dataset

# Check for missing dependencies and load necessary R packages
if(!require(ggplot2)){install.packages('ggplot2')}; library(ggplot2)

# Load dataset
data("ToothGrowth")

# Quick explanation on ToothGrowth dataset
?ToothGrowth

# Check summary
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
# Display different summary
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 ...

2.2. Data Visualization

Now since “supp” is the Supplyment type (namely VC represents Ascorbic Acid and OJ represents Orange Juice), so it is easier to look at Tooth Length vs Dose breakdown by Supplyment type.

gg2 <- ggplot(ToothGrowth, aes(x=factor(dose), y=len, fill=factor(dose))) +
  geom_boxplot() + facet_grid(.~supp) +
  labs(title="Comparison of Different Supplyment Type for Different Vitamin Dose", y="Tooth Length", x="Dose (mg/day)")
gg2

2.3. Calculating Confidence Interval

# Calculate Confidence Interval for Dose=0.5 mgrams/day.
dose.05 <- subset(ToothGrowth, dose==0.5)
test.05 <- t.test(len ~ supp, paired=F, var.equal=F, data=dose.05)


# Calculate Confidence Interval for Dose=0.5 mgrams/day.
dose.1 <- subset(ToothGrowth, dose==1)
test.1 <- t.test(len ~ supp, paired=F, var.equal=F, data=dose.1)


# Calculate Confidence Interval for Dose=0.5 mgrams/day.
dose.2 <- subset(ToothGrowth, dose==2)
test.2 <- t.test(len ~ supp, paired=F, var.equal=F, data=dose.2)


# Summarizing p-value and Confidence Interval in a table
table1 <- data.frame(
  "p.value"=c(test.05$p.value, test.1$p.value, test.2$p.value), 
  "Conf.Low"=c(test.05$conf.int[1], test.1$conf.int[1], test.2$conf.int[1]),
  "Conf.High"=c(test.05$conf.int[2], test.1$conf.int[2], test.2$conf.int[2]),
  row.names=c("Dose.05", "Dose.1", "Dose.2")
)
table1
##             p.value  Conf.Low Conf.High
## Dose.05 0.006358607  1.719057  8.780943
## Dose.1  0.001038376  2.802148  9.057852
## Dose.2  0.963851589 -3.798070  3.638070

2.4. Assumptions and Conclusion

For this ToothGrowth dataset, I assume the data is collected from random Guinea pigs given either Orange Juice or Asorbic Acid. Hence, when doing the t-test, we have to use paired=FALSE. I also assume the experiment is conducted on the same species of Guinea pigs, hence it is assumed to be no error term.

Based on the p-value, for Dose=0.05mg/day & 1mg/day, since the p-value is less than 5%, we reject the null hypothesis and conclude there is significant difference between Orange Juice and Ascorbic Acid at low dose (less than or equal 1mg/day). For Dose=2mg/day, since the p-value is greater than 5%, we failed to reject the null hypothesis and conclude there is no significant difference between Orange Juice and Ascorbic Acid at high dose (2mg/day).