Tooth Growth Dataset - Statistical Analysis

Overview

In this exercise ,I am going to analyze the Toothgrowth dataset provided in the r package datasets. The dataset contains the data of growth of teeth by giving Vitamin c (VC) and orange juice (OJ). It also has 3 dosage quantity i-e 0.5mg, 1mg, 2mg.

1. Loading the dataset and neccessary libraries

library(ggplot2)

## Warning: package 'ggplot2' was built under R version 4.0.5

data(ToothGrowth)

2. Basic summary and struture of dataset

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

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 ...

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

dim(ToothGrowth)

## [1] 60  3

3. Basic exploratory Analysis

g<- ggplot(data=ToothGrowth, aes(x=paste(supp,dose) , y=len, fill=factor(dose)))
g<- g+geom_boxplot() 
g<- g+labs(title = "Tooth growth of 60 guinea pigs by dosage and delivery method of vitamin C", x = "Dose in milligrams/day", y = "Tooth Lengh")
g<- g+ scale_fill_discrete(name="dosage type")
g<- g+theme(plot.title = element_text(hjust = 0.5))
print(g)

4. Data Manipulation to separate data by dosage

data_0.5<-subset(ToothGrowth, dose==0.5)
data_1<-subset(ToothGrowth, dose==1)
data_2<-subset(ToothGrowth, dose==2)

5. Performing T test to accept or reject hypothesis

t1<-t.test(len~supp, data=data_0.5)
t2<-t.test(len~supp, data=data_1)
t3<-t.test(len~supp, data=data_2)

6. Creating DataFrame to analyze the result.

Conclusion<-data.frame("p-value"=c(t1$p.value,t2$p.value,t3$p.value),
                       "Low-Confidence"=c(t1$conf.int[1],t2$conf.int[1],t3$conf.int[1]),
                       "High-Confidence"=c(t1$conf.int[2],t2$conf.int[2],t3$conf.int[2]),
                       "OJ mean" = c(t1$estimate[1],t2$estimate[1],t3$estimate[1]),
                       "VC mean" = c(t1$estimate[2],t2$estimate[2],t3$estimate[2]),
                       row.names = c("Dosage_.5","Dosage_1","Dosage_2"))

Conclusion

##               p.value Low.Confidence High.Confidence OJ.mean VC.mean
## Dosage_.5 0.006358607       1.719057        8.780943   13.23    7.98
## Dosage_1  0.001038376       2.802148        9.057852   22.70   16.77
## Dosage_2  0.963851589      -3.798070        3.638070   26.06   26.14

7.Conclusion

1. Since P value for dosage 0.5 and 1 are less than threshold value (0.5), we reject the null hypothesis which states that there is no relation between tooth growth and supplement method for 0.5 and 1mg dose.

2. Since P value for dosage 2mg is greater than threshold value (0.5), we accept the null hypothesis which states that there is no relation between tooth growth and supplement method for 2mg dose.

3. From datafarme last 2 columns, it is concluded that OJ provides more growth than VC when dosage is 0.5mg or 1mg