ToothGrowth analysis
Pedro M Gallardo
5 de abril de 2016
Exploratory data analysis
The general information of the dataset[¹].
#datasets::ToohtGrowth
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
library(ggplot2)
ggplot(ToothGrowth, aes(x=factor(dose), y=len, color=supp))+geom_boxplot()+labs(x="Vitamin C dose (mg)",y="Teeth length (mm)")
Data summary
From the exploratory analysis the following observations might be done:
- There is an observable trend between teeth length and vitamin C dose,
- Orange juice (OC) as a delivery method of vitamin C seems to be more effective (in terms of teeth growth) than Ascorbic Acid (VC)
Data analysis
In the following hyphotesis study, the previous two observations are further investigated. The departing hyphothesis according to each observation are:
For the observation 1:
- Null hyphotesis: there is no relation between the Vitamin C dose and the teeth length.
- Alternative hyphotesis: there is a relation, the higher the dose the higher the teeth length
a<-t.test(x=ToothGrowth[ToothGrowth$dose==1,]$len,y=ToothGrowth[ToothGrowth$dose==0.5,]$len,alternative="greater", var.equal=TRUE)For the observation 2:
- Null hyphotesis: There is no difference in the delivery method of the Vitamin C,
- Alternative hyphotesis: Delivery by Orange Juice performs better than Ascorbic Acid
library(knitr)
b <- t.test(x=ToothGrowth[ToothGrowth$dose==0.5 &ToothGrowth$supp=="VC",]$len,y=ToothGrowth[ToothGrowth$dose==0.5 &ToothGrowth$supp=="OJ",]$len, alternative="less", mu=0, var.equal = TRUE)
c <- t.test(x=ToothGrowth[ToothGrowth$dose==1 &ToothGrowth$supp=="VC",]$len,y=ToothGrowth[ToothGrowth$dose==1 &ToothGrowth$supp=="OJ",]$len, alternative="less", mu=0, var.equal = TRUE)
d <- t.test(x=ToothGrowth[ToothGrowth$dose==2 &ToothGrowth$supp=="VC",]$len,y=ToothGrowth[ToothGrowth$dose==2 &ToothGrowth$supp=="OJ",]$len, alternative="less", mu=0, var.equal = TRUE)
test <- c("Dose vs teeth length",
"Orange Juice vs Ascorbic Acid (dose=0.5mg)",
"Orange Juice vs Ascorbic Acid (dose 1 mg)",
"Orange Juice vs Ascorbic Acid (dose = 2 mg)")
Lower.CI<-c(a$conf[1],b$conf[1],c$conf[1],d$conf[1])
Higher.CI<-c(a$conf[2],b$conf[2],c$conf[2],d$conf[2])
pvalue<-c(a$p.value,b$p.value,c$p.value,d$p.value)
final=data.frame(test,Lower.CI,Higher.CI,pvalue)Conclusion
From the table below, the following conclusions might be drawn:
kable(final)| test | Lower.CI | Higher.CI | pvalue |
|---|---|---|---|
| Dose vs teeth length | 6.753344 | Inf | 0.0000001 |
| Orange Juice vs Ascorbic Acid (dose=0.5mg) | -Inf | -2.377886 | 0.0026518 |
| Orange Juice vs Ascorbic Acid (dose 1 mg) | -Inf | -3.380140 | 0.0003904 |
| Orange Juice vs Ascorbic Acid (dose = 2 mg) | -Inf | 3.086866 | 0.5181451 |
- For the observation 1 (dose vs teeth length) the p-value is \(<<0.01\) so the null hyphotesis is rejected and it is accepted the relation of a higher dose the higher teeth length.
- For the observation 2 (the delivery method of vitamin C). According to the p-values, it is accepted the Orange Juice as better delivery method than the Ascorbic Acid for doses of 0.5 and 1 mg (\(p-value<<0.01\)), however it is not conclusive for doses of 2 mg, therefore it can not be rejected the null hyphotesis for 2 mg.
[¹]: C. I. Bliss (1952) The Statistics of Bioassay. Academic Press.