This report analyses tooth growth data in the R dataset package. The aims of this analysis are: 1. Perform some basic exploratoty data analysis and provide a basic summary of data 2. Compare tooth growth by supp and dose using confidence interval and hyphotesis tests. 3. State conclucions and the assumptions made that lead to the conclusions.

1. Load the ToothGrowth data and perform some exploratory data analysis

library(datasets)
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 3.2.2
p <-ggplot(ToothGrowth, aes(factor(dose),len))
p+geom_boxplot(aes(fill=supp))+facet_grid(.~supp)+ labs(title ="Figure 1: Tooth Growth by Supp and Dose")

q <- ggplot(ToothGrowth,aes(factor(supp),len))
q+geom_boxplot(aes(fill=supp))+facet_grid(.~dose)+labs(title="Figure 2: Difference of Tooth Growth by Supp for each Dose")

For Figure 1, it shows that both supps have an impact to the growth of the teeth. At all 3 doses of 0.5, 1.0 and 2.0, there are increases shown for both supps.

For Figure 2, it shoes that there is a relationship between the dose of supp and the growth of teeth. The higher the doses, the faster the the growth of the teeth. at the dose of 0. and 1.0, OJ has a better impact compared to VC. However at the dose of 2.0, vC seems to have higher impact to OJ.

2. Provide a basic summary of the data

library(plyr)
## Warning: package 'plyr' was built under R version 3.2.2
data(ToothGrowth)
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
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
TGSummary <- ddply(ToothGrowth,.(dose,supp),summarize, mean = mean(len), sd = sd(len)) 
#as.factor(TGSummary$dose)
TGSummary
##   dose supp  mean       sd
## 1  0.5   OJ 13.23 4.459709
## 2  0.5   VC  7.98 2.746634
## 3  1.0   OJ 22.70 3.910953
## 4  1.0   VC 16.77 2.515309
## 5  2.0   OJ 26.06 2.655058
## 6  2.0   VC 26.14 4.797731

3. Use confidence intervals and hyphothesis tests to compare tooth growth by supp and dose

#ToothGrowth <-transform(ToothGrowth, dose = as.factor(dose))
s<- split(ToothGrowth,list(ToothGrowth$supp, ToothGrowth$dose))
t1 <- t.test(s[[1]][[1]],s[[2]][[1]], paired = TRUE, alternative = "greater")
t1
## 
##  Paired t-test
## 
## data:  s[[1]][[1]] and s[[2]][[1]]
## t = 2.9791, df = 9, p-value = 0.007736
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
##  2.019552      Inf
## sample estimates:
## mean of the differences 
##                    5.25
t2 <- t.test(s[[3]][[1]],s[[4]][[1]], paired = TRUE, alternative = "greater")
t2
## 
##  Paired t-test
## 
## data:  s[[3]][[1]] and s[[4]][[1]]
## t = 3.3721, df = 9, p-value = 0.004115
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
##  2.706401      Inf
## sample estimates:
## mean of the differences 
##                    5.93
t3 <- t.test(s[[5]][[1]],s[[6]][[1]], paired = TRUE, alternative = "greater")
t3
## 
##  Paired t-test
## 
## data:  s[[5]][[1]] and s[[6]][[1]]
## t = -0.042592, df = 9, p-value = 0.5165
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
##  -3.523109       Inf
## sample estimates:
## mean of the differences 
##                   -0.08

For dose 0.5, the confidence level is 2.0196 and the p-value is 0.0077364. Since it is less than 0.05, it means there is a difference between the 2 methods.

For dose 1.0, the confidence level is 3.3721 and the p-value is 0.00411. Since it is less thab 0.05, it means there is a differnece between both methods.

For dose 2.0, the confidence level is -0.042592 and the p-value is 0.5165.Since it is greater than 0.05, it means there is a not much difference between both methods.

4. State conclusions and assumptions needed for conclusions

Assumptions

  1. The variables must be independent and identicaly distributed
  2. Variances of tooth growth are different when using different supplement and dosage
  3. Tooth growth follows a normal distibution.

Conclusions

  1. Both orange juice(JC) and vitamin C (VC) has effect on the growth of teeth
  2. Increasing the dose of JC or VC leads to incereased tooth growth.