Overview

we’re going to analyze the ToothGrowth data in the R datasets package. Load the ToothGrowth data and perform some basic exploratory data analyses Provide a basic summary of the data. Use confidence intervals and/or hypothesis tests to compare tooth growth by supp and dose. We will state the conclusions and the assumptions needed for the conclusions.

library(dplyr)
## Warning: package 'dplyr' was built under R version 3.4.3
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 3.4.3
data("ToothGrowth")


dim(ToothGrowth)
## [1] 60  3
head(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
class(ToothGrowth)
## [1] "data.frame"
names(ToothGrowth)
## [1] "len"  "supp" "dose"
unique(ToothGrowth$supp)
## [1] VC OJ
## Levels: OJ VC
unique(ToothGrowth$dose)
## [1] 0.5 1.0 2.0

Create a plot using ggplot to view the data across supplement type and dose type

hist(ToothGrowth$len, col = "red", main = "Tooth Length")

ggplot(aes(x=supp, y=len), data=ToothGrowth) + geom_boxplot(aes(fill=supp)) + xlab("Supplement")+
 ylab("Tooth Length") + facet_grid(~ dose) +
 ggtitle("Tooth Length vs Supp method \n by Dose Amount") + 
  theme(plot.title = element_text(lineheight=.9, face="bold"))

ToothGrowth$dose<-as.factor(ToothGrowth$dose)

ggplot(aes(x=dose, y=len), data=ToothGrowth) + geom_boxplot(aes(fill=dose)) + xlab("Dose Amount") + ylab("Tooth Length") + facet_grid(~ supp) + ggtitle("Tooth Length vs. Dose Amount \nby Supplement method") + 
  theme(plot.title = element_text(lineheight=.9, face="bold"))

## Run t test on the Tooth Growth against the dose type

ToothGrowth_subset <-  subset(ToothGrowth, ToothGrowth$dose %in% c(1.0,0.5))
t.test(len~dose,data=ToothGrowth_subset)
## 
##  Welch Two Sample t-test
## 
## data:  len by dose
## t = -6.4766, df = 37.986, p-value = 1.268e-07
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -11.983781  -6.276219
## sample estimates:
## mean in group 0.5   mean in group 1 
##            10.605            19.735
ToothGrowth_subset <-  subset(ToothGrowth, ToothGrowth$dose %in% c(1.0,2.0))
t.test(len~dose,data=ToothGrowth_subset)
## 
##  Welch Two Sample t-test
## 
## data:  len by dose
## t = -4.9005, df = 37.101, p-value = 1.906e-05
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -8.996481 -3.733519
## sample estimates:
## mean in group 1 mean in group 2 
##          19.735          26.100
ToothGrowth_subset <-  subset(ToothGrowth, ToothGrowth$dose %in% c(0.5,2.0))
t.test(len~dose,data=ToothGrowth_subset)
## 
##  Welch Two Sample t-test
## 
## data:  len by dose
## t = -11.799, df = 36.883, p-value = 4.398e-14
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -18.15617 -12.83383
## sample estimates:
## mean in group 0.5   mean in group 2 
##            10.605            26.100

Run the t-test on the ToothGrowth against the supplement type

 t.test(len~supp,data=ToothGrowth)
## 
##  Welch Two Sample t-test
## 
## data:  len by supp
## t = 1.9153, df = 55.309, p-value = 0.06063
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.1710156  7.5710156
## sample estimates:
## mean in group OJ mean in group VC 
##         20.66333         16.96333

Conclusion

Given the following assumptions: The sample is representative of the population The distribution of the sample means follows the Central Limit Theorem In reviewing our t-test analysis from above, we can conclude that supplement delivery method has no effect on tooth growth/length, however increased dosages do result in increased tooth length.