Statistical Inference Final Project Part 2
library("ggplot2")
# Load ToothGrowth data
data("ToothGrowth")
# Display a summary of the data
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 the first few rows of data
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
#Unique Values
unique(ToothGrowth$len)
## [1] 4.2 11.5 7.3 5.8 6.4 10.0 11.2 5.2 7.0 16.5 15.2 17.3 22.5 13.6
## [15] 14.5 18.8 15.5 23.6 18.5 33.9 25.5 26.4 32.5 26.7 21.5 23.3 29.5 17.6
## [29] 9.7 8.2 9.4 19.7 20.0 25.2 25.8 21.2 27.3 22.4 24.5 24.8 30.9 29.4
## [43] 23.0
unique(ToothGrowth$supp)
## [1] VC OJ
## Levels: OJ VC
unique(ToothGrowth$dose)
## [1] 0.5 1.0 2.0
# Convert dose to a factor
ToothGrowth$dose<-as.factor(ToothGrowth$dose)
# Plot tooth length ('len') vs. the dose amount ('dose'), broken out by supplement delivery method ('supp')
ggplot(aes(x=dose, y=len), data=ToothGrowth) + geom_boxplot(aes(fill=dose)) + xlab("Dose Amount") + ylab("Tooth Length") + facet_grid(~ supp) + ggtitle("Tooth Length vs. Dose Amount \nby Delivery Method") +
theme(plot.title = element_text(lineheight=.8, face="bold"))
# Plot tooth length ('len') vs. supplement delivery method ('supp') broken out by the dose amount ('dose')
ggplot(aes(x=supp, y=len), data=ToothGrowth) + geom_boxplot(aes(fill=supp)) + xlab("Supplement Delivery") + ylab("Tooth Length") + facet_grid(~ dose) + ggtitle("Tooth Length vs. Delivery Method \nby Dose Amount") +
theme(plot.title = element_text(lineheight=.8, face="bold"))
# run t-test
t.test(len~supp,data=ToothGrowth)
##
## Welch Two Sample t-test
##
## data: len by supp
## t = 1.9153, df = 55.309, p-value = 0.06063
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -0.1710156 7.5710156
## sample estimates:
## mean in group OJ mean in group VC
## 20.66333 16.96333
# run t-test using dose amounts 0.5 and 1.0
ToothGrowth_sub <- subset(ToothGrowth, ToothGrowth$dose %in% c(1.0,0.5))
t.test(len~dose,data=ToothGrowth_sub)
##
## 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
Since the p-value is 0.06, which is greater than 0.05, we conclude that supplement types appear to have no impact on tooth growth.
# run t-test using dose amounts 0.5 and 2.0
ToothGrowth_sub <- subset(ToothGrowth, ToothGrowth$dose %in% c(0.5,2.0))
t.test(len~dose,data=ToothGrowth_sub)
##
## Welch Two Sample t-test
##
## data: len by dose
## t = -11.799, df = 36.883, p-value = 4.398e-14
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
## -18.15617 -12.83383
## sample estimates:
## mean in group 0.5 mean in group 2
## 10.605 26.100
# run t-test using dose amounts 1.0 and 2.0
ToothGrowth_sub <- subset(ToothGrowth, ToothGrowth$dose %in% c(1.0,2.0))
t.test(len~dose,data=ToothGrowth_sub)
##
## 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
Because the p-value of each test was <0.05, we conclude that the average tooth length increases with an increasing dose.