Overview

We analyze the ToothGrowth data set by comparing the guinea tooth growth by supplement and dose. 1. Load the ToothGrowth data and perform some basic exploratory data analyses

# load the sample dataset containing ToothGrowth data
library(datasets)
data(ToothGrowth)
library(ggplot2)

# perform data exploratory analysis with summary function
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
  1. Provide a basic summary of the data
d = ToothGrowth
ggplot(d, aes(x=factor(dose), y=len, fill=supp)) +
    geom_bar(stat="identity") +
    facet_grid(. ~ supp) +
    xlab("Dose (mg/day)") +
    ylab("Tooth length") +
    ggtitle("Inferential Data Analysis on Toothgrowth")

The plots seem to show the basic fact that increasing the dosage of supplements increases the tooth growth.

Hypothesis1: Both supplements are delivering same tooth growth

h1 <- t.test(len ~ supp, data = ToothGrowth)
h1$conf.int
## [1] -0.1710156  7.5710156
## attr(,"conf.level")
## [1] 0.95
h1$p.value
## [1] 0.06063451

The P value is greater than the significance level, we cannot reject the null hypothesis.

Hypothesis2: OJ delivers same tooth growth at low concentration 0.5

h2 <- t.test(len ~ supp, data = subset(ToothGrowth, dose == 0.5))
h2$conf.int
## [1] 1.719057 8.780943
## attr(,"conf.level")
## [1] 0.95
h2$p.value
## [1] 0.006358607

The P value is less than the significance level, the null hypothesis can be rejected. The alternative hypothesis that 0.5 mg/day dosage of OJ delivers more tooth growth than VC is accepted.

Hypothesis3: OJ delivers same tooth growth at low concentration 1

h3 <- t.test(len ~ supp, data = subset(ToothGrowth, dose == 1))
h3$conf.int
## [1] 2.802148 9.057852
## attr(,"conf.level")
## [1] 0.95
h3$p.value
## [1] 0.001038376

The P value is less than the significance level, the null hypothesis can be rejected. The alternative hypothesis that 1 mg/day dosage of OJ delivers more tooth growth than VC is accepted.

Hypothesis4: OJ and VC delivers same tooth growth at low concentration 2

h4 <- t.test(len ~ supp, data = subset(ToothGrowth, dose == 2))
h4$conf.int
## [1] -3.79807  3.63807
## attr(,"conf.level")
## [1] 0.95
h4$p.value
## [1] 0.9638516

The P value is greater than the significance level, the null hypothesis cannot be rejected.

Conculsions

The tooth growth with supplement OJ for lower dosages 0.5 & 1.0 shows higher impact compared to VJ while with high dosage both supplements yield same result.