The Effect of Vitamin C on Tooth Growth in Guinea Pigs

Description of data :This data represents the effect of Vitamin C supplement on Tooth Growth in Guinea Pigs. The datasets records the length of odontoblasts(cell responsible for tooth growth) in 60 guinea pigs. Each animal recieved one of three dose levels of vitamin C(0.5,1 and 2mg/day) by one of two delievery methods, (orange juice a.k.a OJ or ascorbic acid a.k.a VC)

data("ToothGrowth")
attach((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

The box plot is convenient way of graphically depicting length of odontoblasts for different groups of supplements and dose amount.

boxplot(len~supp*dose,data=ToothGrowth,col=c("orange","dark green"), main="ToothGrowth by Supplement & Dose")

The boxplot shows that the tooth length and increase in the dosage amount has a positive correation. Also it seems the impact of OJ and VC on the tooth growth depends on the dosage.

library("dplyr")

Impact of vitamin C doses on tooth growth cells

Comparision of dose amount 0.5mg/day and 1 mg/day

Null Hypothesis \(H_o\): the mean length of tooth growth cell for a dose of 0.5mg/day is equal to the mean length tooth growth lcell for dose of 1mg/day.Alternate hypothesis \(H_a\): the mean toothgrowth length’s are different.

tg_05_1 <- filter(ToothGrowth,dose==0.5| dose==1)
t.test(len ~ dose, data = tg_05_1)$statistic

##         t 
## -6.476648

The t-statistic =6.467 is quite high, the null hypothesis rejected. 2. Comparision of dose amount 1mg/day and 2 mg/day

Null Hypothesis \(H_o\): the mean length of tooth growth cell for a dose of 1mg/day is equal to the mean length of tooth growth cell for a dose amount of 2mg/day.Alternate hypothesis \(H_a\): the mean toothgrowth length’s are different.

tg_1_2  <- filter(ToothGrowth,dose==1| dose==2)
t.test(len ~ dose, data = tg_1_2)$statistic

##         t 
## -4.900484

The t-statistic is 4.9, which is more than critical t value,do the so null hypothesis is rejected.

Impact of vitamin C Supplement on tooth growth cells

Are both Vitamin C supplement equally good ? or Orange Juice supplement was better than the Ascorbic Acid supplement for ToothGrowth in Guinea pig. Lets see what the t.test tells about the hypothesis.Null Hypothesis \(H_o\): The mean length of tooth growth cell for both supplement (OC, VC) is equal for a dose ( 0.5, 1 and 2 mg/day).Alternative Hypothesis \(H_a\): TThe mean length of tooth growth cell with orange juice supplement is higher than the ascorbic acid, for a dose( 0.5, 1 and 2 mg/day)

Comparision of supplement(OJ or VC) for a dose = 0.5mg/day

tg_05 <- filter(ToothGrowth,dose==0.5)
t.test(len ~ supp, data = tg_05,alternative = c("greater"))

## 
##  Welch Two Sample t-test
## 
## data:  len by supp
## t = 3.1697, df = 14.969, p-value = 0.003179
## alternative hypothesis: true difference in means is greater than 0
## 95 percent confidence interval:
##  2.34604     Inf
## sample estimates:
## mean in group OJ mean in group VC 
##            13.23             7.98

Due to the high t-statistic value (3.17) and low p-value, we reject the null hypothesis that both the supplement has equal impact on the ToothGrowth.

Comparision of supplement(OJ or VC) for a dose = 1 mg/day

Null Hypothesis \(H_o\): The mean length of tooth growth cell for both supplement (OC, VC) is equal for a dose = 1mg/day.Alternative Hypothesis \(H_a\): The mean length of tooth growth cell with orange juice supplement is higher than the ascorbic acid, with dose size =1mg/day.

tg_1 <- filter(ToothGrowth,dose==1)
t.test(len ~ supp,data = tg_1,alernative=c("greater"))

## 
##  Welch Two Sample t-test
## 
## data:  len by supp
## t = 4.0328, df = 15.358, p-value = 0.001038
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  2.802148 9.057852
## sample estimates:
## mean in group OJ mean in group VC 
##            22.70            16.77

The Null hypothesis is rejected.

Comparision of supplement(OJ or VC) for a dose = 2 mg/day

Null Hypothesis \(H_o\): The mean length of tooth growth cell in Guinea pigs for both Vitamin C supplements (OC, VC) is equal for a dose = 2mg/day.Alternative Hypothesis \(H_a\): The mean length of tooth growth cell in Guinea pigs taking Vitamin C supplement as orange juice is higher than supplement taken as ascorbic acid, with dose size =2mg/day.

tg_2  <- filter(ToothGrowth,dose==2)
t.test(len ~ supp, data = tg_2)

## 
##  Welch Two Sample t-test
## 
## data:  len by supp
## t = -0.046136, df = 14.04, p-value = 0.9639
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -3.79807  3.63807
## sample estimates:
## mean in group OJ mean in group VC 
##            26.06            26.14

With a low t-value 0f 0.046 and high p value of 0.9639, we fail to reject the Null hypothesis which is consistent with the above box plot, which shows the median for both OJ an VC for dosage of 2mg/day is more or less same.