Overview

This projects demonstrates the difference in the tooth growth of ginie pigs per dose of Vitamin c with each supplement, Vitamin C(VC) pill, and Orange Juice(OJ). According to the data, supplementing Vitamin C directly shows the significant contritution to tooth growth compared to Orange Juice when the dose is from 0.5 to 1. But when the dose is 2, it shows no significant difference. To prove how the difference is significant, I used the t.test with two assumptions, variance is equal, and not equal.

Summary of the data set

Here is the summary of data set

Dt <- ToothGrowth
summary(Dt)
##       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

T.test for when does is the same but the supplement is different.

T is for Var.equal = TRUE, and F is for Var.equal = FALSE

VCOCP5 <- filter(Dt, supp == "VC" & dose == 0.5 | supp == "OJ" & dose == 0.5)
t.test1F <- t.test(len~supp, var.equal = FALSE, data = VCOCP5)
t.test1T <- t.test(len~supp, var.equal = TRUE, data = VCOCP5)
VCOC1 <- filter(Dt, supp == "VC" & dose == 1 | supp == "OJ" & dose == 1)
t.test2F <- t.test(len~supp, var.equal = FALSE, data = VCOC1)
t.test2T <- t.test(len~supp, var.equal = TRUE, data = VCOC1)
VCOC2 <- filter(Dt, supp == "VC" & dose == 2 | supp == "OJ" & dose == 2)
t.test3F <- t.test(len~supp, var.equal = FALSE, data = VCOC2)
t.test3T <- t.test(len~supp, var.equal = TRUE, data = VCOC2)

Here is the table for t.test. As you see, the difference is significant when the dose is from 0.5 to 1, but not siginficant when the dose is 2.

##     Test   Var.F   Var.T
## 1 VCOCP5 0.00636 0.00530
## 2  VCOC1 0.00104 0.00078
## 3  VCOC2 0.96385 0.96371

T.test for when does is the different but the supplement is same.

As you see in both tables, when dose goes from 1 to 2, there is no significant growth of tooth regardless any supplement.

Vitamin C pill

##        Test1   Var.F   Var.T
## 1 VC .5 TO 1 0.00636 0.00530
## 2 VC .5 TO 2 0.00104 0.00078
## 3  VC 1 TO 2 0.96385 0.96371

Orange Juice

##        Test2   Var.F   Var.T
## 1 OJ .5 TO 1 0.00636 0.00530
## 2 OJ .5 TO 2 0.00104 0.00078
## 3  OJ 1 TO 2 0.96385 0.96371

Conclusion.

Given the tables, to maximize the tooth growth for ginie pigs, the dose one Vitamin C is a better supplement than Orange Juice.