Introduction

The ToothGrowth data in R datasets will be analyzed accordingly to find the data summary and use hypothesis tests to compare the tooth growth factor by either the supplement type and does type.

Preliminary Setup & Store Data

# load graphing tool interface package
library(ggplot2)
## Warning: 套件 'ggplot2' 是用 R 版本 4.1.1 來建造的
# initialize data category
Tooth <- ToothGrowth


Provide Initial Summaries for the data structure.

# General summaries for the data frame
summary(Tooth)
##       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
# Examine the characteristics for each section
str(Tooth)
## 'data.frame':    60 obs. of  3 variables:
##  $ len : num  4.2 11.5 7.3 5.8 6.4 10 11.2 11.2 5.2 7 ...
##  $ supp: Factor w/ 2 levels "OJ","VC": 2 2 2 2 2 2 2 2 2 2 ...
##  $ dose: num  0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 ...


Plot Tooth grow length and dose by splitting the supplement

# Use boxplot by having the classified grid for supplement
  ggplot(aes(x = as.factor(dose),y = len), data = Tooth) +     
        geom_boxplot(aes(fill = dose)) + 
        labs(x = "dose (mg)", 
             y = "Tooth Length", 
             title = "Tooth Length & Dose Amount by Supplement") + 
        facet_grid(~ supp)


Plot Tooth grow length and supplement by splitting the dosage amount

# Use boxplot by having the classified grid for dosage
  ggplot(aes(x = supp,y = len), data = Tooth)+ 
      geom_boxplot(aes(fill = supp)) + 
      labs(x = "Supplement", 
           y = "Tooth Length", 
           title = "Tooth Length & Dose Amount by Dosage") +
  facet_grid(~ dose)


Have Initial Hypothesis Test for the supplement classification

In this Hypothesis testing, the following hypothesis test is listed below:

H0 = Both supplement will generate the same impact towards tooth length growth.
H1 = Both supplement will generate different impact towards tooth length growth. 

# Use 2 sample t-test to compare
t.test(len ~ supp, data = Tooth)
## 
##  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 between group OJ and group VC 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


Have Initial Hypothesis Test for the dosage classification

In this Hypothesis testing, the following hypothesis test is listed below:

H0 = Both dosage will generate the same impact towards tooth length growth.
H1 = Both dosage will generate different impact towards tooth length growth. 

# Use 2 sample t-test to compare where the dosage is 0.5 and 1
Tooth1 <- subset(Tooth, Tooth$dose %in% c(0.5,1))
t.test(len ~ dose, data = Tooth1)
## 
##  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 between group 0.5 and group 1 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


# Use 2 sample t-test to compare where the dosage is 1 and 2
Tooth2 <- subset(Tooth, Tooth$dose %in% c(1,2))
t.test(len ~ dose, data = Tooth2)
## 
##  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 between group 1 and group 2 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


# Use 2 sample t-test to compare where the dosage is 0.5 and 2
Tooth3 <- subset(Tooth, Tooth$dose %in% c(0.5,2))
t.test(len ~ dose, data = Tooth3)
## 
##  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 between group 0.5 and group 2 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


gc()
##           used (Mb) gc trigger  (Mb) max used (Mb)
## Ncells  963938 51.5    1959164 104.7  1266377 67.7
## Vcells 1700599 13.0    8388608  64.0  2393891 18.3


Statistical Conclusion

Based on the t-test results and p-value description, the following conclusions are made.

  1. Supplement type will NOT contribute different impact towards the tooth length based on the given p-value.
  2. Dosage type will contribute different impact towards the tooth length based on the given p-value across all 3 factors of dosage. (H0 was rejected)