Instructions

1.Load the ToothGrowth data and perform some basic exploratory data analyses

2.Provide a basic summary of the data.

3.Use confidence intervals and/or hypothesis tests to compare tooth growth by supp and dose. (Only use the techniques from class, even if there’s other approaches worth considering)

4.State your conclusions and the assumptions needed for your conclusions.

Including Plots

You can also embed plots, for example:

Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.

Exploratory data Analysis

First me load the packages, and dataset

library(ggplot2)
library(knitr)
library(datasets)

Load the ToothGrowth data and perform basic Exploratory Data Analysis

data(ToothGrowth)
str(ToothGrowth)
## '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 ...
head(ToothGrowth, 4)
##    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
tail(ToothGrowth, 4)
##     len supp dose
## 57 26.4   OJ    2
## 58 27.3   OJ    2
## 59 29.4   OJ    2
## 60 23.0   OJ    2

Calculate the 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

Calculate the mean of the length

suppl_mean = split(ToothGrowth$len, ToothGrowth$supp)
sapply(suppl_mean, mean)
##       OJ       VC 
## 20.66333 16.96333
suppl_mean
## $OJ
##  [1] 15.2 21.5 17.6  9.7 14.5 10.0  8.2  9.4 16.5  9.7 19.7 23.3 23.6 26.4 20.0
## [16] 25.2 25.8 21.2 14.5 27.3 25.5 26.4 22.4 24.5 24.8 30.9 26.4 27.3 29.4 23.0
## 
## $VC
##  [1]  4.2 11.5  7.3  5.8  6.4 10.0 11.2 11.2  5.2  7.0 16.5 16.5 15.2 17.3 22.5
## [16] 17.3 13.6 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

Basic Exploratory Analysis, Graph below

ggplot(aes(x=supp, y=len), data=ToothGrowth) + geom_boxplot(aes(fill=supp))+ 
  xlab("Supplement Type") +ylab("Tooth length")

Get the confidence intervals

unique(ToothGrowth$dose)
## [1] 0.5 1.0 2.0

Unique dose groups are 0.5, 1, 2

Graph below, shows the relationship between Tooth Length and Dosages

 ggplot(aes(x = factor(dose), y = len), data = ToothGrowth) + 
  geom_boxplot(aes(fill = factor(dose))) +
  ggtitle("Tooth length relation to  Dosage")

Graph below show the tooth Length realation to dosage of each supplement

ggplot(aes(x=supp, y=len), data=ToothGrowth) + 
  geom_boxplot(aes(fill=supp)) + xlab("Supplements") + 
  ylab("Tooth Length") + facet_grid(~ dose) + 
  ggtitle("Tooth length relation dosage of each Supplement")

Hypothesis test defined below :

𝐻0 : tooth length does not depend of different supplements 𝐻𝑎: tooth length are effected by different supplement

t.test(len ~ supp, ToothGrowth[ToothGrowth$dose == .5, ])
## 
##  Welch Two Sample t-test
## 
## data:  len by supp
## t = 3.1697, df = 14.969, p-value = 0.006359
## alternative hypothesis: true difference in means between group OJ and group VC is not equal to 0
## 95 percent confidence interval:
##  1.719057 8.780943
## sample estimates:
## mean in group OJ mean in group VC 
##            13.23             7.98
t.test(len ~ supp, ToothGrowth[ToothGrowth$dose == 1, ])
## 
##  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 between group OJ and group VC 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
t.test(len ~ supp, ToothGrowth[ToothGrowth$dose == 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 between group OJ and group VC 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

Conclusion

we reject the Null Hypothesis, give more explanation on each test, CHATGPT use.