Part 2

DataScience Specialization - Data Inference

Introduction

This analysis represents the use of two treatments in three different dosses, and observe their effect on tooth growth.

The two medicaments are OJ and VC, with dosses of 0.5, 1 and 2.

For this inference analysis we will assume “iid”" meaning they were different individuals, divided ramdonly in 6 different groups.

Exploratory Analysis

Here is a summary of the data base 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

rbind(head(ToothGrowth, n=3L), tail(ToothGrowth, n=3L))

##     len supp dose
## 1   4.2   VC  0.5
## 2  11.5   VC  0.5
## 3   7.3   VC  0.5
## 58 27.3   OJ  2.0
## 59 29.4   OJ  2.0
## 60 23.0   OJ  2.0

For the exploratory analysis will check the Lenght of the Tooth Growth (len) distribution and identify the behavior of lenght by Treatment (sup) and Dose (dose).

dataOJ <- subset(ToothGrowth, supp = "OJ")
dataVC <- subset(ToothGrowth, supp = "VC")
par(mfrow = c(2,2))
hist(dataOJ$len, main = "Histogram of lenght - OJ", xlab = "lenght", ylab = "frecuency")
hist(dataVC$len, main = "Histogram of lenght - VC", xlab = "lenght", ylab = "frecuency")
boxplot(dataOJ$len ~ dataOJ$dose, main = "OJ Treatment length by dose")
boxplot(dataVC$len ~ dataVC$dose, main = "VC Treatment lenght by dose")

Means for the boxplots groups:

## [1] 10.605

## [1] 19.735

## [1] 26.1

## [1] 10.605

## [1] 19.735

## [1] 26.1

The dose of either treatment appears to be a cause for the lenght of the tooth growth.

The next figure represents the effectiveness by treatment.

boxplot(ToothGrowth$len ~ ToothGrowth$supp, main = "Lenght by Treatment")

mean(ToothGrowth$len[ToothGrowth$supp == "OJ"])

## [1] 20.66333

mean(ToothGrowth$len[ToothGrowth$supp == "VC"])

## [1] 16.96333

The OJ treatment appears to be more effective than VC treatment.

Inferential Analysis

Because the dose seems to be a cause of the lenght of the tooth growth, we make a hypothesis test for each treatment based on the dose.

Hypothesis 1

T Test for the OJ treatment. We will compare low dose 0.5 and 1 vs. a high dose 2

dataOJ$Hdose <- dataOJ$dose == 2
t.test(dataOJ$len~dataOJ$Hdose)

## 
##  Welch Two Sample t-test
## 
## data:  dataOJ$len by dataOJ$Hdose
## t = -8.3085, df = 56.202, p-value = 2.347e-11
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -13.565108  -8.294892
## sample estimates:
## mean in group FALSE  mean in group TRUE 
##               15.17               26.10

For the OJ treatment with a 95% confidence the high dose (2) increments the lenght of the tooth growth by

## [1] 10.93

Hypothesis 2

T Test for the VC treatment. We will compare low dose 0.5 and 1 vs. a high dose 2

dataVC$Hdose <- dataVC$dose == 2
t.test(dataVC$len~dataVC$Hdose)

## 
##  Welch Two Sample t-test
## 
## data:  dataVC$len by dataVC$Hdose
## t = -8.3085, df = 56.202, p-value = 2.347e-11
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -13.565108  -8.294892
## sample estimates:
## mean in group FALSE  mean in group TRUE 
##               15.17               26.10

For the VC treatment with a 95% confidence the high dose (2) increments the lenght of the tooth growth by

## [1] 10.93

Hypothesis 3

T Test for the type of treatment. We will compare OJ treatment vs. VC treatment

t.test(ToothGrowth$len~ToothGrowth$supp)

## 
##  Welch Two Sample t-test
## 
## data:  ToothGrowth$len by ToothGrowth$supp
## t = 1.9153, df = 55.309, p-value = 0.06063
## alternative hypothesis: true difference in means 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

With a 95% CI, there is no statistical difference for lenght tooth growth between treatment OJ and VC.