Project - Statistical Inference - part 2 - The Effect of Vitamin C on Tooth Growth in Guinea Pigs

Sergio Vicente Simioni

May, 18, 2015

1. Synopsis
2. Data Processing
3. Results
4. Summary

SYNOPSIS

This second portion of the class, we’re going to analyze the ToothGrowth data in the R datasets package.

The response is the length of odontoblasts (teeth) in each of 10 guinea pigs at each of three dose levels of Vitamin C (0.5, 1, and 2 mg) with each of two delivery methods (orange juice or ascorbic acid).

Load the ToothGrowth data and perform some basic exploratory data analyses Provide a basic summary of the data. Use confidence intervals and/or hypothesis tests to compare tooth growth by supp and dose.

DATA PROCESSING

library(ggplot2)

ToothGrowth$supp<- gsub("VC", "Vitamin C" ,ToothGrowth$supp)
ToothGrowth$supp<- gsub("OJ", "Orange Juice" ,ToothGrowth$supp)
head(ToothGrowth)

##    len      supp dose
## 1  4.2 Vitamin C  0.5
## 2 11.5 Vitamin C  0.5
## 3  7.3 Vitamin C  0.5
## 4  5.8 Vitamin C  0.5
## 5  6.4 Vitamin C  0.5
## 6 10.0 Vitamin C  0.5

summary(ToothGrowth,supp)

##       len            supp                dose      
##  Min.   : 4.20   Length:60          Min.   :0.500  
##  1st Qu.:13.07   Class :character   1st Qu.:0.500  
##  Median :19.25   Mode  :character   Median :1.000  
##  Mean   :18.81                      Mean   :1.167  
##  3rd Qu.:25.27                      3rd Qu.:2.000  
##  Max.   :33.90                      Max.   :2.000

A) COMPARISON BETWEEN TOOTH LENGTH AND ASCORBIC ACID SUPPLEMENT TYPE

g<- ggplot(ToothGrowth,  aes(supp, len, fill =factor(supp)))+
        labs(title = "Supplement Type Effect")+ ylab("Tooth Length")
plot1<- g + geom_boxplot(notch = F)
print(plot1)

T.TEST ANALYSIS: Null Hypotesys ( Ho): States that supplement Type ( Orange Juice or Vitamin C ) has no influence on tooth length

t.test(len~supp, ToothGrowth, paired=F)

## 
##  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 is not equal to 0
## 95 percent confidence interval:
##  -0.1710156  7.5710156
## sample estimates:
## mean in group Orange Juice    mean in group Vitamin C 
##                   20.66333                   16.96333

RESULT

Based on the results of the T.Test, as p-value is higher than 0.05, we have not enough evidence to reject the Null Hypothesis

B) COMPARISON BETWEEN TOOTH LENGTH AND ACID ASCORBIC DOSAGE

g<- ggplot(ToothGrowth,  aes(dose, len, fill =factor(dose)))+
        labs(title = "Dosage Effect")+ ylab("Tooth Length")
plot2<- g + geom_boxplot(notch = F)
print(plot2)

dosage1<- subset(ToothGrowth, dose == 0.5)
dosage2<- subset(ToothGrowth, dose == 1.0)
dosage3<- subset(ToothGrowth, dose == 2.0)

dosage12<- rbind(dosage1,dosage2)
dosage13<- rbind(dosage1,dosage3)
dosage23<- rbind(dosage2,dosage3)

T.TEST ANALYSIS:Null Hypotesys ( Ho): States that different dosage of the acid arcorbic ( 0.5 mg, 1.0 mg or 2.0 mg ) has no influence on tooth length

t.test(len~dose, dosage12, paired=F)

## 
##  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 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

t.test(len~dose, dosage13, paired=F)

## 
##  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 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

t.test(len~dose, dosage23, paired=F)

## 
##  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 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

RESULT

As p-value is lower than 0.05 for all three analysis ,we can reject the null hypothesis

SUMMARY

Based on the analysis performed using the t.test is possible to affirm that the dosage of the acid ascorbic has influence in the tooth growth while there is no evidence to conclude that the delivery method has influence on the tooth growth.

Sergio Vicente Simioni May/23/2015