Independent or Two Sample T Test - comparing two different groups of data

Suppose we have data on cholesterol levels for males and females and we wish to see if one sex has higher/lower LDL cholesterol (i.e., the bad kind) than the other. Is there any difference in terms of cholesterol level between male and female?

#dataset
male <- c(169, 175, 172, 122, 135, 149, 177, 99, 103, 123, 256)
male

##  [1] 169 175 172 122 135 149 177  99 103 123 256

female <- c(123, 105, 122, 136, 136, 156, 142, 109 ,123, 151, 107)
female

##  [1] 123 105 122 136 136 156 142 109 123 151 107

sd(male)

## [1] 44.61186

sd(female)

## [1] 17.47466

var(male)

## [1] 1990.218

var(female)

## [1] 305.3636

#Variance of male and female is not equal

#converting the data into data.frame
data <- data.frame(male, female)
data

##    male female
## 1   169    123
## 2   175    105
## 3   172    122
## 4   122    136
## 5   135    136
## 6   149    156
## 7   177    142
## 8    99    109
## 9   103    123
## 10  123    151
## 11  256    107

summary(data)

##       male           female     
##  Min.   : 99.0   Min.   :105.0  
##  1st Qu.:122.5   1st Qu.:115.5  
##  Median :149.0   Median :123.0  
##  Mean   :152.7   Mean   :128.2  
##  3rd Qu.:173.5   3rd Qu.:139.0  
##  Max.   :256.0   Max.   :156.0

library(moments)
library(car)

## Warning: package 'car' was built under R version 3.6.2

## Loading required package: carData

#Normality Test
plot(density(male))

agostino.test(male)

## 
##  D'Agostino skewness test
## 
## data:  male
## skew = 0.94417, z = 1.67165, p-value = 0.09459
## alternative hypothesis: data have a skewness

qqnorm(male)

shapiro.test(male)

## 
##  Shapiro-Wilk normality test
## 
## data:  male
## W = 0.89988, p-value = 0.1842

plot(density(female))

agostino.test(female)

## 
##  D'Agostino skewness test
## 
## data:  female
## skew = 0.14679, z = 0.26992, p-value = 0.7872
## alternative hypothesis: data have a skewness

qqnorm(female)

shapiro.test(female)

## 
##  Shapiro-Wilk normality test
## 
## data:  female
## W = 0.93798, p-value = 0.497

#independent or 2 sample t test
res <- t.test(male, female, var.equal = FALSE) #Variance of male and female is not equal
res

## 
##  Welch Two Sample t-test
## 
## data:  male and female
## t = 1.6991, df = 12.998, p-value = 0.1131
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -6.663878 55.754787
## sample estimates:
## mean of x mean of y 
##  152.7273  128.1818

#Two sample T test shows that there is no significant difference between male and female cholesterol levels because p-value > 0.05 fails to reject the null hypothesis

Independent or Two Sample T Test

Mikhilesh Dehane

7/31/2020

Independent or Two Sample T Test - comparing two different groups of data

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