Comparing Two Samples

# changing the directory 
setwd('/Users/stp48131/Library/CloudStorage/Dropbox/WKU/Teaching/ECON_307/Class_Materials/Honors/Comparing_Two_Samples')

# loading packages
library(readxl) # for loading the Excel file
library(tidyverse) # for the lag function to generate returns

# loading the excel file and assigning it to the data frame named data
data <- read_excel("comparing_two_samples_R.xlsx")
# attaching so I do not have to reference the data frame each time
attach(data)

# generating the return variables
# we do not have to use data$ on the right side of the <-
# since we attached the data dataframe. If we wanted to put this
# variable in the data dataframe we would have to add data$ before BTC_return,
# ETH_return, and LTC_return
BTC_return <-  BTC / lag(BTC) -1
ETH_return <-  ETH / lag(ETH) -1
LTC_return <-  LTC / lag(LTC) -1

We can conduct the t-test using the t.test() function. This will display a test statistic and p-value that you can use to determine the result of the test. The alternative option could be “two.sided”, “greater”, or “less” depending on the test you are using.

# T-test
# BTC vs ETH
t.test(BTC_return,ETH_return, # variables you want to test
       alternative = 'two.sided', # this is for a two-tailed test
       paired=FALSE,              # TRUE if it is a paired-sample
       var.equal = FALSE,         # always use FALSE here
       conf.level = .95)          # confidence level

## 
##  Welch Two Sample t-test
## 
## data:  BTC_return and ETH_return
## t = -0.73325, df = 94.358, p-value = 0.4652
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.07188807  0.03311043
## sample estimates:
##  mean of x  mean of y 
## 0.03230173 0.05169055

Fail to reject null hypothesis because p-value>\(\alpha\).

#BTC vs LTC
t.test(BTC_return,LTC_return, 
       alternative = 'two.sided', 
       paired=FALSE, 
       var.equal = FALSE, 
       conf.level = .95)

## 
##  Welch Two Sample t-test
## 
## data:  BTC_return and LTC_return
## t = -0.25478, df = 85.152, p-value = 0.7995
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.06732693  0.05203191
## sample estimates:
##  mean of x  mean of y 
## 0.03230173 0.03994924

Fail to reject null hypothesis because p-value>\(\alpha\).

#ETH vs LTC
t.test(ETH_return,LTC_return, 
       alternative = 'two.sided', 
       paired=FALSE, 
       var.equal = FALSE, 
       conf.level = .95)

## 
##  Welch Two Sample t-test
## 
## data:  ETH_return and LTC_return
## t = 0.35402, df = 98.679, p-value = 0.7241
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  -0.05406961  0.07755223
## sample estimates:
##  mean of x  mean of y 
## 0.05169055 0.03994924

Fail to reject null hypothesis because p-value>\(\alpha\).

We can also conduct a test for the variances. This uses the var.test() function. The options are similar to the one used in the t.test().

# F-test
# BTC vs ETH
var.test(BTC_return, ETH_return, 
         alternative = "two.sided", 
         conf.level = .95)

## 
##  F test to compare two variances
## 
## data:  BTC_return and ETH_return
## F = 0.55692, num df = 51, denom df = 51, p-value = 0.03889
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.3196876 0.9702061
## sample estimates:
## ratio of variances 
##          0.5569227

Reject null hypothesis because p-value<\(\alpha\).

# BTC vs LTC
var.test(BTC_return, LTC_return, 
         alternative = "two.sided", 
         conf.level = .95)

## 
##  F test to compare two variances
## 
## data:  BTC_return and LTC_return
## F = 0.38426, num df = 51, denom df = 51, p-value = 0.0008464
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.2205732 0.6694082
## sample estimates:
## ratio of variances 
##          0.3842571

Reject null hypothesis because p-value<\(\alpha\).

# ETH vs LTC
var.test(ETH_return, LTC_return, 
         alternative = "two.sided", 
         conf.level = .95)

## 
##  F test to compare two variances
## 
## data:  ETH_return and LTC_return
## F = 0.68996, num df = 51, denom df = 51, p-value = 0.1885
## alternative hypothesis: true ratio of variances is not equal to 1
## 95 percent confidence interval:
##  0.3960572 1.2019770
## sample estimates:
## ratio of variances 
##           0.689965

Fail to reject null hypothesis because p-value>\(\alpha\).