Q2

Question 2

Research Question - Is there an association between student nationality (domestic versus international) and whether or not they have a scholarship (yes versus no)?

Null Hypothesis (H0) There is no association between student nationality and scholarship status.

Alternative Hypothesis (H1) There is an association between student nationality and scholarship status.

#Load required libraries
library(readxl)

## Warning: package 'readxl' was built under R version 4.6.1

library(ggpubr)

## Warning: package 'ggpubr' was built under R version 4.6.1

## Loading required package: ggplot2

## Warning: package 'ggplot2' was built under R version 4.6.1

library(rcompanion)

## Warning: package 'rcompanion' was built under R version 4.6.1

#Read dataset
Q2 <- read_excel("A5Q2.xlsx")

#Create contingency table
Table <- table(Q2$nationality, Q2$scholarship_awarded)
print(Table)

##                
##                   0   1
##   Domestic       39 111
##   International 118  32

#Create grouped bar chart
barplot(Table, 
        beside = TRUE,
        col = rainbow(nrow(Table)),
        legend = rownames(Table),
        main = "Nationality and Scholarship Awarded",
        xlab = "Scholarship (0 = No, 1 = Yes)",
        ylab = "Count")

#Conduct Chi-Square Test of Independence
chi_result <- chisq.test(Table)
print(chi_result)

## 
##  Pearson's Chi-squared test with Yates' continuity correction
## 
## data:  Table
## X-squared = 81.297, df = 1, p-value < 2.2e-16

# Calculate effect size (Cramer's V)
effect_size <- rcompanion::cramerV(Table)
print(effect_size)

## Cramer V 
##   0.5272

interpretation

A Chi-Square Test of Independence was conducted to determine if there was an association between student nationality (domestic versus international) and whether or not the student got a scholarship. There was a significant association between the two variables, chi^2(1) = 81.30, p < .001. The association was strong (Cramer’s V = .53).