Research scenario B

read the libraries

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(effsize) 

Load the data

Dataset6.2 <- read_excel("/Users/komakechivan/Downloads/Dataset6.2.xlsx")

Calculate Descriptive Statistics

stats_6.2 <- Dataset6.2 %>%
  group_by(Work_Status) %>%
  summarise(
    Mean = mean(Study_Hours, na.rm = TRUE),
    Median = median(Study_Hours, na.rm = TRUE),
    SD = sd(Study_Hours, na.rm = TRUE),
    N = n()
  )
print(stats_6.2)

## # A tibble: 2 × 5
##   Work_Status    Mean Median    SD     N
##   <chr>         <dbl>  <dbl> <dbl> <int>
## 1 Does_Not_Work  9.62   8.54  7.45    30
## 2 Works          6.41   5.64  4.41    30

Histograms

hist(Dataset6.2$Study_Hours[Dataset6.2$Work_Status == "Works"], 
     main = "Histogram: Working Students", 
     xlab = "Study Hours", col = "lightblue", border = "black")

hist(Dataset6.2$Study_Hours[Dataset6.2$Work_Status == "Does_Not_Work"], 
     main = "Histogram: Non-Working Students", 
     xlab = "Study Hours", col = "lightgreen", border = "black")

Boxplot for Outlier Detection

ggboxplot(Dataset6.2, x = "Work_Status", y = "Study_Hours", 
          color = "Work_Status", palette = "jco", add = "jitter")

Shapiro-Wilk Test of Normality

shapiro.test(Dataset6.2$Study_Hours[Dataset6.2$Work_Status == "Works"])

## 
##  Shapiro-Wilk normality test
## 
## data:  Dataset6.2$Study_Hours[Dataset6.2$Work_Status == "Works"]
## W = 0.94582, p-value = 0.1305

shapiro.test(Dataset6.2$Study_Hours[Dataset6.2$Work_Status == "Does_Not_Work"])

## 
##  Shapiro-Wilk normality test
## 
## data:  Dataset6.2$Study_Hours[Dataset6.2$Work_Status == "Does_Not_Work"]
## W = 0.83909, p-value = 0.0003695

Conduct Inferential Test (Mann-Whitney U)

wilcox.test(Study_Hours ~ Work_Status, data = Dataset6.2)

## 
##  Wilcoxon rank sum exact test
## 
## data:  Study_Hours by Work_Status
## W = 569, p-value = 0.07973
## alternative hypothesis: true location shift is not equal to 0

Calculate Effect Size (Cliff’s Delta)

cliff.delta(Study_Hours ~ Work_Status, data = Dataset6.2)

## 
## Cliff's Delta
## 
## delta estimate: 0.2644444 (small)
## 95 percent confidence interval:
##       lower       upper 
## -0.03422594  0.51975307

Interpretation

There was not a significant difference in weekly study hours between students who Do Not Work (Mdn = 8.54) and those who Work (Mdn = 5.64), \(U = 569, p = .080\). The effect size was small (\(r_{rb} = 0.26\)).