Step 2: Open the Installed Packages

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(effectsize)
library(effsize)

Step 3: Import and Name Dataset

Dataset6.2 <- read_excel("C:/Users/cniti/Documents/AA-5221 Applied Analytics/Assignment 6/Dataset6.2.xlsx")

Step 4: Calculate Descriptive Statistics for Each Group

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()
  )
## # 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

Step 5: Create Histograms for Each Group

hist(Dataset6.2$Study_Hours[Dataset6.2$Work_Status == "Works"],
     main = "Histogram of Working Hours",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightblue",
     border = "black",
     breaks = 10)

hist(Dataset6.2$Study_Hours[Dataset6.2$Work_Status == "Does_Not_Work"],
     main = "Histogram of No Working Hours",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightgreen",
     border = "black",
     breaks = 10)

Step 6: Create Boxplots for Each Group

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

Step 7: 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

Step 7: Conduct Inferential Test

t.test(Study_Hours ~ Work_Status, data = Dataset6.2, var.equal = TRUE)
## 
##  Two Sample t-test
## 
## data:  Study_Hours by Work_Status
## t = 2.0306, df = 58, p-value = 0.04688
## alternative hypothesis: true difference in means between group Does_Not_Work and group Works is not equal to 0
## 95 percent confidence interval:
##  0.04572065 6.37400708
## sample estimates:
## mean in group Does_Not_Work         mean in group Works 
##                    9.616468                    6.406604
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

Step 7: Calculate the Effect Size

cohens_d_result <- cohens_d(Study_Hours ~ Work_Status, data = Dataset6.2, pooled_sd = TRUE)
print(cohens_d_result)
## Cohen's d |       95% CI
## ------------------------
## 0.52      | [0.01, 1.04]
## 
## - Estimated using pooled SD.

Rank Biserial Correlation for Mann-Whitney U

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

Step 8: Report the Results Students who did not work (Mdn = 8.54) were not significantly different from students who worked (Mdn = 5.64) in weekly study hours, U = 569, p = .080. The effect size was small (r₍rb₎ = 0.26).