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)
Dataset6.2 <- read_excel("C:/Users/pooja/Downloads/Dataset6.2-2 (1).xlsx")

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

Create Histograms for Each Group

hist(Dataset6.2$Study_Hours[Dataset6.2$Work_Status == "Does_Not_Work"],
     main = "Histogram of does not work",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightblue",
     border = "black",
     breaks = 10)

For the non-working students histogram, the data appears positively skewed. The kurtosis also appears abnormal due to the extreme values on the right side.

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

For the working students histogram, the data appears positively skewed. It is difficult to state the exact kurtosis, but it appears short and slightly flat rather than perfectly bell-shaped.

Create Boxplots for Each Group

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

For the working students boxplot, the data appears normal. There are no dots past the whiskers.

For the non-working students boxplot, the data appears abnormal. There are several dots past the whiskers. Some of the dots are far away from the whiskers.

We may need to use a Mann-Whitney U test.

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

The data for working students was normal (p > .05). The data for non-working students was abnormal (p < .05).

After conducting all three normality tests, it is clear we must use a Mann-Whitney U test.

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

If p > .05 (greater than .05), this means the results were NOT significant. Does_Not_Work (Mdn = 8.54) were not significantly different from Works (Mdn = 5.64) in weekly study hours, U = 569, p > .05.