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/elapr/Downloads/Dataset6.2-2.xlsx")
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
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)

The Graph appears to be tall and kind of postively skewed. The data is abnormal.

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

The Graph appears to be postively skewed. The data is abnormal.

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

The Dots for Works are in the Box ans close to whiskers. so, the data is normal. Some dots for Does_Not_work are far away from the whiskers which makes the data abnormal.

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
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

The p-value for Does_Not_Work is < 0.05 (0.00036) which means the data is abnormal. The p-value for Works is >0.05 (0.1305) which means the data is normal.

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

p > .05 (0.0797), this means the results were NOT significant.

Since they were not significant we dont have to calculate the effect size.

Does_Not_Work ((Mdn = 8.54) was not significantly different from Works (Mdn = 5.64), U = 569, p = 0.0797.