Open the Required 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)

Import & Name Dataset

Dataset6.2 <- read_excel("D:/SLU/AdvAppliedAnalytics/Dataset6.2.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

Does_Not_Work (M = 9.62, SD = 7.45) and Works (M = 6.41, SD = 4.41)

Create Histograms for Each Group

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

For the Works Histogram, the data appears Positively Skewed (not-normal). The kurtosis also does not appears bell-shaped (not-normal)

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

For the Does not Works Histogram, the data appears Positively Skewed (not-normal). The kurtosis also appears tall and flat (not-normal)

Create Boxplots for Each Group

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

In the Works group, the dots are close to the whiskers and the data looks normal. In the No Tutoring group, few dots are far from the whisker and the data does not look normal. Therefore, the data is not normally distributed.

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

The data for Works(p-value = 0.13) was normal (p > .05)

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 Does not Works(p-value = 0.0003695) was not normal (p < .05) After conducting all three normality tests, it is clear we must use a Mann-Whitney U test.

Conduct Inferential Test - 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

p-value = 0.07973 which is greater than 0.05, this means the results were NOT SIGNIFICANT(p > .05).

Report the Results

Does_Not_Work (M = 9.62, SD = 7.45) was not significantly different from Works (M = 6.41, SD = 4.41), p = .08