Assignment 6 Datset 6.2

Step 1: Install the Required Packages install.packages(“readxl”) install.packages(“ggpubr”) install.packages(“dplyr”) install.packages(“effectsize”) install.packages(“effsize”)

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/srina/OneDrive/Documents/Madhu Master's/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 Works Scores",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightblue",
     border = "black",
     breaks = 10)

The data appears symmetrical. It is difficult to state the exact kurtosis, but it appears bell-shaped (normal).

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_Work histogram, the data appears symmetrical.The kurtosis also appears bell-shaped (normal).We may use an Independent T-Test.

Step 6: Create Boxplots for Each Group

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

The Works boxplot appears normal. There are no dots past the whiskers.The Does_Not_Work boxplot appears normal. There are no dots far past the whiskers. We may use an Independent T-Test.

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

The data for who Works was normal (p > .05).The data for who Does not work was abnormal (p < .05). After conducting all three normality tests, it is clear we must use a Mann-Whitney U test.

Step 8: Conduct Inferential 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 > .05 (greater than .05), this means the results were NOT significant.

Report the Results

The Does_Not_Work group (Mdn = 8.54) was not significantly different from the Works group (Mdn = 5.64), U = 569, p > .05. The data was not statically significant.