Assignment 6 Research Scenario 4

Step 1: Open the installed packages

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

#library(effectsize)
library(rstatix)

## 
## Attaching package: 'rstatix'

## The following object is masked from 'package:stats':
## 
##     filter

Step 2: Import Data Set

Dataset6.4 <- read_excel("D:/SLU/APPLIED ANALYTICS/ASSIGNMENT 6/Dataset6.4.xlsx")

Step 3: Seperate the Data by Condition

Before <- Dataset6.4$Stress_Pre
After <- Dataset6.4$Stress_Post

Differences <- After - Before

Step 4: Calculating Descriptive Statistics for Each Group

mean(Before, na.rm = TRUE)

## [1] 51.53601

median(Before, na.rm = TRUE)

## [1] 47.24008

sd(Before, na.rm = TRUE)

## [1] 17.21906

mean(After, na.rm = TRUE)

## [1] 41.4913

median(After, na.rm = TRUE)

## [1] 40.84836

sd(After, na.rm = TRUE)

## [1] 18.88901

Step 5: Create a Histogram of the Difference Scores

hist(Differences,
     main = "Histogram of Difference in Stress Levels",
     xlab = "Stress",
     ylab = "Frequency",
     col = "lightblue",
     border = "black",
     breaks = 20)

The histogram appears negatively skewed and does not have a proper bell curve.

Step 6: Creating a Boxplot of the Difference Scores

boxplot(Differences,
        main = "Distribution of Stress Level Differences (After - Before)",
        ylab = "Difference in Stress Level",
        col = "blue",
        border = "darkblue")

There are two outliers in the boxplot. However, they are not very far away from the whisker.

Step 7: Shapiro-Wilk Test of Normality

shapiro.test(Differences)

## 
##  Shapiro-Wilk normality test
## 
## data:  Differences
## W = 0.87495, p-value = 0.0008963

p < .05 (0.0008963 less than .05), the data is NOT NORMAL. We may proceed with Wilcoxon Sign Rank

Step 8: Conducting Wilcoxon Sign Rank

wilcox.test(Before, After, paired = TRUE)

## 
##  Wilcoxon signed rank exact test
## 
## data:  Before and After
## V = 620, p-value = 2.503e-09
## alternative hypothesis: true location shift is not equal to 0

p<0.05, this means results are significant, effect size is calculated in the next step.

Step 9: Calculating (Rank Biserial Correlation for Mann-Whitney U) Effect Size

df_long <- data.frame(
  id = rep(1:length(Before), 2),
  time = rep(c("Before", "After"), each = length(Before)),
  score = c(Before, After)
)

wilcox_effsize(df_long, score ~ time, paired = TRUE)

## # A tibble: 1 × 7
##   .y.   group1 group2 effsize    n1    n2 magnitude
## * <chr> <chr>  <chr>    <dbl> <int> <int> <ord>    
## 1 score After  Before   0.844    35    35 large

The effect size is 0.844 which is very large

Step 10: Reporting of Results

There was a significant difference in stress levels between Stress_Pre (Mdn = 47.24) and Stress_Post (Mdn = 40.84), V = 620, p < .001. The effect size was very large (r₍rb₎ = .84).

library(rmarkdown)

Assignment 6 Research Scenario 4

Varuna

2026-02-23