Installing the Required Packages install.packages(“readxl”) install.packages(“ggpubr”) install.packages(“effectsize”) install.packages(“rstatix”)

Opening the Installed Packages:

library(readxl)
library(ggpubr)
## Loading required package: ggplot2
library(effectsize)
library(rstatix)
## 
## Attaching package: 'rstatix'
## The following objects are masked from 'package:effectsize':
## 
##     cohens_d, eta_squared
## The following object is masked from 'package:stats':
## 
##     filter

Loading Dataset:

Dataset6.4 <- read_excel("C:/Users/datta/Downloads/Dataset6.4.xlsx")

Separating the Data by Condition:

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

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

Creating a Histogram of the Difference Scores:

hist(Differences,
     main = "Histogram of Difference Scores",
     xlab = "Value",
     ylab = "Frequency",
     col = "red",
     border = "black",
     breaks = 20)

Creating a Boxplot of the Difference Scores:

boxplot(Differences,
        main = "Distribution of Score Differences (After - Before)",
        ylab = "Difference in Scores",
        col = "red",
        border = "black")

Shapiro-Wilk Test of Normality:

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

Since the p-value is smaller than.05, we have to continue with the Wilcoxon Sign Rank in order to conduct the Inferential Test..

Conduct Inferential Test: 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

The p-value is less than .05, so we need to calculate the effect size.

Calculating the Effect Size: Rank Biserial Correlation for Mann-Whitney U

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 (Large).

Reporting Results: There was a significant difference in stress levels between Before participation in the exercise program (Mdn = 47.24) and After participation in the exercise program (Mdn = 40.848), V = 620, p < .001. The effect size was large (r₍rb₎ = .84).