assignment 6.4

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

goop <- read_excel("D:/Vedant Work/SLU/Spring Sem (Jan to May 2026)/Applied Analytics/Assignment 6/Assignment 6.4/goop.xlsx")

Before <- goop$stresspre
After  <- goop$stresspost

Differences <- After - Before

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

hist(Differences,
     main = "Histogram of Stress Score Differences",
     xlab = "Post - Pre Stress",
     ylab = "Frequency",
     col = "skyblue",
     border = "black",
     breaks = 20)

boxplot(Differences,
        main = "Distribution of Stress Score Differences",
        ylab = "Difference in Stress Scores",
        col = "lightgreen",
        border = "navyblue")

shapiro.test(Differences)

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

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

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

There was a significant difference in stress levels between before the program (Mdn = 47.24) and after the program (Mdn = 40.85), V = 620, p < .001. The effect size was very large (r₍rb₎ = .84).