Dataset6.4

Step 1: Open 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

Step 2: Import and Name Dataset

Dataset6.4 <- read_excel("C:/Users/tejas/Downloads/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: Calculate 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 Stress Levels",
     xlab = "Value",
     ylab = "Frequency",
     col = "blue",
     border = "black",
     breaks = 20)

The histogram looks negatively skewed and it does not have proper bell curve(not normal).

Step 6: Create a Boxplot of the Difference Scores

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

There are two outliers and but one is far away so the data is NOT normal. Switch to Wilcoxon-Sign Rank.

Step 7: Shapiro-Wilk Test of Normality

shapiro.test(Differences)

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

The p-value was below .05(0.0008), which means we should proceed with the Wilcoxon-Sign Rank test.

Step 8: Wilcoxon-Sign Rank test

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 < .05, (0.0000000025), this means the results were SIGNIFICANT. Will calculate the Effect Size.

Step 9: Calculate the 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 means there was large difference between the group averages.

Result

There was a significant difference in Stress Levels between Stress_pre(Mdn = 47.24008) and Stress_post (Mdn = 40.84836), V = 620, p = 2.503e-09. The effect size was large (r₍rb₎ = .84).