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

Dataset6.3 <- read_excel("C:/Users/tejas/Downloads/Dataset6.3.xlsx")

Step 3: Seperate the Data by Condition

Before <- Dataset6.3$Stress_Pre
After <- Dataset6.3$Stress_Post

Differences <- After - Before

Step 4: Calculate Descriptive Statistics for Each Group

mean(Before, na.rm = TRUE)
## [1] 65.86954
median(Before, na.rm = TRUE)
## [1] 67.33135
sd(Before, na.rm = TRUE)
## [1] 9.496524
mean(After, na.rm = TRUE)
## [1] 57.90782
median(After, na.rm = TRUE)
## [1] 59.14539
sd(After, na.rm = TRUE)
## [1] 10.1712

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 positively skewed and it does not have proper bell curve.

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 no dots so the data is normal and we will continue with Dependent T-Test.

Step 7: Shapiro-Wilk Test of Normality

shapiro.test(Differences)
## 
##  Shapiro-Wilk normality test
## 
## data:  Differences
## W = 0.95612, p-value = 0.1745

The p-value was above .05(0.174), which means we should proceed with the Dependent t-test.

Step 8: Dependent T-Test

t.test(Before, After, paired = TRUE)
## 
##  Paired t-test
## 
## data:  Before and After
## t = 3.9286, df = 34, p-value = 0.0003972
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##   3.843113 12.080317
## sample estimates:
## mean difference 
##        7.961715

The p < .05, (0.00039), this means the results were SIGNIFICANT. Will calculate the Effect Size.

Step 9: Calculate the Effect Size

effectsize::cohens_d(Before, After, paired = TRUE)
## For paired samples, 'repeated_measures_d()' provides more options.
## Cohen's d |       95% CI
## ------------------------
## 0.66      | [0.29, 1.03]

The effect size is 0.66 which means there was medium difference between the group averages.

Result

There was a significant difference in Stress Levels between Stress_pre (M = 65.8, SD = 9.49) and Stress_post (M = 57.90, SD = 10.17), t(34) = 3.928, p < .001. The effect size was medium (Cohen’s d = 0.66).