library(effsize)
library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(rstatix)

## 
## Attaching package: 'rstatix'

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

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

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

Differences <- After - Before

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

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

Histogram Interpretation

The histogram appears symmetrical.

It is difficult to state the exact kurtosis, but it appears bell-shaped (normal).

We may use a Dependent T-Test.

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

Boxplot Interpretation

There are no dots past the whiskers.

The data appears normal.

We may use a Dependent T-Test.

shapiro.test(Differences)

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

The p-value was above .05, which means we should proceed with the 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

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]

week 6 set c

Siddhartha Bharathwaj Yeluri

2026-02-23

Histogram Interpretation

The histogram appears symmetrical.

It is difficult to state the exact kurtosis, but it appears bell-shaped (normal).

We may use a Dependent T-Test.

Boxplot Interpretation

There are no dots past the whiskers.

The data appears normal.

We may use a Dependent T-Test.

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

There was a significant difference in stress levels between

Before (M = 65.87, SD = 9.50) and

After (M = 57.91, SD = 10.17),

t(34) = 3.93, p < .001.

The mean difference was 7.96.

The effect size was medium (Cohen’s d = 0.66).