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
Dataset6.3 <- read_excel("/Users/srikarthikeya/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 of Pre & Post",
       ylab = "Frequency",
       col = "blue",
       border = "black",
       breaks = 20)

Histogram is positively Skewed And had perfect bell curves on Right side

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

There is no Outliers in Boxplot graph

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

The p-value was above .05 (p-value = 0.1745), which means we should proceed with the Dependent t-test. p > .05 (greater than .05), the data was NORMAL.

  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

p < .05 (0.0003972), (less than .05), this means the results were SIGNIFICANT. So we are Calculating 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]

There was a significant difference in Pre Stress (median = 67.33, SD = 9.49) and Post Stress (Median = 59.14, SD = 10.1712), t = 3.92, p < .001.(0.000392) The effect size was medium (Cohen’s d = 0.66).