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("C:/Users/Leyav/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)

the histogram appears Slightly negatively skewed and Kurtosis is Slightly flat

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

there is no outlier in the data hence it is normal.

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

If p < .05, (0.000), this means the results were SIGNIFICANT

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

There was significant difference in the dependent variable between Before training (M = 65.86, SD = 9.49) and after training (M = = 57.91, SD = 10.2), t(34) = 3.93, p = 0.000. The effect size was medium (Cohen’s d = -0.66).