assignment6(3)

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/elapr/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 stress",
     xlab = "Value",
     ylab = "Frequency",
     col = "blue",
     border = "black",
     breaks = 20)

The Graph looks slightly flat and slightly bell shape.

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

There is no outlier in this boxplot.

shapiro.test(Differences)

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

p > .05 (0.175), the data was NORMAL. Continuing with 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

p-value = 0.00039, which is less than 0.05 which means the difference between pre & post stresscscores is significant. Since the data is significant, we will be calculating the effective size using Cohen’s D test.

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 = .66).