#Open the Installed Packages

library(readxl)
library(ggpubr)
## Loading required package: ggplot2

#Import and Name Dataset

Dataset6.3 <- read_excel("/Users/atharvapitke/Documents/Analytics/Assignment6/Dataset6.3.xlsx")

#Seperate the Data by Condition

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

#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

#Create a Histogram of the Difference Stress

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

The histogram appears symmetrical and bell-shaped (normal).

#Create a Boxplot of the Difference Scores

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

There was no outlier in the boxplot.

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, which means we should proceed with the Dependent t-test.

Conduct Inferential Test - 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 < .05, (less than .05), this means the results were SIGNIFICANT.

library(effectsize)

Calculate the Effect Size - Cohen’s D for Dependent T-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]

Report the results

There was a significant difference in Student pre stress (M = 65.87 SD = 9.5) and post stress (M = 57.90, SD = 10.18), t(34) = 3.92, p = 0.00039. The effect size was very large (Cohen’s d = 0.66).