Step 1: Open the Installed Packages

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

Step 2: Import Dataset

Dataset6.3 <- read_excel("C:/Users/yenug/OneDrive/Documents/Assignment 6/Dataset6.3.xlsx")

Step 3: Seperate the Data by Condition

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

Differences <- After - Before

Step 4: 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

Step 5: Create a Histogram of the Difference Scores

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

The histogram appears positively skewed and looks tall and thin (Abnormal).

Step 6: Create a Boxplot of the Difference Scores

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

There are no outliers in the boxplot so the data is normal and we will continue with Dependent T-Test.

Step 7: 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, the data is NORMAL which means we should proceed with the Dependent T-Test.

Step 8: Conduct Inferential 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. Effect Size is calculated in the next step.

Step 9: Calculate the Effect Size

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]

Cohen’s D effect size is 0.66 which means the the difference between the group averages is Medium.

Step 10: Results

There was a significant difference in Stress levels between Stress_Pre (65.86, SD = 9.49) and Stress_Post (M = 57.90, SD = 10.17), t(34) = 3.92, p < .001. The effect size was Medium (Cohen’s d = 0.66).

library(rmarkdown)