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

Dataset6.3 <- read_excel("/Users/ishujha/Downloads/AppliedAnalytics/Assignment6/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 positively skewed and bell-shaped (normal).

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

There was no dots or outliers in the boxplot. The data 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
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 the stress levels of students before the mindfulness program (M = 51.53, SD = 17.21) than the students after the program (M = = 41.49, SD = 18.89), t(34) = 6.207, p < .01 The effect size was large (Cohen’s d = 1.05).