AAssignment6_6.3

https://rpubs.com/anup0stha/1398786

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("/Volumes/Anup/SLU/3rd Sem/Applied Analytics/Assignment 6/Dataset6.3.xlsx")

Separating the Data by Condition

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

Differences <- Before - After

##Calculating 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 Scores

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

the Histogram appears symmetrical and bell shaped

Create a Boxplot of the Difference Scores

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

There was one outlier in the boxplot. However, it is not very far away from the whisker.

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

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

Calculate the Effect Size

cohens_d <- effectsize::cohens_d (Dataset6.3$Stress_Pre, Dataset6.3$Stress_Post, paired = TRUE)

## For paired samples, 'repeated_measures_d()' provides more options.

print(cohens_d)

## Cohen's d |       95% CI
## ------------------------
## 0.66      | [0.29, 1.03]

Interpretation of Effect Size

the Effect Size is Medium

Report the Results

There was a significant difference in stress level Before (M = 65.86, SD = 9.49) and after (M = 57.90, SD = 10.17) mindfulness training , t(34) = 3.92, p < .00039. The effect size was medium (Cohen’s d = 0.66).