Assignment 6 Datset 6.3

Step 1: Open the Installed Packages

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

Step 2: Import and Name Dataset

Dataset6.3 <- read_excel("C:/Users/srina/OneDrive/Documents/Madhu Master's/Applied Analytics/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 Scores",
     xlab = "Value",
     ylab = "Frequency",
     col = "orange",
     border = "black",
     breaks = 20)

The histogram appears positively skewed. Kutosis : It is difficult to state the exact kurtosis, but it appears bell-shaped (normal).

Step 7: Create a Boxplot of the Difference Scores

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

There are no dots, so the data is normal.

Step 8: 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.

Step 9: 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

Here, p < .05, (less than .05), this means the results were SIGNIFICANT.

Step 10: Calculate the Effect Size

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 stress levels between Stress_Pre (M = 65.87, SD = 9.50) and Stress_Post (M = 57.91, SD = 10.17),t(34) = 3.93, p < .001.The mean difference was 7.96.The effect size was medium (Cohen’s d = 0.66).