Assignment_6_Dataset6.4

#Step 2: Open the Installed Packages

``` r
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 3: Import and Name Dataset

Dataset6.4 <- read_excel("C:/Users/cniti/Documents/AA-5221 Applied Analytics/Assignment 6/Dataset6.4.xlsx")

#Step 4: Seperate the Data by Condition

Before <- Dataset6.4$Stress_Pre
After <- Dataset6.4$Stress_Post

Differences <- After - Before

#Step 5: Calculate Descriptive Statistics for Each Group

mean(Before, na.rm = TRUE)

## [1] 51.53601

median(Before, na.rm = TRUE)

## [1] 47.24008

sd(Before, na.rm = TRUE)

## [1] 17.21906

mean(After, na.rm = TRUE)

## [1] 41.4913

median(After, na.rm = TRUE)

## [1] 40.84836

sd(After, na.rm = TRUE)

## [1] 18.88901

#Step 6: Create a Histogram of the Difference Scores

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

#Step 7: Create a Boxplot of the Difference Scores

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

#Step 8: Shapiro-Wilk Test of Normality

shapiro.test(Differences)

## 
##  Shapiro-Wilk normality test
## 
## data:  Differences
## W = 0.87495, p-value = 0.0008963

#Step 8: Conduct Inferential Test #Dependent T-Test

t.test(Before, After, paired = TRUE)

## 
##  Paired t-test
## 
## data:  Before and After
## t = 6.2067, df = 34, p-value = 4.649e-07
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##   6.755787 13.333620
## sample estimates:
## mean difference 
##         10.0447

#Wilcoxon Sign Rank

wilcox.test(Before, After, paired = TRUE)

## 
##  Wilcoxon signed rank exact test
## 
## data:  Before and After
## V = 620, p-value = 2.503e-09
## alternative hypothesis: true location shift is not equal to 0

#Step 8: Calculate the Effect Size #Cohen’s D for Dependent T-Test

effectsize::cohens_d(After, Before, paired = TRUE)

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

## Cohen's d |         95% CI
## --------------------------
## -1.05     | [-1.46, -0.63]

#Rank Biserial Correlation for Mann-Whitney U

df_long <- data.frame(
  id = rep(1:length(Before), 2),
  time = rep(c("Before", "After"), each = length(Before)),
  score = c(Before, After)
)

wilcox_effsize(df_long, score ~ time, paired = TRUE)

## # A tibble: 1 × 7
##   .y.   group1 group2 effsize    n1    n2 magnitude
## * <chr> <chr>  <chr>    <dbl> <int> <int> <ord>    
## 1 score After  Before   0.844    35    35 large

Step 9: Report the Results There was a significant difference in stress levels between Before (Mdn = 47.24) and After (Mdn = 40.85), V = 620, p < .001. The effect size was large (r₍rb₎ = 0.84)