Assignment6_Dataset6.4

Open the Installed Packages

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

Import and Name Dataset

Dataset6.4 <- read_excel("/Users/atharvapitke/Documents/Analytics/Assignment6/Dataset6.4.xlsx")

Separate the Data by Condition

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

Differences <- After-Before

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

Create a Histogram of the Difference Stress

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

The histogram appears negatively skewed and abnormal.

Create a Boxplot of the Difference Stress

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

There was two outliers in the boxplot. However, one is not very far away from the whisker and another is little far.

Shapiro-Wilk Test of Normality

shapiro.test(Differences)

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

The p = 0.0008963 (less than .05), the data was NOT normal. Proceed with Wilcoxon Sign Rank.

Conduct Inferential Test - Wilcoxon Sign Rank

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

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

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

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

Report the Result

There was a significant difference in the dependent variable between pre stress (Mdn = 47.24) and post stress (Mdn = 40.85), V = 620, p = 2.503e-09. The effect size was large (r₍rb₎ = 0.844).