Assignment 6 Question 4

library(readxl)
library(rcompanion)

A6Q4 <- read_excel("C:/Users/nehab/OneDrive/A5221/Assignment 6/A6Q4.xlsx")

# Check the weightlifting groups
table(A6Q4$Exercise)

## 
##   lift nolift 
##     25     25

# Descriptive statistics for each group
aggregate(
  Weight ~ Exercise,
  data = A6Q4,
  FUN = mean
)

##   Exercise    Weight
## 1     lift 120.08238
## 2   nolift  33.02525

aggregate(
  Weight ~ Exercise,
  data = A6Q4,
  FUN = sd
)

##   Exercise   Weight
## 1     lift 53.31766
## 2   nolift 56.70695

aggregate(
  Weight ~ Exercise,
  data = A6Q4,
  FUN = median
)

##   Exercise    Weight
## 1     lift 115.58898
## 2   nolift  40.83897

# Examine weight distributions for both groups
boxplot(
  Weight ~ Exercise,
  data = A6Q4,
  main = "Body Weight by Weightlifting",
  xlab = "Regular Weightlifting",
  ylab = "Body Weight"
)

# Test normality separately for both groups
by(
  A6Q4$Weight,
  A6Q4$Exercise,
  shapiro.test
)

## A6Q4$Exercise: lift
## 
##  Shapiro-Wilk normality test
## 
## data:  dd[x, ]
## W = 0.78786, p-value = 0.0001436
## 
## ------------------------------------------------------------ 
## A6Q4$Exercise: nolift
## 
##  Shapiro-Wilk normality test
## 
## data:  dd[x, ]
## W = 0.70002, p-value = 7.294e-06

# Both groups are not normally distributed because both p-values are less than .05.
# The boxplot also shows possible outliers.
# Therefore, a Mann-Whitney U Test will be used.

# Conduct the Mann-Whitney U Test
wilcox.test(
  Weight ~ Exercise,
  data = A6Q4,
  exact = FALSE
)

## 
##  Wilcoxon rank sum test with continuity correction
## 
## data:  Weight by Exercise
## W = 603, p-value = 1.836e-08
## alternative hypothesis: true location shift is not equal to 0

# Calculate the effect size
wilcoxonR(
  A6Q4$Weight,
  A6Q4$Exercise
)

##     r 
## 0.798

Interpretation

A Mann-Whitney U test was conducted to compare body weight between participants who regularly lift weights and participants who do not. Body weight was significantly higher for the weightlifting group (Mdn = 115.59) than for the no-weightlifting group (Mdn = 40.84), W = 603, p < .001. The effect size was large (r = .80). Therefore, the null hypothesis was rejected.