Assignment 6, Question 4

Is there a difference in body weight (kg) between participants who lift weights versus participants who do not lift weights?

Load Required Packages

library(readxl)

## Warning: package 'readxl' was built under R version 4.6.1

library(ggpubr)

## Warning: package 'ggpubr' was built under R version 4.6.1

## Loading required package: ggplot2

## Warning: package 'ggplot2' was built under R version 4.6.1

library(dplyr)

## Warning: package 'dplyr' was built under R version 4.6.1

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(effectsize)

## Warning: package 'effectsize' was built under R version 4.6.1

library(effsize)

## Warning: package 'effsize' was built under R version 4.6.1

library(rmarkdown)

Import dataset

A6Q4_2 <- read_excel("C:/Users/rteno/OneDrive - Saint Louis University/AA 5221/Assignment 6/Question 4/A6Q4-2.xlsx")

Calculate the Descriptive Statistics

A6Q4_2 %>%
  group_by(Exercise) %>%
summarise(
  Mean = mean(Weight, na.rm = TRUE),
  Median = median(Weight, na.rm = TRUE),
  SD = sd(Weight, na.rm = TRUE),
  N = n()
  )

## # A tibble: 2 × 5
##   Exercise  Mean Median    SD     N
##   <chr>    <dbl>  <dbl> <dbl> <int>
## 1 lift     120.   116.   53.3    25
## 2 nolift    33.0   40.8  56.7    25

Create Histograms (Normality Check #1)

  # Histogram for lift
hist(A6Q4_2$Weight[A6Q4_2$Exercise == "lift"],
     main = "Histogram of lift Weight",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightgreen",
     border = "black",
     breaks = 10)

# Histogram for nolift
hist(A6Q4_2$Weight[A6Q4_2$Exercise == "nolift"],
     main = "Histogram of nolift Weight",
     xlab = "Value",
     ylab = "Frequency",
     col = "lightblue",
     border = "black",
     breaks = 10)

# Interpret the Histograms
#Group 1: lift
#The lift group looks abnormally distributed.
#The data is positively skewed.
#The data does not have a proper bell curve.

#Group 2: nolift
#The nolift group looks abnormally distributed.
#The data is negatively skewed.
#The data does not have a proper bell curve.

Create Boxplots for Outliers (Normality Check #2)

ggboxplot(A6Q4_2, 
          x = "Exercise", 
          y = "Weight",
          color = "Exercise",
          palette = "jco",
          add = "jitter")

# Interpret the Boxplots
# Boxplot 1: lift
# There are two dots outside the boxplot.
# The dots are not close to the whisker.
# The dots are very far away from the whisker.
# Based on these findings, the boxplot is abnormal.

# Boxplot 2: nolift
# There is one dot outside the boxplot.
# The dot is not close to the whisker.
# The dot is very far away from the whisker.
# Based on these findings, the boxplot is abnormal.

Shapiro-Wilk Tests (Normality Check #3)

shapiro.test(A6Q4_2$Weight[A6Q4_2$Exercise == "lift"])

## 
##  Shapiro-Wilk normality test
## 
## data:  A6Q4_2$Weight[A6Q4_2$Exercise == "lift"]
## W = 0.78786, p-value = 0.0001436

shapiro.test(A6Q4_2$Weight[A6Q4_2$Exercise == "nolift"])

## 
##  Shapiro-Wilk normality test
## 
## data:  A6Q4_2$Weight[A6Q4_2$Exercise == "nolift"]
## W = 0.70002, p-value = 7.294e-06

# Interpret the Shapiro-Wilk Tests
# Group 1: lift
# The lift group is abnormally distributed, (p <.001).

# Group 2: nolift
# The nolift group is abnormally distributed, (p <.001).

Determine Overall Normality

# Histograms: Abnormal
# Boxplots: Abnormal
# Shapiro-Wilks: Abnormal
# Overall Decision: Abnormal

Conduct the Mann-Whitney U

wilcox.test(Weight ~ Exercise, data = A6Q4_2)

## 
##  Wilcoxon rank sum exact test
## 
## data:  Weight by Exercise
## W = 603, p-value = 7.132e-11
## alternative hypothesis: true location shift is not equal to 0

Calculate Effect Size for Mann-Whitney U

mw_effect <- cliff.delta(Weight ~ Exercise, data = A6Q4_2)
print(mw_effect)

## 
## Cliff's Delta
## 
## delta estimate: 0.9296 (large)
## 95 percent confidence interval:
##     lower     upper 
## 0.7993841 0.9764036

Report the Mann-Whitney U

# A Mann-Whitney U Test was conducted to determine if there was a difference in
# body weight between participants who lift weights and participants who do not lift weights.
# Lift scores (Mdn = 116.00) were significantly different from nolift scores
# (Mdn = 40.80), U = 603, p < .001.
# The effect size was large, Cliff's Delta = .93.