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

library(readxl)
library(ggpubr)
## Loading required package: ggplot2
library(rmarkdown)
library(dplyr)
## 
## 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)
library(effsize)

A6Q4_2 <- read_excel("~/Documents/Documents - Marshall’s MacBook Pro/Education/SLU/2026/AA 5221/Data/Week 6 data/A6Q4-2.xlsx")

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

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

Group 1: Lift. The Cardio data looks abnormally distributed. The data is positively skewed. The data does not have a proper bell curve.

Group 2: NoLift. The NoCardio data looks abnormally distributed. The data is negatively skewed. The data does not have a proper bell curve.

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

Boxplot 1: NoLift. There are dots outside the boxplot. There is one dot not close to the whiskers. The dot is very far away from the whiskers. The outliers are not balanced. Based on these findings, the boxplot is not normal.

Boxplot 2: Lift. There are dots outside the boxplot. The dots are not close to the whiskers. The dots are very far away from the whiskers. The outliers are not balanced. Based on these findings, the boxplot is not normal.

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

Group 1: Lift. The first group is abnormally distributed, (p < .001).

Group 2: NoLift. The second group is abnormally distributed, (p < .001).

Data is not normal. Conduct the Mann-Whitney U test.

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.

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

A Mann-Whitney U test was conducted to determine if there was a difference in between Lift and NoLift groups. 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.