Correction - Add Research question Is there a difference in body weight (kg) between participants who lift weights versus participants who do not lift weights?

library(readxl)
library(ggpubr)
library(dplyr)
library(effectsize)
library(effsize)
library(ggplot2)
library(rstatix)

Descriptive Stats

A6Q4_2 %>%
  group_by(Exercise) %>%
  summarise(
    Mean = mean(Weight),
    SD = sd(Weight),
    N = n()
)
## # A tibble: 2 × 4
##   Exercise  Mean    SD     N
##   <chr>    <dbl> <dbl> <int>
## 1 lift     120.   53.3    25
## 2 nolift    33.0  56.7    25

Create Historgram

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

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

Group 1: Lifters The first variable looks abnormally distributed. The data is Positive skewed. Correction - student error. Modify to positive. The data does not have a proper bell curve.

Group 2: Non-Lifters The second variable looks abnormally distributed. The data is negative skewed. Correction - student error. Modify to negative. The data does not have a proper bell curve.

NOTE for Professor - This flagged me to review the data. There are some weights that are negative. Not possible. Errors in the data.

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

Boxplot 1: Lifters 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.

#Boxplot 2: Non Lifters 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.

Check normality.

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: Lifters. The first group is abnormally distributed, (p < .001).

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

Mann Whitney 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

Correction: Remove t test and remove Cohen’s D.

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

Results: A Mann-Whitney U test was conducted to determine if there was a difference in Weight between Lifters and Non-Lifters. Lifters weights (Mdn = 116.0) were significantly different from Non-Lifters weights (Mdn = 40.8) U = 603, p < .001. The effect size was large, Cliff’s Delta = .930.