##Question: 4: Is there a difference in body weight (kg) between participants who lift weights versus participants who do not lift weights?

#Open packages
library(readxl)
library(ggpubr)
library(dplyr)
library(effectsize)
library(effsize)
library(rmarkdown)

#Import dataset
Q4 <- read_excel("C:/Users/Julia/OneDrive/Desktop/Assignment 6/Question 4/A6Q4-2.xlsx")

#Descriptive Statistics
Q4 %>%
  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

#No Lift Histogram
hist(Q4$Weight[Q4$Exercise == "nolift"],
     main = "Histogram of No Lift Weight",
     xlab = "Weight (kg)",
     ylab = "Frequency",
     col = "lightblue",
     border = "black",
     breaks = 10)

#Group 1: No Lift
#The first variable looks abnormally distributed.
#The data is negatively skewed.
#The data does not have a proper bell curve.

#Lift Histogram
hist(Q4$Weight[Q4$Exercise == "lift"],
     main = "Histogram of Lift Weight",
     xlab = "Weight (kg)",
     ylab = "Frequency",
     col = "lightgreen",
     border = "black",
     breaks = 10)

#Group 2: Lift
#The second variable looks abnormally distributed.
#The data is positively skewed. 
#The data does not have a proper bell curve.

#Create Boxplot for Outliers
ggboxplot(Q4, x = "Exercise", y = "Weight",
          color = "Exercise",
          palette = "jco",
          add = "jitter")

#Boxplot 1: No 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.

#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-Wilk Tests
shapiro.test(Q4$Weight[Q4$Exercise == "nolift"])
## 
##  Shapiro-Wilk normality test
## 
## data:  Q4$Weight[Q4$Exercise == "nolift"]
## W = 0.70002, p-value = 7.294e-06
shapiro.test(Q4$Weight[Q4$Exercise == "lift"])
## 
##  Shapiro-Wilk normality test
## 
## data:  Q4$Weight[Q4$Exercise == "lift"]
## W = 0.78786, p-value = 0.0001436

Shapiro-Wilk Interpretation: Group 1: No Lift The first group is abnormally distributed, (p < .001).

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

#Independent T-Test
t.test(Weight ~ Exercise, data = Q4, var.equal = TRUE)
## 
##  Two Sample t-test
## 
## data:  Weight by Exercise
## t = 5.5923, df = 48, p-value = 1.045e-06
## alternative hypothesis: true difference in means between group lift and group nolift is not equal to 0
## 95 percent confidence interval:
##   55.75715 118.35710
## sample estimates:
##   mean in group lift mean in group nolift 
##            120.08238             33.02525

Independent T-Test Interpretation: An Independent T-Test was conducted to determine if there was a difference in body weight (kg) between No lift and lift. No lift scores (M = 33.03, SD = 56.7) were not significantly different from lift scores (M = 120.08, SD = 53.3), t(48) = 5.59, p < .001.

#Mann-Whitney U Test
wilcox.test(Weight ~ Exercise, data = Q4)
## 
##  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
#Effect Size for Mann-Whitney U
mw_effect <- cliff.delta(Weight ~ Exercise, data = Q4)
print(mw_effect)
## 
## Cliff's Delta
## 
## delta estimate: 0.9296 (large)
## 95 percent confidence interval:
##     lower     upper 
## 0.7993841 0.9764036

Mann-Whitney U Interpretation: A Mann-Whitney U test was conducted to determine if there was a difference in body weight (kg) between No Lift and Lift groups. No Lift scores (Mdn = 40.84) were significantly different from Lift scores (Mdn = 115.59), U = 603, p < .001. The effect size was large, Cliff’s Delta = .93.