library(readxl)
library(ggpubr)
library(dplyr)
library(effectsize)
library(effsize)
library(ggplot2)
library(rstatix)
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
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 negatively skewed]. #The data does not have a proper bell curve.

#Group 2: Non-Lifters #The second variable looks abnormally distributed. #The data is positively skewed. #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.

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).

t.test(Weight ~ Exercise, data = A6Q4_2, 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
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

NOTE TO PROFESSOR: R required me to use Rstatix, needed to research what to do due to unused arguement error.

cohens_d_result <- rstatix::cohens_d(
  Weight ~ Exercise,
  data = A6Q4_2
)

print(cohens_d_result)
## # A tibble: 1 × 7
##   .y.    group1 group2 effsize    n1    n2 magnitude
## * <chr>  <chr>  <chr>    <dbl> <int> <int> <ord>    
## 1 Weight lift   nolift    1.58    25    25 large
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
A6Q4_2 %>%
  group_by(Exercise) %>%
  summarise(
    Median = median(Weight),
    N = n()
  )
## # A tibble: 2 × 3
##   Exercise Median     N
##   <chr>     <dbl> <int>
## 1 lift      116.     25
## 2 nolift     40.8    25

#An Independent T-Test was conducted to determine if there was a difference in Weight between Lifters and Non-Lifters. #Lifters weights (M = 120.0, SD = 53.3) were significantly different from Non-Lifters weights (M = 33.0, SD = 56.7), t(48) = 5.59, p < .001. #The effect size was large, Cohen’s d = 1.5.

#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.