library(dplyr)

## 
## Caricamento pacchetto: 'dplyr'

## I seguenti oggetti sono mascherati da 'package:stats':
## 
##     filter, lag

## I seguenti oggetti sono mascherati da 'package:base':
## 
##     intersect, setdiff, setequal, union

library(effectsize)
library(effsize)
library(readxl)
library(ggpubr)

## Caricamento del pacchetto richiesto: ggplot2

A6Q4 <- read_excel("C:\\Users\\sonis\\OneDrive\\Desktop\\SLU\\AA 5221\\Assignment6\\A6Q4.xlsx")

A6Q4 %>%
  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$Weight[A6Q4$Exercise == "lift"],
     breaks = 15,
     col = "skyblue",
     border = "white")

hist(A6Q4$Weight[A6Q4$Exercise == "nolift"],
     breaks = 15,
     col = "firebrick",
     border = "white")

#Data for lift group appears abnormally distributed.
#Data for nolift group appears abnormally distributed.

ggboxplot(A6Q4, x = "Exercise", y = "Weight",
          color = "Exercise",
          palette = "jco",
          add = "jitter")

# The lift group boxplot does have outliers.
# The nolift group boxplot does have outliers.

shapiro.test(A6Q4$Weight[A6Q4$Exercise == "lift"])

## 
##  Shapiro-Wilk normality test
## 
## data:  A6Q4$Weight[A6Q4$Exercise == "lift"]
## W = 0.78786, p-value = 0.0001436

shapiro.test(A6Q4$Weight[A6Q4$Exercise == "nolift"])

## 
##  Shapiro-Wilk normality test
## 
## data:  A6Q4$Weight[A6Q4$Exercise == "nolift"]
## W = 0.70002, p-value = 7.294e-06

#The lift group is abnormally distributed, (p < .001).
#The nolift group is abnormally distributed, (p < .001).

wilcox.test(Weight ~ Exercise, data = A6Q4)

## 
##  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

mw_effect <- cliff.delta(Weight ~ Exercise, data = A6Q4)
print(mw_effect)

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

# An Independent T-Test was conducted to determine if there was a difference in weight (kg) between participants who lift weights and those who do not lift weights.
# Those who do not lift weights (Mdn = 40.8) were significantly different from those who lift weights (Mdn = 116), W = 603, p < .001.
# The effect size was large, Cliff's Delta = .930.

#reflection:
#Honestly, I know that is not an excuse but I was playing the chess Olympiad and I was probably very tired, I can't explain otherwise the fact that I chose the wrong test even knowing that the groups were abnormally distributed.