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 < .01).
#The nolift group is abnormally distributed, (p < .01).

t.test(Weight ~ Exercise, data = A6Q4, 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

cohens_d_result <- cohens_d(Weight ~ Exercise, data = A6Q4)
print(cohens_d_result)

## Cohen's d |       95% CI
## ------------------------
## 1.58      | [0.94, 2.21]
## 
## - Estimated using pooled SD.

# An Independent T-Test was conducted to determine if there was a difference in Weight between people who lift weights and don't lift weights
# The lift group scores (M = 120.08, SD = 53.3) were significantly different from nolift group scores (M = 33.02, SD = 56.7), (t(df 48) = 5.60, p < .01).
# The effect size was very large, Cohen's d = 1.58.