library(readxl)
library(ggpubr)

## Caricamento del pacchetto richiesto: ggplot2

library(effsize)
library(rstatix)

## 
## Caricamento pacchetto: 'rstatix'

## Il seguente oggetto è mascherato da 'package:stats':
## 
##     filter

A6Q2 <- read_excel("C:\\Users\\sonis\\OneDrive\\Desktop\\SLU\\AA 5221\\Assignment6\\A6Q2.xlsx")

Before <- A6Q2$Before
After <- A6Q2$After

Differences <- After - Before

mean(Before, na.rm = TRUE)

## [1] 76.13299

median(Before, na.rm = TRUE)

## [1] 75.95988

sd(Before, na.rm = TRUE)

## [1] 7.781323

mean(After, na.rm = TRUE)

## [1] 57.17874

median(After, na.rm = TRUE)

## [1] 58.36459

sd(After, na.rm = TRUE)

## [1] 14.39364

hist(Differences,
     main = "Histogram of Difference Scores",
     xlab = "Value",
     ylab = "Frequency",
     col = "blue",
     border = "black",
     breaks = 20)

#Data for the difference scores appears abnormally distributed.

boxplot(Differences,
        main = "Distribution of Score Differences (After - Before)",
        ylab = "Difference in Scores",
        col = "blue",
        border = "darkblue")

# The difference scores boxplot does have outliers.

shapiro.test(Differences)

## 
##  Shapiro-Wilk normality test
## 
## data:  Differences
## W = 0.89142, p-value = 0.02856

#Shapiro-Wilk Difference Scores
#The data is abnormally distributed, (p = .029).

wilcox.test(Before, After, paired = TRUE, na.action = na.omit)

## 
##  Wilcoxon signed rank exact test
## 
## data:  Before and After
## V = 210, p-value = 1.907e-06
## alternative hypothesis: true location shift is not equal to 0

df_long <- data.frame(id = rep(1:length(Before), 2), time = rep(c("Before", "After"), each = length(Before)), score = c(Before, After))

wilcox_effsize(df_long, score ~ time, paired = TRUE)

## # A tibble: 1 × 7
##   .y.   group1 group2 effsize    n1    n2 magnitude
## * <chr> <chr>  <chr>    <dbl> <int> <int> <ord>    
## 1 score After  Before   0.877    20    20 large

#A Wilcoxon Signed-Rank Test was conducted to determine if there was a difference in body weight between Before versus After keto diet.
#Before scores (Mdn = 75.96) were significantly different from after scores (Mdn = 58.36), V = 210, p < .001.
#The effect size was large, r = .877.