library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(effsize)
library(rstatix)

## 
## Attaching package: 'rstatix'

## The following object is masked from 'package:stats':
## 
##     filter

A6Q1 <- read_excel("C:/Users/giuli/Downloads/A6Q1.xlsx")
Before <- A6Q1$Before
After <- A6Q1$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] 71.58994

median(After, na.rm = TRUE)

## [1] 70.88045

sd(After, na.rm = TRUE)

## [1] 6.639509

hist(Differences,
     breaks = 15,
     col = "blue",
     border = "white")

#Data for the difference scores appears normally distributed.
boxplot(Differences,
        main = "Distribution of Score Differences (After - Before)",
        ylab = "Difference in Scores",
        col = "blue",
        border = "darkblue")

# The difference scores boxplot does not have outliers.
shapiro.test(Differences)

## 
##  Shapiro-Wilk normality test
## 
## data:  Differences
## W = 0.94757, p-value = 0.3318

#Shapiro-Wilk Difference Scores
#The data is normally distributed, (p = 0.331).
t.test(Before, After, paired = TRUE, na.action = na.omit)

## 
##  Paired t-test
## 
## data:  Before and After
## t = 1.902, df = 19, p-value = 0.07245
## alternative hypothesis: true mean difference is not equal to 0
## 95 percent confidence interval:
##  -0.4563808  9.5424763
## sample estimates:
## mean difference 
##        4.543048

cohen.d(Before, After, paired = TRUE)

## 
## Cohen's d
## 
## d estimate: 0.6284306 (medium)
## 95 percent confidence interval:
##      lower      upper 
## -0.1035207  1.3603820

# A Dependent T-Test was conducted to determine if there was a difference in weight between Before and After.
# Before scores (M = 76.1, SD = 7.8) were significantly different from After scores (M = 71.5, SD = 6.6), t(19) = 1.9, p = 0.072)
#The effect size was medium, Cohen's d = 0.63.


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   0.359    20    20 moderate

#A Wilcoxon Signed-Rank Test was conducted to determine if there was a difference in After before low-calorie diet versus after Before.
#Before scores (Mdn = 75.96) were significantly different from after scores (Mdn = 70.88), V = 148, p = 0.114
#The effect size was medium, r = 0.36