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("Desktop/AA HOMEWORK/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,
     main = "Histogram of Difference Scores",
     xlab = "Value",
     ylab = "Frequency",
     col = "blue",
     border = "black",
     breaks = 20)

#Histogram of Difference Scores #The Difference scores look abnormally distritubed. #The data is negatively Skewed. #The data does not have a proper bell curve.

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

#Boxplot #There is one dot outside the boxplot. #The dot is close to the whiskers. #The dot is not very far away from the whiskers. #Based on these findings, the boxplot is normal.

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

#Shapiro-Wilk Difference Scores #The data is normal distributed, (p = .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
wilcox.test(Before, After, paired = TRUE, na.action = na.omit)
## 
##  Wilcoxon signed rank exact test
## 
## data:  Before and After
## V = 148, p-value = 0.114
## alternative hypothesis: true location shift is not equal to 0
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 body weight before the low-calorie diet versus after the low-calorie diet. #Before scores (M = 76.13, SD = 7.78) were not significantly different from after scores (M = 71.59, SD = 6.64), t(19) = 1.90, p > .05.