library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(effsize)
library(rstatix)

## 
## Attaching package: 'rstatix'

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

library(readxl)
A6Q1 <- read_excel("C:/Users/mercy/OneDrive - Saint Louis University/AA 5221/Assignment 6/A6Q1.xlsx")
View(A6Q1)
Before <- A6Q1$Before
After <- A6Q1$After

#Calculate the Descriptive Statistics.
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

#Normality Check1:Histogram.
hist(Differences,
     breaks = 15,
     col = "blue",
     border = "white")

#Reporting
#Data for the difference in body weight before and after low calore diet appears normally distributed

#Normality Check2:Boxplot.
boxplot(Differences,
        main = "Body Weight  Differences (After - Before)",
        ylab = "Difference in Weight",
        col = "blue",
        border = "darkblue")

#Reporting
#The body weight difference  boxplot has one outlier.

#Normality Check3: Shapiro-Wilk.
shapiro.test(Differences)

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

#Reporting
#Shapiro-Wilk Body Weight Differences
#The data is normally distributed, (p = .33).

# Dependent T-Test.
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

#Calculate Cohen's.
cohen.d(Before, After, paired = TRUE)

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

#Report.
# A Dependent T-Test was conducted to determine if there was a difference in weight between Before and After a low calorie diet.
#Before (M = 76.13, SD = 7.78) After (M = 71.59, SD = 6.64) t(19) = 1.90 p > .001
#The effect size was medium  d = 0.65.