library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(effectsize)
library(effsize)
library(readxl)
library(rstatix)

## 
## Attaching package: 'rstatix'

## The following objects are masked from 'package:effectsize':
## 
##     cohens_d, eta_squared, omega_squared

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

A6Q1 <- read_excel("C:/Users/USER/OneDrive - Saint Louis University/AA 5221/Assignment 6/A6Q1.xlsx")
View(A6Q1)

beforeb <- A6Q1$Before
afterb <- A6Q1$After

Differences <- afterb-beforeb

# Descriptive Statistics for Before

mean(beforeb, na.rm = TRUE)

## [1] 76.13299

median(beforeb, na.rm = TRUE)

## [1] 75.95988

sd(beforeb, na.rm = TRUE)

## [1] 7.781323

#Descriptive statistics for After

mean(afterb, na.rm = TRUE)

## [1] 71.58994

median(afterb, na.rm = TRUE)

## [1] 70.88045

sd(afterb, na.rm = TRUE)

## [1] 6.639509

#Histogram

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

#Interpretations
#Data for the difference scores appears normally distributed

#Boxplot

boxplot(Differences,
        main = "Distribution of Score Differences (afterb - beforeb)",
        ylab = "Difference in Scores",
        col = "blue",
        border = "red")

#Interpretation of Boxplot
# The difference scores boxplot has one outlier.

#Shapiro wilk test
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 = .33).

#The Dependent T-Test
t.test(beforeb, afterb, paired = TRUE, na.action = na.omit)

## 
##  Paired t-test
## 
## data:  beforeb and afterb
## 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 the cohen's d(Effect Size)
cohen.d(beforeb, afterb, paired = TRUE)

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

#Report the Dependent T-Test

# A Dependent T-Test was conducted to determine if there was a difference in body weight between before and after a low-calorie diet.
#before scores (M= 76.13, SD = 7.78,) were significantly different from after scores (M=71.59, SD = 6.64), t(19) = 1.90, p < .05. 
#The effect size was Large, Cohen's d = .63.