library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(effsize)
library(rstatix)

## 
## Attaching package: 'rstatix'

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

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

WeightBefore <- LowCalorie$Before
WeightAfter <- LowCalorie$After

Differences <- WeightAfter - WeightBefore

mean(WeightBefore, na.rm = TRUE)

## [1] 76.13299

median(WeightBefore, na.rm = TRUE)

## [1] 75.95988

sd(WeightBefore, na.rm = TRUE)

## [1] 7.781323

mean(WeightAfter, na.rm = TRUE)

## [1] 71.58994

median(WeightAfter, na.rm = TRUE)

## [1] 70.88045

sd(WeightAfter, 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 Weight Differences (After - Before)",
        ylab = "Difference in Weight",
        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 = .33).

t.test(WeightBefore, WeightAfter, paired = TRUE, na.action = na.omit)

## 
##  Paired t-test
## 
## data:  WeightBefore and WeightAfter
## 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

#mean difference is 4.54

cohen.d(WeightBefore, WeightAfter, paired = TRUE)

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

# the effect is medium to large

# A Dependent T-Test was conducted to determine if there was a difference in weight between Before and After.
#Weight before (M = 76.13, SD = 7.78) were significantly different from weight after (M = 71.58, SD = 6.63), t(19) = 1.90, p > .05.
#The effect size was large, Cohen's d = 0.63.