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(ggpubr)

## Loading required package: ggplot2

A6Q1 <- read_excel("//apporto.com/dfs/SLU/Users/brentgallagher_slu/Desktop/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

# Before - Mean:76.13, Median:75.96, sd: 7.79
# After - Mean: 71.59, Median: 70.89, sd: 6.64
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 have outliers.
shapiro.test(Differences)

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

# Shapiro-Wilk Normality test - w = 0.95, p-value = 0.33
# The data is normally distributed, (p = 0.33)
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

# data: Before and After
# t = 1.90, df = 19, p-value = 0.07245
# alternative hypothesis: true mean difference is not equal to 0
# 95 percent confidence interval:
# -0.46, 9.54
# Sample Estimates: mean difference 4.54
cohen.d(Before, After, paired = TRUE)

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

# Medium Effect: 0.63
# A Dependent T-Test was conducted to determine if there was a difference in weight between Before and After.
# Before scores (M = 76.13, SD = 7.79) were not significantly different from After scores (M = 71.59, SD = 6.64), t(19), p < .001.
# The effect size was medium, Cohen's d = 0.63