Assignment 6, Question 1

Is there a mean difference in body weight (kg) before versus after all participants tried the low calorie diet?

Load Required Packages

library(readxl)

## Warning: package 'readxl' was built under R version 4.6.1

library(ggpubr)

## Warning: package 'ggpubr' was built under R version 4.6.1

## Loading required package: ggplot2

## Warning: package 'ggplot2' was built under R version 4.6.1

library(effsize)

## Warning: package 'effsize' was built under R version 4.6.1

library(rstatix)

## Warning: package 'rstatix' was built under R version 4.6.1

## 
## Attaching package: 'rstatix'

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

library(rmarkdown)

Import dataset

A6Q1 <- read_excel("C:/Users/rteno/OneDrive - Saint Louis University/AA 5221/Assignment 6/Question 1/A6Q1.xlsx")

Create Groups for Before and After

Before <- A6Q1$Before
After <- A6Q1$After
Differences <- After - Before

Calculate the Descriptive Statistics

# Descriptive Statistics for 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

# Descriptive Statistics for After
mean(After, na.rm = TRUE)

## [1] 71.58994

median(After, na.rm = TRUE)

## [1] 70.88045

sd(After, na.rm = TRUE)

## [1] 6.639509

Create Histogram (Normality Check #1)

hist(Differences,
     main = "Histogram of Difference Scores",
     xlab = "Value",
     ylab = "Frequency",
     col = "blue",
     border = "black",
     breaks = 20)

# Interpret the Histogram 
# Histogram of Difference Scores
# The difference scores look abnormally distributed.
# The data is negatively skewed.
# The data does not have a proper bell curve.

Create Boxplot for Outliers (Normality Check #2)

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

# Interpret the Boxplot
# Boxplot of Difference Scores
# There is one dot outside the box.
# 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-Wilk Tests (Normality Check #3)

shapiro.test(Differences)

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

# Interpret the Shapiro-Wilk Test
# Shapiro-Wilk Difference Scores
# The data is normally distributed, (p = .332).

# Determine Overall Normality
# Histogram: Abnormal
# Boxplot: Normal
# Shapiro-Wilk: Normal
# Overall Decision: Normal

Conduct the 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

Report the Dependent T-Test

# A Dependent T-Test was conducted to determine if there was a 
# difference in body weight before versus after all participants tried 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