A6Q1

Open the Installed Packages

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(effectsize)
library(rstatix)

## 
## Attaching package: 'rstatix'

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

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

Import and Name the Dataset

A6Q1<- read_excel("C:/Users/krish/Downloads/A6Q1.xlsx")

Create Groups for Before and After

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

Calculate the Descriptive Statistics

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

Create Histograms (Normality Check #1)

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

Interpret the Histograms

Histogram of Difference Scores The difference scores look abnormally distributed. The data is negetively skewed. The data has a no proper bell curve.

Create Boxplots for Outliers (Normality Check #2)

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

Interpret the Boxplots

There is one dot outside the boxplot. 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 >.05).

Conduct the Dependent T-Test since the data was NORMAL to determine if there was a difference before versus after

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 weight before the diet versus after the diet.

Before scores (M = 76.13, SD = 6.63) were significantly different from after scores (M = 71.58, SD = 6.63), t(19) = 1.90, p >0.05.