A6Q1

##Installing packages

library(effsize)
library(rstatix)

## 
## Attaching package: 'rstatix'

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

##Opening libraries

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(effsize)
library(rstatix)

##Importing dataset

A6Q1 <- read_excel("A6Q1.xlsx")

##Creating groups for Before and After

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

Differences <- After - Before

##Descritpive 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

##Normality Check 1, Histogram

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

##Histogram Interpetation #Histogram of Difference Scores The difference scores look normally distributed. The data is symmetrical. The data has a proper bell curve

##Normality Check 2, Box Plot for outliers

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

##Boxplot Interpretation #Boxplot 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.

##Normality check 3, 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 = .331).

##Overall Normality Data normal.

##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

##Effect Size for Dependent T-Test (Cohen’s d)

cohen.d(Before, After, paired = TRUE)

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

##Dependent T-Test Report 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 = 7.78) were not significantly different from after scores (M = 71.59, SD = 6.64), t(19) = 1.90, p > .05. The effect size was medium, Cohen’s d = 0.62.