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library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(effsize)
library(rstatix)

## 
## Attaching package: 'rstatix'

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

A6Q1 <- read_excel("C:/Users/mn Technology Group/Desktop/Applied Analytics and Methods/Assignment 6/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

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

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

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

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.

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 = .332).

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

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

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

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 = 76.12, SD = 7.78) were significantly different from after scores (M = 71.58, SD = 6.64), t(19) = 1.9, p < .05