Assign 6_Q1

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(effectsize)

A6Q1 <- read_excel("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 normally distributed.
#The data is symmetrical.
#The data has 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

cohens_d(Before, After, paired = TRUE)

## For paired samples, 'repeated_measures_d()' provides more options.

## Cohen's d |        95% CI
## -------------------------
## 0.43      | [-0.04, 0.88]

#A Dependent T-Test was conducted to determine if there was a difference in weight before the low calorie diet versus after 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(d19) = 1.90, p > .05.