A6Q1

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

library(ggpubr)

## Loading required package: ggplot2

library(effsize)
library(rstatix)

## 
## Attaching package: 'rstatix'

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

library(readxl)
A6Q1 <- read_excel("A6Q1.xlsx")

Before <- A6Q1$Before
After <- A6Q1$After
Differences = After - Before
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 negatively skewed. The data does have a proper bell curve.

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

Boxplot There are dots outside the boxplot. The dots are not close to the whiskers The dots are 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

Shaprio-Wilk Difference Scores The data is normally distributed, (p=0,3318).

wilcox.test(Before, After, paired = TRUE, na.action = na.omit)

## 
##  Wilcoxon signed rank exact test
## 
## data:  Before and After
## V = 148, p-value = 0.114
## alternative hypothesis: true location shift is not equal to 0

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 Dependenet T-Test was conducted to determine if there was a difference in weight before the diet verus after the diet. Before scores (M = 76.13, SD = 7.78) were significantly different from after scores (M = 71.58, SD = 6.63), t(1.902) = 19, P = 0.07245. The effect size was Large, Cohen’s d = 0.6284