A6Q1

Question #1: 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)

Import Data

A6Q1 <- read_excel("A6Q1.xlsx")

Before and After Score Creation

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

Differences Score Creation

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

Verifying Normality via Histogram

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

Histogram of Difference Scores Interpretation Histogram of Difference Scores The difference scores look normally distributed. The data is symetricial. Correction on analysis interpretation. The data does have a proper bell curve.

Using boxplot to check normality and outliers

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. Correction to interpretation. The dots are not very far away from the whiskers. Based on these findings, the boxplot is normal.

Statistically check normality

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=0.332). Rouded up one decmial place.

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

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. There was no significant difference in weight before the diet (M = 76.13, SD = 7.78) verse after the diet (M = 71.59, SD = 6.64), t(19) = 1.90, p > .05. Correction was made to the interpretation of the before and after analysis. The numbers were correct but needed to correct the analysis. The effect size was Large, Cohen’s d = 0.6284