A6Q1

Import lIbrary

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(dplyr)

## 
## Attaching package: 'dplyr'

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

library(effectsize)
library(effsize)

Import file path

D1 <- read_excel("A6Q1.xlsx")

##Descriptive Stastistics

Before <- D1$Before
After <- D1$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

Normality check Histograms

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

Histogram of Difference Scores

The difference scores look [normally] distributed. The data is [positively skewed]. The data [has] a proper bell curve.

Box plot for outliers

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

Boxplot

There [is a] dot outside the boxplot. The dot [is] close to the whiskers. Based on these findings, the boxplot is [ not normal]

Shapiro Test

shapiro.test(Differences)

## 
##  Shapiro-Wilk normality test
## 
## data:  Differences
## W = 0.94757, p-value = 0.3318

Observarions

There is NO significant difference between our data’s distribution and a normal distribution The data is normally distributed

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

Report

A Dependent T-Test was conducted to determine if there was a difference in body weight (kg) before the diet versus after the diet. Before scores (M = 76.133, SD = 7.781) were not significantly different from after scores (M = 71.590, SD = 6.640), t(19) = 1.902, p > 0.05.