library(readxl)
library(ggpubr)
## Loading required package: ggplot2
library(effectsize)
library(rstatix)
## 
## Attaching package: 'rstatix'
## The following objects are masked from 'package:effectsize':
## 
##     cohens_d, eta_squared
## The following object is masked from 'package:stats':
## 
##     filter
library(effsize)
A6Q1 <- read_excel("C:/Users/raadrish/Downloads/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
par(mar=c(4,4,2,1))
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 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

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

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 body weight (kg) 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(19) = -1.90, p > .05.

The effect size was medium, Cohen’s d = 0.63.