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

library(readxl)
library(ggpubr)
## Loading required package: ggplot2
library(rmarkdown)
library(effsize)
library(rstatix)
## 
## Attaching package: 'rstatix'
## The following object is masked from 'package:stats':
## 
##     filter
A6Q1 <- read_excel("~/Documents/Documents - Marshall’s MacBook Pro/Education/SLU/2026/AA 5221/Data/Week 6 data/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 = "Weight (kg)",
     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).

Data is normal. Conduct the 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

A Dependent T-Test was conducted to determine if there was a difference in body weight (kg) before a low calorie diet versus after a 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 not calculated since the Dependent T-test result is not statistically significant (p > .05).