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

library(readxl)
library(ggpubr)
library(effsize)
library(rstatix)
A6Q1 <- read_excel("/Users/murphy/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
hist(Differences,
     main = "Histogram of Body Weight Differences",
     xlab = "Value",
     ylab = "Frequency",
     col = "blue",
     border = "black",
     breaks = 20)

Histogram of Body Weight Differences The difference scores look abnormally distributed. The data is negatively skewed The data has a proper bell curve.

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

Boxplot of Body Weight Differences There is one dot outside the boxplot. The dot is past 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 = 0.332).

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 the low calorie diet versus after the low calorie diet. Before scores (M = 76.13, SD = 7.81) were not significantly different from after scores (M = 71.59, SD = 6.64), t(19) = 1.90, p > 0.05. The effect size was not calculated as p > 0.05.