Is there a difference in body weight (kg) before versus after all participants tried the keto 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
A6Q2 <- read_excel("~/Documents/Documents - Marshall’s MacBook Pro/Education/SLU/2026/AA 5221/Data/Week 6 data/A6Q2.xlsx")

Before <- A6Q2$Before
After <- A6Q2$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] 57.17874
median(After, na.rm = TRUE)
## [1] 58.36459
sd(After, na.rm = TRUE)
## [1] 14.39364
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 abnormally distributed. The data is negatively skewed. The data does not have 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 not close to the whiskers. The dot is very far away from the whiskers. Based on these findings, the boxplot is not normal.

shapiro.test(Differences)
## 
##  Shapiro-Wilk normality test
## 
## data:  Differences
## W = 0.89142, p-value = 0.02856

Shapiro-Wilk Difference Scores. The data is abnormally distributed, (p = .029).

Data is not normal. Conduct the Wilcoxon Signed Rank test.

wilcox.test(Before, After, paired = TRUE, na.action = na.omit)
## 
##  Wilcoxon signed rank exact test
## 
## data:  Before and After
## V = 210, p-value = 1.907e-06
## alternative hypothesis: true location shift is not equal to 0

Calculate the effect size.

df_long <- data.frame(
  id = rep(1:length(Before), 2),
  time = rep(c("Before", "After"), each = length(Before)),
  score = c(Before, After)
)

wilcox_effsize(df_long, score ~ time, paired = TRUE)
## # A tibble: 1 × 7
##   .y.   group1 group2 effsize    n1    n2 magnitude
## * <chr> <chr>  <chr>    <dbl> <int> <int> <ord>    
## 1 score After  Before   0.877    20    20 large

A Wilcoxon Signed-Rank Test was conducted to determine if there was a difference in body weight (kg) before the keto diet versus after the keto diet. Before scores (Mdn = 75.96) were significantly different from after scores (Mdn = 58.36), V = 210, p = < .001. The effect size was large, r = .88.