Assignment 6 Question 2

library(readxl)
library(ggpubr)

## Loading required package: ggplot2

library(effsize)
library(rstatix)

## 
## Attaching package: 'rstatix'

## The following object is masked from 'package:stats':
## 
##     filter

ds2 <- read_excel("~/Downloads/ds2.xlsx")

Before <- ds2$Before
After <- ds2$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 = "Value",
      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 are no dots outside the boxplot. Based on these findings, the boxplot is 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).

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

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 before keto diet versus after 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.