Assignment 6 Question 2

Question 2:Is there a difference in body weight (kg) before versus after all participants tried the keto diet?

#Import dataset
Q2 <- read_excel("C:/Users/Julia/OneDrive/Desktop/Assignment 6/Question 2/A6Q2.xlsx")

# Calculate descriptive statistics
#Groups: Before and After
Before <- Q2$Before
After <- Q2$After
Differences <- After - Before


#Descriptive Statistics
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

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


#Create histogram for Before and After
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 not symmetrical.
#The data does not have a proper bell curve.

#Create Boxplot - Change from blue to light blue to help visibility.
boxplot(Differences,
        main = "Distribution of Score Differences (After - Before)",
        ylab = "Difference in Scores",
        col = "lightblue",
        border = "darkblue")

#Boxplot Interpretation
#There are dots outside the boxplot.
#The dots are not close to the whiskers.
#The dots are very far away from the whiskers.
#Based on these findings, the boxplot is not normal.

#Shapiro-Wilk normality test
shapiro.test(Differences)

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

Shapiro-Wilk Interpretation: The data is abnormally distributed, (p = .029).

#Wilcoxon Signed Rank
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

#Effect Size for Wilcoxon Signed Rank
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

Wilcoxon Signed Rank Interpretation: A Wilcoxon Signed-Rank Test was conducted to determine if there was a difference in body weight (kg) 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 = 0.877.