Kruskal-Wallis Test

Your name: Ahhyun Lee

The goal of this exercise is to use R to analyze data using the Kruskal-Wallis test.

Let the following simulated dataset reflects BMI among patients with type 2 diabetes. Patients were randomly assigned to one of four medications to reduce hunger, and each continued the medication for six months. BMI was measured at month 6. Assume BMI was the same across all groups at baseline.

Research Question: Does BMI at month 6 differ between the 4 groups after 6 months?

library(car)

## Loading required package: carData

#install.packages("dunn.test")
library(dunn.test)

# Setting up the data
set.seed(89489)
x1 <- rnorm(100, 33.0, 2.8)
x2 <- runif(150, 35, 45)
x3 <- rnorm(125, 38.0, 1.8)
x4 <- runif(110, 25, 38)

bmidata <- as.data.frame(rbind(cbind(x1, "Group 1"),
                               cbind(x2, "Group 2"),
                               cbind(x3, "Group 3"),
                               cbind(x4, "Group 4")))

bmidata[,1] <- as.numeric(bmidata[,1])
colnames(bmidata) <- c("BMI","Group")

Numerically summarize the data.

Briefly describe key findings as related to the research question.

# Numerical summary
tapply(bmidata$BMI, bmidata$Group, length)

## Group 1 Group 2 Group 3 Group 4 
##     100     150     125     110

tapply(bmidata$BMI, bmidata$Group, mean)

##  Group 1  Group 2  Group 3  Group 4 
## 32.80546 39.76490 37.93974 31.15361

tapply(bmidata$BMI, bmidata$Group, sd)

##  Group 1  Group 2  Group 3  Group 4 
## 2.503489 2.976291 1.669114 3.598900

tapply(bmidata$BMI, bmidata$Group, median)

##  Group 1  Group 2  Group 3  Group 4 
## 32.94170 39.48772 38.03233 31.08803

tapply(bmidata$BMI, bmidata$Group, IQR)

##  Group 1  Group 2  Group 3  Group 4 
## 3.344406 4.990172 2.473244 5.252027

Visualize the data

Briefly describe key findings as related to the research question.

# Visualize
par(mfrow = c(1, 2))
boxplot(BMI ~ Group, data = bmidata, ylab = "BMI at month 6")
hist(bmidata$BMI, main = "All groups", xlab = "BMI")

par(mfrow = c(1, 1))

The researcher is not comfortable assuming that the distribution for BMI is “close enough to normal”, and does not want to proceed assuming a normal distribution for BMI. What procedure will you use to address the research question and why?

State the null and alternative hypotheses.

What are the assumptions of the testing procedure?

What is the overall alpha level?

Complete the main test.

Summarize the findings and interpret as related to the null hypothesis.

kruskal.test(BMI ~ Group, data = bmidata)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  BMI by Group
## Kruskal-Wallis chi-squared = 321.88, df = 3, p-value < 2.2e-16

Complete appropriate post-hoc testing.

Use Dunn’s test with the Bonferonni correction. Note: it is possible that you did not reject the overall test in the step above. In that case, please rerun the analysis with a different seed.

Summarize the findings.

# Post hoc: Dunn's test with Bonferroni (install.packages("dunn.test") once)
out <- capture.output(dunn.test(bmidata$BMI, bmidata$Group, method = "bonferroni"))

##   Kruskal-Wallis rank sum test
## 
## data: x and group
## Kruskal-Wallis chi-squared = 321.8806, df = 3, p-value = 0
## 
## 
##                     Dunn's Pairwise Comparison of x by group                    
##                                   (Bonferroni)                                  
## 
## Col Mean-│
## Row Mean │    Group 1    Group 2    Group 3
## ─────────┼─────────────────────────────────
##  Group 2 │  -12.91384
##          │     0.0000*
##          │
##  Group 3 │  -9.881550   2.819187
##          │     0.0000*    0.0144*
##          │
##  Group 4 │   1.467005   14.89586   11.69141
##          │     0.4271     0.0000*    0.0000*
## 
## FWER = 0.05
## Reject Ho if adjusted p ≤ FWER/2, where (unadjusted) p = Pr(Z ≥ |z|)

cat(gsub("\u2502", "|", out), sep = "\n")