Explore BrainMass
Share

# Kruskal-Wallis Test

The Kruskal-Wallis Test is a non-parametric test that examines whether a sample originates from a particular distribution. Much like the ANOVA Test, it is a one-way analysis of variance by ranks. The actual test does not aim to detect the differences between populations being tested, but rather aims to quantify the degree of deviation between the two sets of sample populations – thus, generating a p-value statistic to test for significance.

Much like the Friedman Test, and unlike the ANOVA test, the Kruskal-Wallis Test does not assume a normal distribution of the sample population. However, it does assume that the two groups being tested have the same type of distribution.

The Kruskal-Wallis Test Statistic is commonly written in the following form:

K = (N-1)[( ∑_g_n_i(r_i-r)^2/∑_g∑_n_(r_ij-r)^2)

Where

n_i is the number of observations in group i

r_ij is the rank of observation j from group I

N is the total number of observations

r_i = ∑r_ij/n_i

= 1/2(N+1)

After deriving the value of K, one can look at distribution tables of the K-statistic to obtain the p-value. If the p-value is smaller than 0.05, the null hypothesis of equal population medians can be rejected. However, if the p-value is higher than 0.05, then one would fail to reject the null hypothesis at the 5% significance level. Thus, understanding the Kruskal-Wallis Test is crucial for examining differences in two sets of sample populations.

### Kruskal-Wallis Test: Difference in Distributions

Three teaching methods were tested on a group of 19 students with homogeneous Backgrounds in statistics and comparable aptitudes. Each student was randomly assigned to a method and at the end of a 6-week program was given a standardized exam. Because of classroom space and group size, the students were not equally allocated to e

### Kruskal-Wallis Test for Independent Groups & Sign Test for Matched Pairs

The number of offspring that female blue whales have follows a skewed right distribution. Fifty years ago, researchers tagged ten female blue whales from birth and are counted how many offspring each had over their lifetime. Now researchers want to get similar data to determine if the average number of offspring may be decreasin

### Anova test, Kruskai-Wallis test, t-test, and Wilkoxon Rank Sum

Random samples of populations (in thousands) of U.S. cities in three sections of the country are listed. Is there evidence to conclude a difference in means at the 0.001 level of significance? Eastern Third Middle Third Western Third 187 217 276 146 478 110 362 277 177 186 113 122 174 128 134 248 150 137 335 198 338

### Reaction times of assembly line workers: Kruskal-Wallis Test

An industrial psychologist wants to test whether the reaction times of assembly line workers are equivalent under three different learning methods. From a group of 25 new employees, 9 are randomly assigned to method A, 8 to method B and 8 to method C. After the learning period the workers are given a task to complete, and thei

### Data analysis method

A campus researcher wanted to investigate the factors that affect visitor travel time in a complex. multilevel building on campus. Specifically, he wanted to determine whether different building signs (building map versus wall signs) affect the total amount of time visitors require to reach their destinations and if that time de

### ANALYSIS of VARIANCE

Under what conditions should the Kruskal-Wallis be used instead of analysis of variance?

### Kruskal-Wallis Analysis

I need to complete a Krusal-Wallis Analysis on the following information. I would like to understand the steps necessary and the formula to complete the analysis for the data that is attached. Thanks!

### Compare the effectiveness of three types of pain relievers using the Kruskal-Wallace procedure. The tool for the analysis was SAS using the NPAR1WAY procedure.

To compare the effectiveness of three types of pain relievers, a homogeneous group of 22 students were divided randomly into three groups, and each group took one of three pain relievers for a period of 2 weeks. The average duration of headaches, in minutes, during the two weeks were recorded. Brand A: 5.3, 4.2, 3.7, 7.2, 6.0

### Kruskal-Wallis test assumptions

Which is not an assumption of the Kruskal-Wallis test? a. each sample has five or more values b. the population is not normally distributed c. when the variances are not equal d. all of the above are assumptions of the Kruskal-Wallis test

### Hypothesis testing: ANOVA, Kruskal Wallis test

1 There are four McDonalds restaurants in a particular area. The numbers of burgers sold at the respective restaurants for each of the last 4 days are shown below. Restaurant 1 2 3 4 Day 1 81 79 55 36 2 83 69 65 45 3 67 59 58 62 4 77 69 73 58