Question

For which one of the following situations would a​ Kruskal-Wallace test be​ appropriate? Choose the correct answer below.

A. Comparing the ratings of a new product on a​ 5-point Likert scale by a panel of consumers to their ratings of a​ competitor's product on the same scale.
B. Judging whether the height of the water at high tide at a marina increases more or less consistently as the phase of the moon changes from new to full.
C. Comparing the sweetness of a diet drink​ (rated from 1 to​ 10) as judged by a panel of teenage tasters and a panel of adult tasters.
D. Testing whether the distributions of the ratings of a new distance learning course were the same as rated​ (on the usual​ 5-point Likert​ scale) by​ Freshmen, Sophomores,​ Juniors, and Seniors who had taken the course.
E. Estimating the association between the value of homes and their age in a community known to have a number of very expensive mansions.

Answer 1

D.

Explanation:

Hello!

The Kruskal-Wallis is a non-parametrical test that you can use to test if several groups of data come from the same population, is an extended version of the Mann Whitney U-test instead of two groups you compare 3 or more. It is basically like a classic ANOVA but instead of several populations, you compare categories.

Instead of assuming normality, like the ANOVA, this test assumes under the null hypothesis that every group has the same distribution.

A) No. You have two sets of information coming from the same group. Likert scale for one product and Likert scale for the competitors. I would use a paired test on this one.

B) No. If you have the four phases of the moon as categories you could use this test to compare if the distribution of the height of the water at high tide is homogenous trough all phases. In this case, since the variable is the height of the water (wich can have a normal distribution), a parametric ANOVA should be better. It's not like you cannot apply the Kruskal-Wallis test, the difference is that the ANOVA has better power.

C) No. You have two groups and want to compare the ratings given to the sweetness of a diet drink. In this case, a test for two independent samples would be more appropriate.

D) Yes. You have 4 groups and want to see if the ratings given to the distance learning course are homogenous between them. Rating is an ordinal variable, so a parametrical test would not be appropriate.

E.) No. To test the association between the value and age of homes in a community you have to use a correlation test. Or a linear regression in case you want to know, for example, how does age affect the house value.

I hope it helps!