Chi-square tests for homogeneity and association

[Agent Smith]

How do we know a chi-square test is for homogeneity or association (dependence/independence)?

In my lessons, it says that a chi-square test for homogeneity is done with [imath]2[/imath] samples while a chi-square test for association is done with [imath]1[/imath] sample.

Example questions:
1. Test for association: A sample of 500 people are taken and the number of left-handed and right-handed men and women are counted.
2. Test for homogeneity. Two samples, one of trucks and the other of sedans are taken and we count how many of each colored (blue, green, red) vehicle (sedans & trucks) are there.

How do I tell the difference between the two?

 

[Agent Smith]

 

[Agent Smith]

 

[Agent Smith]

 

[Dr.Peterson]

How do we know a chi-square test is for homogeneity or association (dependence/independence)?

Did you try searching for an answer? Here are two I found (the first two in the list when I pasted in your title):

Chi Square Test of Independence or Homogeneity?

You use a chi-square test to test the relationship between two categorical variables. But which one: a test of independence or homogeneity?

www.theanalysisfactor.com

​

So which test should you say you are using, if they turn out the same?​

​

Again, that comes back to how you have phrased your research question. Are you determining whether gender and union status are related. That is a test of independence. Are you looking for differences between males and females? That is a test of homogeneity.​

Main concepts

If you're thinking, "homogeneity and independence sound the same!", you're nearly right. The difference is a matter of design. In the test of independence, observational units are collected at random from a population and two categorical variables are observed for each unit. In the test of homogeneity, the data are collected by randomly sampling from each sub-group separately. (Say, 100 blacks, 100 whites,100 American Indians, and so on.) The null hypothesis is that each sub-group shares the same distribution of another categorical variable.(Say, "chain smoker", "occasional smoker", "non-smoker".) The difference between these two tests is subtle yet important.​

Both say exactly what I expected. It's a test for homogeneity if that is what you intended to test. And if someone else did the test, you look at what he sampled (and what he said he was doing).

As you said, "Never send a human to do a machine's job."

 

[Agent Smith]

@Dr.Peterson , it's an interesting fact. Thanks for the references. Read them, that you posted the relevant excerpts helped.