Question

Describe when it is appropriate to use (A) one-way or single factor chi-square test, and (B) two-way or two-factor chi-square test.

Answer 1

Solution:

The single-factor chi-square test is appropriate when we have a single population and a single categorical variable under consideration. In such tests, the objective is to see if the observed distribution of data is equal to the claimed distribution. The chi-square goodness of fit is used when we have a single categorical variable under consideration.

The two-factor chi-square test is appropriate when we have a single population and two categorical variables under consideration. In such tests, the objective is to test if there is a significant relationship between the two categorical variables. The appropriate test in such situations is the chi-square test of independence.

The two-factor chi-square test is also appropriate when we have two populations and a single categorical variable under consideration. It is used to test whether the distribution of all the categories is same for the two populations. The appropriate test in such situations is the chi-square test of homogeneity.