These tests are based on data collected in the form of a contingency table of 2 traits, trait X and trait Y, the former having and the latter categories, so the resulting table has rows and columns. Therefore, we can speak of the 2×2 chi-square test (for tables with two rows and two columns) or the RxC chi-square test (with multiple rows and columns)).

We can read the details of the chi-square test of the two features here:

chi-square test 2x2

chi-square test RxC.

Basic assumptions:

• measurement on a nominal scale - any order is not taken into account,
• an independent model.

The additional assumption for the :

• large expected frequencies (according to Cochran interpretation (1952)¹⁾.

General hypotheses:

Hypotheses in the meaning of independence:

The p-value, designated on the basis of the test statistic, is compared with the significance level :

Additionally

• In addition to the chi-square test, another related test may need to be determined. In the event that Cochran's condition is not satisfied, one can determine:

• If we obtain a table of Rx2, and the R categories can be ordered, it is possible to determine the trend:

• When significant relationships or differences are found based on a test performed on a table larger than 2×2, then multiple comparisons can be performed with appropriate correction of the multiple comparisons to locate the location of these relationships/differences. This correction can be done automatically when the table has many columns. In such case, in test option window you should select Multiple column comparisons (RxC).
• In the case where we want to describe the strength of the relationship between feature X and feature Y, we can determine:

• In the case when we want to describe for 2×2 tables the effect size showing the impact of a risk factor, we can determine: