# Statistical test for paired data in an r x c contingency table

To perform statistical test on paired data when we have two dichotomous nominal variables (i.e., in a 2 x 2 contingency table) we can use the McNemar's test. When the number of rows and columns is more than two the McNemar-Bowker test can be used. However, the McNemar-Bowker test works only when the number of rows and columns is the same. I cannot find a statistical test for paired data when we have two multichotomous variables with different number of levels (i.e., in the case of an r x c contingency table). Hence, my question is what is the equivalent of McNemar's test when we have an r x c contingency table?

• Could you please add an example? Is $r\ne c$ just because some levels are empty? – Michael M Feb 18 '16 at 14:36
• How on earth a repeated measures test for c nominal categories can be other than cXc? – ttnphns Feb 18 '16 at 14:41
• Let's say a study was conducted to evaluate the effect of nutrition education on the foods people eat. Hence, they were asked whether or not they eat sea foods, cereals and legumes before the nutrition education was given and also after the nutrition education. So, if I want to test if there is a difference in the foods people eat after the nutrition education, the intervention is dichotomous (i.e., YES/NO) but the food items have more than two categories (in this case three). Hence it is a kind of 2 x 3 table. – Ayalew A. Feb 18 '16 at 14:51
• No. You have, for every respondent, 2 nominal variables ("pre" and "post") with 3 responses (categories) each: foods, cereals and legumes. A respondent may eat only one food of the three (multinomial response). In this settings, you may use Mn-B test. While if your data is "multiple response" wherein a respondent may choose more than one food - you are not in multinomial settings and you can't use Mn-B test its usual way. – ttnphns Feb 18 '16 at 14:58
• (cont.) I mean: You then can do several pre-post Mn tests (with responses yes or no) - each for every food. But they will be separate tests. – ttnphns Feb 18 '16 at 15:03