Contingency tables larger than 2x2

Mirjam

Hi,

Bayesian statistics is new for me, so I hope to find some answers here.

I want to perform a Bayesian contingency table 3x3 and 3x2. However in the results, under the Bayesian Contingency Table, there is a warning "Note: proportion test restricted to 2 x 2". In an earlier post I understood I can ignore this? Or is it necessary to use R (which I rather not use) if table is larger than 2 x 2?

When using Chi square test there is the assumption that no cell has expected counts less than 5. Does this assumption also apply at Bayesian contingency tables or are there other assumptions I have to keep in mind?

Thank you so much.

Mirjam

andersony3k

A proportion test is restricted to 2 X 2 out of logical necessity. When the table size is 2 X 2, "contingency" is translatable to "differences between two proportions. That's not the case for tables larger than 2 X 2. For those large tables one must usually be content with being able to conclude that the "observed frequencies" do or do not differ significantly from the "expected frequencies."

Mirjam

Thanks so much for your response!

I understand that with a larger table I will only able to conclude that observed frequencies do or do not differ significantly from expected frequencies. However, is it possible to use the test like that or is it not recommended? (as the note suggest).

My research question involves an independent variable on three levels A,B,C We expect A=B>C Although we expect A=B we have no proof for this yet, so we would like to compare all three groups. We are planning to start with a 3x3 Contingency table (A,B,C) and then next step is to seperately test 2x3 B>C

Would this be the right way?

Thanks again!

andersony3k

Such an analysis would be appropriate. But you research question suggests that you also need to get down to a set of two-cell chi square analysis. Each would be called a goodness-of-fit rather than a contingency analysis. One analysis would compare A to B; another: B to C; and another: A to C.

EJ

Another (Bayesian) approach is to use the bain module -- Herbert Hoijtink's methods explicitly take into account a combination of equality and inequality constraints.

EJ

Mirjam

Andersony

Thanks for your additional advice!

As I am quite new to the field, I want to double check if I understand it right.

• Would you call a Bayesian Contingency analysis 2x2 also a goodness of fit? In JASP I only see the term Contingency Table?

EJ

Thanks for your suggestion. I have to add that my dependent variable is only a 3-point likert scale (were we expect mainly 1 or 2 points). I assume that BAIN is not appropriate for such an ordinal/categorical variable.

andersony3k