equivalence testing for a chi-squared test

Question

I'm familiar with the concept of equivalence testing for testing whether two means are the same

Is there an equivalent equivalence test as the counterpart to the chi-squared test for contingency tables (specifically demonstrating that two or more variables are independent).

As a starting point, taking the two one-sided t-test as a guide, I imagine performing two one-sided chi-squared test and adjusting the chi-squared value +/- the meaningful difference range I have previously chosen.

two problems arise

1) whether a one-sided chi-squared test is the correct way to think about things given that it is already one sided.

2) choice of my meaningful difference range. For the means example the range is in meaningful units (that of the original variable). I'm not sure how to go about choosing the range in the units of the chi-squared value.

any thoughts are welcome, thanks

Answer 1

An appropriate test statistic used to measure the degree of association between binomial paired variables is the log odds ratio.

The odds ratio expresses how much more likely there is to be a success in one case given a success in the other. for more info on odds ratios see Grimes & Schulz 2008

the important thing is that it is equal to one iff the two variables are independent.

taking the log of the ratio makes it symmetrical around zero.

As described in Testing Statistical Hypotheses of Equivalence and Noninferiority and here, to demonstrate equivalence one has to demonstrate (at a certain alpha) that the estimate of your statistic lies within the a predefined equivalence margin of the value you would expect for perfect equivalence.

The equivalence margin is the difference you would consider not practically different, and does not have a spesific value. It will depend on your spesific case and you will have to exercise some judgement..

For the log odds ratio wellek suggests 0.41 and 0.85 as strict and liberal bounds respectively