I asked two different groups of subjects to answer a questionnaire of 2 yes/no questions. The "correct" way of answering the questionnaire was to answer yes to both questions.

I want to prove or disprove that group2 is answering better than group1.

My idea is to check if a get a "low" p-value in a Chi-square independence test on a 2x2 contingency table (1 degrees of freedom) where rows are group1 and group2 and columns are the number of subjects that replied yes-yes and the number of subjects that replied differently.

However, I am not sure this is the right way to proceed.

Should I use a 4 columns contingency table (3 degree of freedom) dividing subjects in 4 categories (those that replied yes-yes, no-yes, no-no, and yes-no to the two questions) ?



1 Answer 1


You have 2x2 contingency table right as you desribed it for that design if you consider all three other combinations of answers equally wrong. However, if you want to account for that difference (one "yes" answer better than two "no"), you should create the 2x3 table with columns yes-yes, total of yes-no plus no-yes, and no-no. See, the variable correct answers is now ordered categorical. Then you should apply the Cochran-Armitage test.


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