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) ?