Here is, I would assume, a fairly common situation: I would like to know which test to use to assess whether the tendency to answer "Yes" on question 1 of a questionnaire is associated with the tendency to answer "Yes" on question 2 on the same questionnaire. Phrased differently, I want to know whether two categorial variables, both measured on the same individuals, are associated. Which test do I use? For clarity, the questions are "Yes/No"-type questions.

Surprisingly, the above question, which strikes me as a fairly simple and straight-forward methodological question concerning the analysis of 2x2 contingency tables, has resulted in a large amount of head-scratching during the past couple of days. From my understanding, it is advised that one does not use a chi-square test in this scenario, since the measures are dependent (each participant answers both questions). But the commonly suggested alternative, McNemar's test, seems to be applied mainly when having measured the same variable during pre-post tests (or when having matched pairs). This strikes me as a different situation from the one I'm in.

Which test would be appropriate in my situation? I'd be very grateful for your input.

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    $\begingroup$ McNemar is a test of difference between two paired/repeated-measures samples, i.e. between two variables. Homogeneity chi-square test is a test of of difference between two independent samples; which means that it an association measure between two variables - one taken as "grouping" and the other as "response". For 2x2 situation, standardized version of Chi-sq, the phi coefficient, is equivalent of Pearson correlation coefficient. Will that info help you to decide? $\endgroup$ – ttnphns Jan 8 '17 at 10:24
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    $\begingroup$ Have you already looked at this Q&A stats.stackexchange.com/questions/76875/… which has a very detailed answer. $\endgroup$ – mdewey Jan 8 '17 at 15:04
  • $\begingroup$ @mdewey Thank you for the link. I did read it prior to making my post, but unfortunately it did not completely alleviate my confusion... Two separate commentators in the linked post advise the use of the chi-square test of independence. However, the statistics textbooks I've consulted emphasize that the chi-2 test for independence requires two independent samples to work properly. However, as my samples are neither independent nor paired, I'm still a bit confused as to which test applies to my situation. Or am I misunderstanding something? $\endgroup$ – NamelessAmos Jan 9 '17 at 13:10
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    $\begingroup$ Why do you say your samples are not paired? In your question you say that the everybody answered both questions $\endgroup$ – mdewey Jan 9 '17 at 13:12
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    $\begingroup$ You can also test for independence but it answers a different question. Try the later answers in that thread. $\endgroup$ – mdewey Jan 9 '17 at 13:57

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