Let's say I conduct a survey of randomly selected 100 people, asking each of them two questions:

  • "Do you like NY?"
  • "Do you like LA?".

All 100 people responded. Among them, 60 answered "yes" about NY, and 65 answered "yes" about LA.

My null hypothesis is that that the fraction of US population who like New York is the same as the fraction who like Los Angeles. How can I test it?

I was hoping to use two-sample t-test, but I guess it's not right since my two samples are not independent: the same 100 people are answering both questions.


The dependence is not the only problem (there is also a paired sample t-test to take care of it) but also the type of data you have.

This is the classical use case for McNemar's test. The sign test and Cochran Q test would also be applicable. Further information and references on all these is available in Wikipedia.

  • $\begingroup$ Thank you, I'm checking the wiki. I did think about the paired sample t-test, but from what I read about it, it seemed to require the data for each person (like what one person said for each of the questions). For the sake of my example, let's say I only have the aggregate data (60 out of 100, and 65 out of 100), rather than individual data. Can I still use paired test? $\endgroup$ – BLM Nov 28 '12 at 9:57
  • $\begingroup$ You will have the same problem with all the tests I mentioned, you need the original observations. $\endgroup$ – Gala Nov 28 '12 at 10:00
  • $\begingroup$ Oh so with these aggregate numbers, is there nothing useful that can be said? It feels like there's gotta be at least some information in those aggregate statistics.. $\endgroup$ – BLM Nov 28 '12 at 10:31

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