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I am finding correlations between demo characteristics and various variables gathered from a survey report. Some survey questions allowed for multiple responses (ex. Select all types of salmon you have tried from sockeye, pink, and/or king).

When I run the correlation between say, education attainment category (Likert scaled 1- 5 for less than high school, high school, some college, college, and graduate) and a specific response (ex. having tried sockeye salmon, or pink salmon, or king salmon) from the multiple response questions, do I use n = all responses for that question or n = only sockeye responses?

If I use all responses for the question as n, I would divide, for example, sockeye responses for each specific income category by the TOTAL n for that respective income category (this n would include all responses for that education category). If I use only sockeye responses, I would divide that education category's sockeye responses by the TOTAL SOCKEYE n. I would then run a simple correlation between the likert scaled demo characteristic vs the proportion for each category.

Which method is the right way to go about finding the correlation for this type of survey question?

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The answer is TOTAL n. More specifically you want to correlate against the fraction of respondents in that education category that responded with Sockeye. Mathematically that is Number of Sockeye responses from respondents in category c divided by total number of respondents in category c.

A multi-response question is equivalent to many individual yes/no questions (and could have been phrased as such : "Have you tried sockeye salmon?", "Have you tried ...?" . Considered this way the answer should be obvious; you are just asking what is the response rate for a single yes/no question conditional upon education category.

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  • $\begingroup$ Thank you for your response, Andrew. The way you framed the multiple-response questions as many individual yes/no questions made it easy to understand. Very helpful, thanks! $\endgroup$ – vivian Jun 16 '16 at 4:14

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