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Let's say I have some people that moved from country A to country B. Then I have a binary variable that indicates whether they read the news paper when they were in country A and one binary variable that indicates whether they read the news paper at the present, in country B. If I find that the correlation coefficient between the two variables is 0.368, how do I interpret this number? 2-tailed significance is 0.007. Is this number relevant?

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marked as duplicate by kjetil b halvorsen, mdewey, Ferdi, Peter Flom Oct 2 '18 at 11:19

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    $\begingroup$ For us to know whether it is relevant we need to know what your scientific question is. $\endgroup$ – mdewey Jul 9 '16 at 16:01
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The Pearson correlation is a poor choice of metric for comparing two binary variables. There are many ways to slice and dice this kind of data, but one of the simplest and nicest is to calculate proportion agreement (or in the language of classification, accuracy). That means counting the proportion of pairs for which the values are equal.

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  • $\begingroup$ Thanks I tried that right now, (Measure of Agreement Kappa). I got a value of 0.419. However when I look at the values I see that I have 33 out of 46 people either answered (yes, yes) or (no, no). That seems to be a much higher proportion of pairs where values are equal. I guess I'm missing something here. $\endgroup$ – TruckGuy Jul 9 '16 at 15:43
  • $\begingroup$ Cohen's $\kappa$ gives you the proportion of agreement corrected for chance agreement not the proportion of agreement. $\endgroup$ – mdewey Jul 9 '16 at 15:56

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