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I am reading a peer-reviewed paper on psychology and found the author use pearson r on sex (nominal variable):

The correlation table

And then the authors conclude no gender difference on all variables except PB, so they "combined the genders to enhance power in the main statistical analyses".

Is this approach correct?

ceoec
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  • You could look at [this search](http://stats.stackexchange.com/search?q=binary+correlation) at Cross Validated, perhaps you will find a similar question already answered. – Richard Hardy Feb 18 '15 at 14:55
  • Thanks, the closest I have found is this:http://stats.stackexchange.com/questions/96992/running-a-pearsons-correlation-calculation-on-binary-survey-data but it was not answered... others are suggesting the person use tetrachoric/spearman... – ceoec Feb 18 '15 at 15:11
  • An answer is contained within my answer to: http://stats.stackexchange.com/questions/131065/non-transitivity-of-correlation-correlations-between-gender-and-brain-size-and/131069#131069 – kjetil b halvorsen Feb 18 '15 at 16:39
  • @kjetilbhalvorsen, thanks! I read your post and I am confused. Seems we can use pearson with nominal data and sig. different would mean different between group? Is that we can use pearson instead of t-test? This is actually more handy than t-test so if this is okay it would be great, although I don't understand why this is okay.... (This may be a stupid question to you, but I never study statistic so I only have very basic idea on the test....) – ceoec Feb 18 '15 at 17:07
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    How, exactly, did the authors determine the "significance" of the correlations with gender? One issue is that if their method relied on (say) assumed null sampling distributions of $r$, then perhaps it lacked power compared to other tests such as a t-test. It *certainly* lacked power compared to a multivariate t-test. Thus it would be of interest to compare the results of an analysis with genders not combined to the reported results: if important differences in effect sizes appear, then the combined analysis is potentially misleading. – whuber Feb 18 '15 at 17:27
  • @whuber, I agree. The major problem I have with this approach is if r can really detect gender difference. There are two other variables I expect would have gender difference but they reported no using r and that's what made me have this question... Thanks for your clarification so may be there would be gender difference if they run t-test.... – ceoec Feb 18 '15 at 17:32
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    @oce: the (equal variance) t-test and the correlation test are equivalent, so there is no real problem here. The rest of the analysis strategy looks strange though (see whuber's comments) – Michael M Feb 18 '15 at 18:36
  • @MichaelMayer, do you mean even if there are no sig. difference, we should not combined the data to run analysis? Or the problem leads on "enhance the power" due to there may be difference in effect sizes? – ceoec Feb 18 '15 at 18:54
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    It seems to be a heavily data driven analysis with unclear impact on the error rates of the final test results. But maybe the authors address such issues. – Michael M Feb 18 '15 at 19:07

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