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I found a correlation between two variables:

  • Variable A is dichotomous, with values 1 and 2 (for yes/no)

  • Variable B is continous (score, 0 - 50)

They correlated with each other. However, my sample size is small (N = 25), and Variable A is is distributed rather unevenly. Is it even allowed in this case to perform a Pearson correlation? Do you think I should still report this correlation, or does it seem "spurious" because of the small sample size? Additionally, would it make sense to further investigate this correlation with a t-test (or an analogous non-parametric test), or is that a bad idea because of the small sample size and the uneven groups?

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    $\begingroup$ Pearson correlation is allowed to use, however, the results it gives are not really meaningful. Why don't you just compare values of B in 2 subgroups (yes or no for A) using the standard Wilcoxon rank test? $\endgroup$ – German Demidov Nov 25 '19 at 10:51
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    $\begingroup$ One of your variables is discrete and moreover - not even ordinal, but you've coded it with 1 and 2 as continuous numbers. In theory, nobody can prohibit you to use Pearson correlation, but there are types of analysis developed especially for this case, which are much more interpretable and give more strict "guarantees" on what to expect. $\endgroup$ – German Demidov Nov 25 '19 at 10:56
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    $\begingroup$ The usual test for correlation where one variable is a dichotomy is point biserial correlation, which is mathematically equivalent to Pearson's Wikipedia. $\endgroup$ – Peter Flom - Reinstate Monica Nov 25 '19 at 12:09
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    $\begingroup$ That's why I prefer to comment instead of writing answers. Thank you @PeterFlom-ReinstateMonica ! Never heard of such technique. $\endgroup$ – German Demidov Nov 25 '19 at 13:45
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    $\begingroup$ @GermanDemidov Comments for comments. Answers for answers. If you only comment, nobody can see when the question is answered, nobody can accept an answer, CV cannot sort the best answers and CV will bring the question up again and again until there is an answer. Answers are important and if you are wrong, people can criticise your answer much more visibly. Also, you can always remove the answer, should you not like it any more. Please answer if you think you have an answer. $\endgroup$ – Bernhard Nov 26 '19 at 7:17
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Computing Pearson correlation with one dichotomous variable is called a point-biserial correlation. So you can do that and you find information about it under that term, e. g. https://en.wikipedia.org/wiki/Point-biserial_correlation_coefficient

From that same page I may cite:

We can test the null hypothesis that the correlation is zero in the population. A little algebra shows that the usual formula for assessing the significance of a correlation coefficient, when applied to rpb, is the same as the formula for an unpaired t-test

So you may go and try but chances are, the result of the t-test will be very similar and not by chance.

However, with a small sample size (and N = 25 is not small but smallISH) some people will prefer non-parametric tests. In this case a rank-sum test seems approriate.

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