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I'm evaluating a survey and want to test the correlation of independent variables and I do not know which test / coefficient I can use as the variables have the following properties:

  • dichotomous variable
  • continuous variable, data not normally distributed

If there wasn't the problem with the normal distribution, I would use the point-biserial correlation coefficient. However, I have read that people use this coefficient anyway, even if the data is not normally distributed. My sample size is n=147, so I do not think that this would be a good idea.

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I'd recommend considering whether you actually need a correlation per se. If you're interested in the extent to which responses on your continuous variable differ across the levels of your dichotomous variable, you could just do a Mann-Whitney U test (analogous to doing a t-test for parametric data).

Some background and implementation in SPSS: https://statistics.laerd.com/spss-tutorials/mann-whitney-u-test-using-spss-statistics.php

Quick implementation in r: https://www.statmethods.net/stats/nonparametric.html

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    $\begingroup$ Thank you, Caleb. I'm new to statistics and I'm an autodidact. So for me it is not easy to find out what is actually necessary and how. With observing the actual variables, I want to become aware of relations inbetween the independent variables to avoid fallacies regarding the evaluation of the tests of differences/similarities with the independent and dependent variables. If a Mann Whitney U test is appropriate in this purpose, I will use it. $\endgroup$ Commented Feb 25, 2020 at 11:30

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