I want to calculate the correlation of two continuous variables, unfortunately both of them are not normally distributed. (by using Shapiro-Wilk test) There are two categorical confounding variables and two continuous confounding variables. There are two problems for using partial correlation in SPSS here. 1) two categorical confounding variables (interestingly, in SPSS you can enter categorical variables in controlling variables box for partial correlation!!?? is it correct to enter these types of variables?) 2) the continuous variables are not normally distributed. Is there any other test in this situation? I should mention that one of these two variables maybe the predictor of the other variable. (I am not sure that they only have correlation, or maybe have cause-effect relationship.)

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    $\begingroup$ Estimating the correlation does not require normal distribution. $\endgroup$ – user2974951 Oct 17 at 6:27
  • $\begingroup$ Are you sure you want to compute a correlation at all? Your description sounds much more like a regression problem. In any event, normality of those variables is nearly irrelevant. $\endgroup$ – whuber Oct 17 at 10:43
  • $\begingroup$ @user2974951 "Your variables should be approximately normally distributed" reference: statistics.laerd.com/spss-tutorials/… $\endgroup$ – Slow Oct 17 at 13:08
  • $\begingroup$ @whuber I think I can use both of them, initially I decided to use partial correlation because I am not sure there is a cause-effect relationship. Now, the assumptions of partial correlation don't exist. if I use regression, isn't normality of variables (dependent,independent and confounding variables) necessary? $\endgroup$ – Slow Oct 17 at 13:11
  • $\begingroup$ Normality of variables in regression is never a requirement (except in certain very complex models, which aren't being considered here). Regression makes assumptions about the conditional distributions of the responses, which in least squares settings are usually called "error distributions." Regardless, if regression is called for, replacing it by some other procedure (which does something else), just because the data don't seem to conform to preconceptions, is not the solution: the solution is to choose an appropriate regression procedure. $\endgroup$ – whuber Oct 17 at 13:36

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