I have a set of urban morphology index (continuous variable) and I have a set of rate of crimes (per type). I want to apply Pearson correlation to see the relationship between the two set of variables, however, in most of the cases the relationship is not quite linear and the variables are not following the normal distribution.
Please! What is the advice you might give me?
1. What if I scale transform my variable, say using Log ()? I am quite afraid, it seems that transforming the variables will change the relationship and maybe the meaning between those variables.
2. I am thinking about scaling all those variables let say between 0 and 1, although I am not quite sure about it yet.
Note: I am more interested in exploring the direction of the relationship than the strength of the relationship.
If you are interested in the direction, why don't you analyze the monotone association (-> Spearman's correlation = correlation of ranks)? No transformation is required then.
If you are interested in modelling the rate of crimes by the morphology index, you may want to invest some brains and look for a reasonable statistical model. If the functional relationship is not important and the model should be more phenomenological, a spline model will likely be appropriate and sufficiently flexible to follow non-linear local trends. If "rates" are the response, I would consider an exponential or gamma error model, if these rates are bounded in (0,1) I would consider a beta error model..
Thank you, Jochen Wilhelm.
I will try to consider your suggestions, it helps a lot...
Best regards!
The easiest way of getting the direction and magnitude of the relationship is Spearman's rank correlation coefficient as it is appropriate for continuous aand discrete ordinal variables. While Pearson's correlation assesses linear relationships, Spearman's correlation assesses monotonic relationships (whether linear or not).
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