Solved – What are the choices for transforming data that are not normally distributed

I have two sets of data comparing two variables: x and y. I'd like to transform and compare both sets either in r or matlab.

Scatter plot

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Neither are normal and come from (by the looks of it) different distributions)

QQPLOT of data 1

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QQPLOT of data 2

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I would like to transform both data sets to compare them on a level playing field but I know they are not normally distributed, though I don't know from what distribution they come. What are my choices?

1) Why transform at all? If you use a nonparametric test, normality is not assumed.

2) "Statistically significantly similar" is tricky; usually statistical significance applies to a difference (although there are also equivalence tests).

3) I am not sure what your first plot does… what are the two axes?

4) Are your QQPLOTs plots against a normal distribution? It looks like data 1 is truncated

EDIT in response to comments: You do seem to want some kind of regression here. I would first look at a scatterplot of the two variables. Then I'd try an ordinary least square regression for starters, and look at the residuals. If there are problems with normality and homoscedasticity, you might need to do something else.

By the way, I still am not sure what that first plot is.

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