# How to deal with a variable that ranges from 0 to 1 and the distribution has two spikes at these values with normal-like distribution in the middle.

I have the following setting (& would like to pick a model/or transformation that can help): dv is normally distributed continuous variable, all IVs are continuous, but one of them is the above mentioned variable which has values between 0 and 1, having two spikes at 0 and 1. In between there is a normal-like distribution (though slightly skewed and quite flat). What can I do with this variable? Ln(Y) or Ln(Y+c) or other transformation (tried inverse trig, inverse, sqrt)? Is there a nice model? Non-parametric? Dummies? Multiple tests?

Help appreciated, a beginner in statistics

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There's no assumptions about the IVs' distribution in regression (nor about the DVs - only the residuals as representing the error), so, what's the problem? No transformation will change sharp spikes into non-spikes, nor should it. –  Peter Flom May 30 '12 at 10:06
Due to the presence of 0s and 1s. I guess it is pretty skewed to put into e.g. an OLS model... what model should I use that have no assumption about distribution? I guess non-parametric tests have no assumptions, but OLS do. What regression model do you talk about that have no assumption about distributions? I do not want to transform away the spikes, that's why I asked. I wonder what to do with a variable like this? And even if I transform log has problems with 0s... –  VBR May 30 '12 at 10:24
@VBR, in usual regression, no assumptions are made about the distribution of the independent variable since you are conditioning on it. Greater variance in the predictor gives lower standard errors but, other than that, the predictor distribution is irrelevant. You need the dependent variable conditioned on the independent variable to be normally distributed in OLS regression to get $p$-values; not the independent variable. What text is telling you otherwise? –  Macro May 30 '12 at 11:06
I see, so it is enough to check the error distribution, it helps a lot!! I was confused esp. because of some sources like the first: "Simple linear regression allows us to look at the linear relationship between one normally distributed interval predictor and one normally distributed interval outcome variable"... It's confusing... –  VBR May 30 '12 at 12:15
This is a common misconception @VBR! I'm glad you've got it straight now. –  Macro May 30 '12 at 12:16