# Weibull distributed data for correlation analysis

On visual inspection of P-P plots, my time data appears to fit a Weibull distribution better than a normal distribution. I will use the variable for correlations and as a predictor in regression. In SPSS, I could fit the data to a Weibull regression model. I have also read that you can Vincentize the data, but I am unfamiliar with this technique. However, for the correlation analysis:

1) Would I need to transform the data?

2) If so, how do I transform data from a Weibull to an approximate normal distribution?

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I think the Box-Cox transformation is a reasonable choice here for "normalising" the data. One more thing, you do not need the predictor to be normally distributed in a regression model, what you usually assume is that the errors are normally distributed. –  user10525 May 2 '12 at 11:34
OK, so using the Box-Cox SPSS syntax provided in the link above, I was able to estimate the lambda with the least skew at 0.1. Have I then understood correctly that I would need to apply the transform, like so (X^0.1 - 1) / 0.1 –  noumenal May 2 '12 at 12:13
Great! Looks more normal. Thanks. –  noumenal May 2 '12 at 12:24
When $\lambda$ is close to 0, a log-transformation is usually a better choice, because it is more interpretable. –  Aniko May 2 '12 at 12:37