The data I'm trying to analyze are the quadratic estimates from a quadratic fit to a curve. Most of the data vary between -.15 and .15. However, I have outliers in both directions up to things like -23.00. Outlier analysis and removal has been deemed insufficient as the primary coping method. Therefore, I need to transform the data; I wanted to use a log transformation but adding a constant to the data seems sketchy (it would have to be a large constant to cover all extreme outliers).
Any suggestions as to what kinds of transformations might work here? I need normally distributed data in the end so that I can run ANOVAs.