Transform to Normality not possible

Hi Guys,

I hope you can help me. I'm looking at default risk change of companies who have/don't have Investment Covenants & issued Corporate Bonds. I'm using the Black-Scholes-Merton Model to calculate default risk.

My Problem being, the data isn't normally distributed. I can't do parametric test. In addition the standard errors of my regression (linear) are not normally distributed which leave me with Coefficients that can't be interpreted. I'm currently trying to get the depend variable transformed into a normally distributed variable. I tried windsorizing with EXP, SQRT and LN Transformation (with and without Reflection) Link Transformation + a Box Cox Transformation in minitab Link Box Cox.

I'm attaching an Excel file with the data: Data
Colum A has the Default Risk Change Column B the Dummy Variable for Issuers who had Investment Covenants
I'm hoping that someone can either confirm that a transformation is not possible and that I have to use non parametric tests or give me a pointer as to what I'm doing wrong.

Best regards




TS Contributor
Don't have time to jump into this fully, perhaps @staassis will help out more as this is in his neck of the woods.

Quick things: there are parametric tests for nonnormally distributed variables (common misconception); nonnormality of OLS errors doesn't leave coefficients uninterpretable but may have impacts on other elements related to inference (p-values, for example) depending on the sample size and degree of nonnormality.