Hi Babloo, We don't what exactly the purpose of your study. If you just want to determine (statistically prove) that there is a difference between mean balances, then you can conduct a nonparametric-ANOVA test, or maybe (log?)transform your variable, and do an ANOVA. You don’t need to back-transform, because you are in finish. (But don’t forget to test normality of residuals as Steve mentions). If you want to interpret results, you again don’t need to back transform. If you did a log transform, then your parameter estimates mean a percentage change (instead of change of the value on the original scale) If you are interested only in predictions (“What will be the expected balance of new client with age=30 income=100?”), then you don’t need to be worry about the normality so much, just do an ANOVA (regression with indicator variables in your case – but I would also consider to tread age and income as continuous variables, i.e. not binning them). If you are interested in prediction and prediction intervals(“’In what range will be the balance of a usual age=30 income=100 client”), you again need to care about the distribution. 3. A simple back-transform of the predictions (if you used log transform) is: prediction_median_on_original_scale=exp(prediction_mean_on_log_scale) ... View more