Data Transformation/Normalization

>>8630610
Monotone transformation

>>8630610
Monotonic transformation

>>8630610
Gin Tonic transformation

>>8630610
Whether you're allowed to apply such a transformation depends on what type of test you're going to run on the data.

Parametric statistical tests make assumptions about the distribution of the data on which the test is run. So if the data violate these assumptions, then *not* applying a transformation to make sure that the data conform to the assumptions would be bad practice. In essence, your transformation allows you to make a valid statistical inference, which would otherwise not be possible.

Moreover, it's necessary to know if the type of transformation you're using in itself is a valid one. For example, if you are comparing to distributions with a t-test, you can't just go and reduce the standard deviation of one distribution but not the other, because that would again invalidate the statistical inference that you're trying to make. The general rule is that you conserve the statistical properties of the data that you want to make inferences about, but transform the data such that the other statistical properties which violate assumptions are discarded.

>>8630610
Besides the normality assumption for regression residuals (which can be relaxed using other generalized linear models), transformations also facilitate the fitting and interpretation of exponential and power law relationships, and putting covariates on a common scale is also helpful for machine learning and MCMC