There are various normalizations in statistics - nondimensional ratios of errors, residuals, means and standard deviations, which are hence scale invariant - some of which may be summarized as follows.
Note that some other ratios, such as the variance-to-mean ratio \left(\frac{\sigma^2}{\mu}\right), are also done for normalization, but are not nondimensional: the units do not cancel, and thus the ratio has units, and are not scale invariant.