Why are protein measurements stabilised?
For a given protein, the observed abundances at a given abundance level (i.e. expected) are normally distributed with a variance that is proportional to the expected abundance level. In other words, if we expect an abundance of 100 units, then the observed values will be normally distributed about 100 with variance proportional to 100.
Variables (representing proteins) with different variances are said to be heteroscedastic and require variance stabilisation before being used in a parametric statistical analysis such as Anova. This is achieved through log normalisation or arcsinh normalisation.