The question truly does open up a can of worms! I rather suspect that in the quantitative social sciences (incl. medicine) we sometimes imagine that ‘adjustment’ has a status like that of certain transformations in the hard sciences. In fluid mechanics, we have the kinematic viscosity which corrects for fluid density. Likewise in pharmacology, we might divide absolute doses by weight to obtain a biochemically more relevant quantity, concentration. No doubt many of our data transformations in medicine (especially in areas like ICU, where chemistry is ever-present) have similar aims and justifications. (@Drew_Levy recently brought to my attention a new book by @Andrew_Gelman, Hill & @avehtari, with a chapter titled “Only fools work on the raw scale.” I suppose they must have some thoughts on this also.)
Unless you’re appealing to ideas from the hard sciences, however, these sorts of transformations probably have at best the status of seasonal adjustment in economics. Thinking about when and why seasonal adjustment may help/hurt an econ analysis may temper our enthusiasm for adjustment of cognitive outcomes.
Frank, since you brought up Ham-D, I would like to suggest that the summing-up of separate items in this instrument itself amounts to an information-losing projection of a higher-dimensional factor space into 1 dimension. One reason I am a methodologic Bayesian is that Bayesian methods free us from the frequentists’ ‘need’ to do such things.