in the case of these two common methods, estimates of the item-level performance of imagined groups of students—is not entirely confidence-inspiring. Whatever the pros and cons of these methods, they are not a means of uncovering some “true” or objective standard that is waiting to be discovered. This makes the resulting standards a lot less compelling than many people think they are, but it need not render them worthless by any means, and in fact there is a long-standing debate among measurement experts about their utility.

