On 06/06/2013 3:15 AM, Ray Koopman wrote: > Consider two raters assigning the same objects to a set of nominal > categories. How should an ideal measure of agreement change when the > data changes? For instance, if one rater assigns an object to category > A, and the other rater assigns that object to category B but then > changes his mind and puts it in A, it's clear that a proper agreement > measure ought to increase with that change. But what if both raters > change their minds and put the object in category C? How should an > ideal measure respond to that change? Should it ever decrease? >
Here's an illustration of what Ray has described (view with fixed font).
R2-A R2-B R2-C R1-A aa ab ac R2-B ba bb bc R3-C ca cb cc
In a second table (after the change), one observation switches from cell ab to cell cc. (More generally, one observation switches from an off-diagonal cell to a cell on the main diagonal.)
Intuition (or my intuition, at least) suggests that the measure of agreement should increase, because the total number of agreements has increased.
So why do I have the feeling we're being set up? ;-)