Rasch Response 5

More comments from John…

5. Dick: How then do we get to a theoretic scale if not by using the average and distribution of a group of students on a test of selected items we choose to use in measuring the students?

5. John: I don’t really understand what the theoretic scale is, and I really don’t understand the "equal intervals" idea, unless we are truly measuring weight, distance, etc., rather than giving points for a test that measures a wide range of knowledge and skills. In the decathlon, for individual events we can measure things in equal intervals of distance or time, but frankly I have no idea how the scores attributable to each distance or time are calculated. But the overall points for each event and for the whole thing are certainly not intended to be equal intervals [e.g. the difference of one point between 4,905 and 4,906 vs. 8,905 and 8,906].

We are not "giving points" as you put it for right answers. We are using test items like a one pound item that is a certain weight on a weight scale. We can compare another object to the one pounder to see whether it is heavier or lighter. If we have several different benchmark items, we can find out where an object is by finding out for which items it is heavier and for which it is lighter.

Your decathlon example has two measures. One is of distance which has nothing to do with the decathlon. The other is for a decathlon type of athletic ability. The measure of this ability depends on both how difficult the specific test is, say a 4 minute mile, and the ability level of the other athletes. As far as I know, the underlying scale has never been abstracted using the Rasch model although it could be. Instead, a count of points is used to represent some level of the athlete. And you are right, the counts do not form equal intervals. We can abstract equal intervals using the Rasch model but they do not correspond to counts or the number correct but on the underlying scale.