This is an interesting question, Kai and Cricket2. People here often opine that high grade equivalents reported for tests like the ITBS just indicate how an upper-level student would have done on the lower-level test. If that's true, it does imply that the standard scores are supposed to be standardized across grade levels.
On the other hand, I have trouble believing that a lower-level student would do as well as the grade equivalents might indicate on a test leveled many grades above, for example that a third grader who gets the standard score of an average ninth grader would get the same score on the ninth grade test. There must be some above-level questions on each grade to give a little headroom, but this has to be limited; I doubt that too many ninth-grade-level questions appear on the third-grade test. The larger the grade differential, too, the fewer questions at the lower level will appear on the higher-level test.
Let's imagine a hypothetical perfectly accurate third grade math student who has been exposed to no concepts introduced in the fourth grade or above, and who won't learn new concepts on the test. A high achiever and hard worker, but not extremely smart, say. I doubt that there are so many third-grade questions on the ninth-grade test that even a perfect score on those would give the standard score of an average ninth grader, who probably will find the third grade questions easy and get at least some of the rest correct too. Now, some high-scoring third graders will be able to learn during a test, and some will have been exposed to higher than third-grade concepts as well, but the bigger the grade differential, the less likely I think it will be that a high grade equivalent will actually be accurate.
I have none of the statistical thinking tools needed to analyze these issues, but I do know that testing experts often regard grade equivalents as less accurate the further out they're cast. I think it's likely that Kai is right that the standard scores are intended to really be standard across grades, but I also would bet that they aren't, at least when applied in an upward direction across the entire range. Thus we get incredulous questions every so often on this from parents new to testing or the site, and they're right to be incredulous.
