<p>Thanks for the clarification. I had not seen this explained before. But isn't the "test of 'known' difficulty" -- to which a new test is made equivalent -- one that has its raw scores converted to standard scores that are normally distributed, i.e., curved? Is it really likely that one administration of the test would yield scores that aren't distributed in this fashion -- that, say, someone scoring a 30 would NOT be roughly at the 97th percentile of those taking that particular test? You've added a technical detail, but I don't know that in practice whether it makes much difference to a testtaker. It is theoretically possible that the distribution of scores would be different, but it hardly seems at all likely. </p>
<p>My understanding came from a discussion of the SAT and the ACT in an introductory statistics book in its section on normal distributions. I can't see why you say it has nothing to do with percentiles. The chart shows percentiles and the scores show a normal distribution (what I call a "curve"). Why is the 97th percentile at 30? Because you are dealing with an original mean of 18 and a standard deviation of 6. Two standard deviations above the mean is 30 -- and two standard deviations above the mean in a normal distribution is the 97th percentile. </p>
<p>Are you saying that ACT scores ever do NOT fall in a normal distribution?</p>