IQ scores - fixed raw scores vs infinite tails of the underlying normal distribution of standard scores

Question

When taking an IQ test, if a subject responds to all questions correctly, they will achieve the maximum (raw) score, a finite number. Yet, due to the test's normalisation that takes the median raw score across the population and defines it into a standardised score of 100, IQ scores are expressed not as raw scores but as standardised scores, or equivalently, a number of standard deviations (SDs) away from 100.

My question is: what sense does it make to speak of very high IQ scores, such as for instance 170, that correspond to an extreme in the distribution's tail, when, if one were to convert back to raw scores, this would seem to result in a raw score higher than the one corresponding to an "all answers correct" result.

Put more simply, my question is: since there is a hard-limit on raw scores, why is it that the normal distribution used to describe an IQ score can (theoretically) lead, along its tails, to infinitely-large numbers - as well as, conversely, to negative numbers - as raw scores, both extremes being out of the raw-scores range?

Answer 1

The answer is provided by the Test theory, which distinguishes between the true value of a latent (=unobservable) psychological construct, in this case the IQ of a person, and the IQ score measured with an IQ test. A good test is objective, reliable and valid which ultimately means that each measured score reflects the underlying construct (measured IQ= true IQ). High validity means that the test measures what it claims to measure. If a person has an IQ 170 but the IQ test assigns that person IQ 160, because this is the highest possible score in that test, then this result is invalid and the test is not a good tool for measuring high IQ.

In practice, the test manual should clarify what is the IQ range, in which the test provides reliable and valid estimates of person's IQ. Furthermore, the authors may provide multiple test versions which differ in difficulty. For instance, Raven's Progressive Matrices come in three test versions: test for normal adults, test for children and mentally impaired individuals, and a test for people with above-average IQ. As you can imagine, the last-mentioned test features higher number of tasks than the normal version.