In article <[EMAIL PROTECTED]>, Robert J. MacG. Dawson <[EMAIL PROTECTED]> wrote:
>Herman Rubin wrote: >> This is not done that often, and is generally quite difficult. >> It requires changing the form of the model. The more typical >> transformations attempt to get normal marginals, and there is >> rarely justification for this. It has done harm; many of the >> newer IQ tests never return "profoundly gifted", as this is >> beyond the range which the "normal" transformation of the scores >> from the too-small sample yields. > This may not be a bad thing, as it is not clear that the tests are >designed to make accurate distinctions for that part of the range of >intellectual ability. As it is used, it is a VERY bad thing. There is no way now that a gifted child can get anything like an appropriate education in the public schools, and failing to recognize giftedness, or its extent, is really criminal. The point is that the use of the normal distribution makes what would be 20 or 30 or even more differences come out to 5 point differences. > I am not an expert on IQ tests (or a particular believer in the utility >of what they measure), but from what I have seen of them, the maximum >possible score does not represent an extraordinarily high ability level. The maximum REPORTED score is of that type. The maximum POSSIBLE score is very much higher, and the 2% or so up there are the ones missed. Also, the reported score is based on the normal distribution, and this is not what the original IQ scores were. The right tail is especially highly skewed, so the difference between a reported 130 and 125 might be several times the difference between 110 and 100. >Moreover, a score that falls moderately short of the maximum may result >from traits such as carelessness that are not what the test is trying to >measure, rather than from lack of ability - or even from giving a >logical but obscure answer to a question intended to be obvious. If rawer scores were reported, or scores on a real scale, this would be treated better. As to the accuracy of the test, you are right; educationists stress memorization and routine, and thus miss what is important. What raw scores will badly miss is too short or too easy an exam; this can be corrected, but not by those who think in terms of a normal distribution, or any other enforced type. We may report temperatures in Fahrenheit or Celsius or Kelvin, but these are scales. We might use a logarithmic scale, such as pH. But we should be using absolute measured scales, or understood transformations of them, and ignore the distribution. > We see this in other tests as well. One can probably say less about >the distinction in ability between students who get 95% and 100% >respectively on an exam than about that between students who get 70% and >75% respectively. Standard grading schemes tend to echo this, assigning >various flavors of A over a wider range than for B's or C's. Similarly, >a smart graduate committee will pay more attention to the recommendation >of a summer research supervisor or honors thesis advisor than to the >distinction between a GPA of 4.1 and one of 4.2. For students wishing to do graduate work in mathematics or statistics, a graduate committee has little to go by, and the GPA is one of the worst parts. This is especially the case as the great majority of American students getting undergraduate degrees in mathematics have not had even one decent real mathematics course. Courses in how to calculate solutions do not help in understanding anything. > Similarly, at the lower end, most standard adult IQ tests presumably do >not distinguish below a certain level at which the subject is incapable >of following the instructions. > Extremes of ability need to be measured with special instruments. Possibly special instruments, but still use the idea of a scale, not of an arbitrary distribution, or contortion to fit an inappropriate cookbook probability course. We do not use the same instruments to measure temperatures of .001 K as we do for the surface of the Sun, or for the interior of a thermonuclear reactor, but we are still using the same scale. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
