Grady Towers' remarks about the Ferguson formula would seem to explain the counterintuitively large discrepancy between single test scores and the conclusions that can be drawn from combining them, but the metrics Grady is using depend on the populations that the tests have been administered to and would, presumably, change if the tests were given to, say, a population of Mega members. What is required instead is a correction of the correlation between tests for range restriction, which yields a correlation of .784, using Grady's average SD of 9.5. Making use of this figure in the Ferguson formula, we arrive at 172 as the average score on two tests required for equivalence to a score of 176 on one test, a figure very close to Grady's.
There is one obvious drawback to combining high-level tests: the time required to do these tests is already daunting for testees.
My experience suggests that many super-high-IQ people are in fact psychotic. For those who are familiar with the history of the societies examples are easy to identify.
Some years ago, an investigation by a number of people into the sources of Ron Hoeflin's test items found some similarity of items to problems in various puzzle books (including Martin Gardner's), but no outright copying; because the findings were negative, these suspicions were never made public.
I'm sorry that Grady is under the impression that I don't listen to him. I share the common opinion in the societies community that his is one of the most important voices among us. Grady's essays, such as ``The Outsiders,'' are certainly among the best material ever published in the journals of the societies. What is the case is that I have not often responded to Grady, but he has not been singled out. I am one of those who have suffered from the afflictions pointed out by Hank Pfeffer in his discussion of TMA's (which Grady also alludes to in the last of the five letters included here). Recently, I have begun to unify my diverse interests and catch up with the loose ends I've left behind me all my life.
Grady's observations about the difference in the relative magnitude of various ability factors for the general population and highly selected groups such as the members of the super-high-IQ societies are of great interest, theoretically and practically.
Apparently, Grady has not yet familiarized himself with Arthur Jensen's book released this year, The g Factor. In this book, Dr. Jensen makes it clear that he is, in fact, a believer in Vernon's hierarchical model. And Dr. Jensen had some very interesting observations about fluid g and g:
The following quotation is from Chapter 5 of The g Factor, ``Challenges to g'' (p. 125):
What happens when a very large battery of tests yielding Gf and Gc, along with all the other second-order factors listed above (and a good many other second-order factors not listed here), are subjected to a hierarchical factor analysis in which the analysis is carried all the way, allowing a third-order g to emerge? This has been done in five independent studies by the Swedish psychometrician Jan-Eric Gustafsson and also by others, all with the same result. Gustafsson found Gf and Gc and most of the other above-mentioned second-order factors, and quite a few others. But Gustafsson's most interesting and important finding, which was consistent in all five studies, was that the third-order g is perfectly correlated with Gf, so that when all the second-order factors, including Gf, were residualized (i.e., the common-factor part of each second-order factor that went into the g factor was removed), Gf completely disappeared.
I believe that Dr. Jensen is correct and that the explanation for the pattern that Grady has delineated is an artifact of the limitations of most ability tests with regard to the measurement of g at high levels.
There is a distinctive mentality that appears somewhere above 4.5 sigma. The hallmark of this mentality is the need not to be a mere specialist but to understand the whole of things. As Dr. Linda Silverman emphasizes in her work with highly gifted children and adults, the needs of such people usually go unmet. Their situation is analogous to that of the proverbial boy raised by wolves. Their great potential is not only undeveloped (which can often be rectified by proper education) but wrongly developed, and in many cases their development is permanently stunted.
The material Grady has provided is highly useful and bears directly on the matters before us. I hope that he will honor us with more of it. :-)