The most important cause of the need to revisit our admission standards is the fact that we presently accept only one test which is currently scored, the Mega Test [and now also the Titan Test]. For various reasons, it would be a good idea to find a few other tests to add to our list if we can do so without compromising our standards.
The standard tests are not designed to discriminate anywhere near the one-per-million level--and the psychometricians who designed them and work with them would be the first to say so. Even the new high-range tests are hard-pressed to determine who qualifies at the 99.9999th percentile. The upper limit of the ranges of the LAIT and the Mega just barely reaches this level (see my remarks about the scaling of the Mega near the test ceiling, below). These tests permit discrimination superior to that of the standard tests above approximately I.Q. 150, and this is why they are the primary instruments for admission to the higher-I.Q. societies (those with cutoffs at or above three sigma).
The Mega Society is facing the difficult task of attempting to determine the practical limits of discrimination of the available high-end tests and then deciding on this basis whether a one-in-a-million claim is credible.
I have examined much of the available data on the tests we accept. Here
are statistics on the highest scores on the LAIT (from Sigma Four #5, January 1980; out of
15,000 testees) and the Mega Test (sixth norming report, May 1989; out of 3920). The fifth
column shows the number of Mega testees at each level per 15,000, to facilitate
comparison. As about 27,000 people have taken the LAIT, I estimate that the current totals
are about twice the figures for this early sample.
|I.Q.||Number||Raw Score||Number||Per 15,000|
It should be clear that the ceilings of the two tests are comparable. A score of 43 on the Mega corresponds to an I.Q. of about 172, not 177 (with sigma=16), according to my calculations. I view Ron Hoeflin's curvilinear fitting of raw score to I.Q. at the top and bottom of the test range as highly suspect because there is little real data very near the extremes of a test's range; the signal is drowned out in the noise, particularly near the top, where careless errors and subtle defects in the test become important. Multiple-choice tests have a lot of noise at the bottom end, too, due to rewards and penalties for right and wrong guesses.
I believe that we must apply the same standards to high-end data for the LAIT and the Mega, despite the differences between Dr. Hoeflin's norming methods and mine. Mega accepted a score of 173 on the LAIT before the membership voted to set our standards at 43 on the Mega or 175 on the LAIT (which I equate to a Mega score of 46). Therefore, Mega's de facto cutoff is either 43/172 (approximately the 99.9997th percentile, one in 300,000, or 44/173 (approximately the 99.99975th percentile, one in 400,000), and this is about as high as the tests currently in use can reasonably be claimed to measure.
We must face the question of the limits to discrimination of the available selection instruments. We must either make a serious attempt to accept members at the 99.9999th percentile and raise our standards to the one-per-million level or accept that our qualifying level is 2.5- or 3-per-million and cannot be higher (due to the state of the art of high-range psychometrics) and drop our qualifying scores. (The old Mega Society Bylaws provide some flexibility in this connection; Article IVa, Section 5 provides that Mega's qualifying score shall be no less than 4.25 and no more than 4.76 standard deviations above the general population mean.)
The one-per-million level is 47 on the Mega and 176 on the LAIT, by my calculations. But, as there have been no perfect scores on the LAIT or the Mega and frequencies of scores very near the test ceilings suddenly drop off, we can reasonably allow one point for ceiling bumping and accept 46/175 as our qualifying level and still claim to be accepting members at the 99.9999th percentile.
A preliminary and experimental precursor to the long-awaited third norming of the LAIT indicates a floor of 119 and a ceiling of 178. While psychometricians generally believe that item weighting does not significantly increase the accuracy of a measurement instrument, use of item weighting enables this norming of the LAIT to reach a ceiling two points higher than that of the second norming, by placing the greatest emphasis on difficult items that correlate well with total scores.
This approach could also be made use of to lift the ceilings of Dr. Hoeflin's tests slightly, compensating, to a degree, for the reduction in ceiling due to the strictly linear relationship of I.Q. to scaled score which I insist upon as reflecting the conclusions that can validly be drawn from the data.
Even if we reduce our cutoff percentile, we are still pushing the limits of the tests involved, which have ceilings in the vicinity of five sigma. There are new, somewhat-higher-range tests in various stages of development, including Ron Hoeflin's new Hoeflin Power Test, Alan Aax' Eight Item Test, and Polymath Systems' forthcoming STAR [as the state of California now uses an achievement test called the STAR, I am no longer contemplating the use of that name].
Other new tests are marginal or unacceptable as selection instruments. Noesis #121 included a report on a norming (with a very small sample, N=33) of Ron Hoeflin's Ultra Test. Noesis #125 contained a report on a preliminary norming of The Mobius Test (N=47). According to Dr. Hoeflin's Ultra Test norms, a perfect score on the test is I.Q. 180, 13 points lower than that of the Mega Test. I agree that the Ultra has a lower ceiling than the Mega; I place it somewhere in the mid-170's, comparable to the I.Q. 175 ceiling of The Mobius Test, according to my preliminary norms.
I expect these points to be controversial. I hope that this controversy will lead to active scientific investigation by members of the Mega Society knowledgeable in psychometrics, and not only rhetoric, in order that we may arrive at a consensus of experts regarding these matters with a minimum of subjective wrangling.
An extended table, with additional columns, appears in ``On Mega Admission Standards,'' [in this issue]. I am now dubious about the benefits of item weighting.