The Triple Nine Society ExCom Memo

October 5, 1996

To: TNS ExCom, Volunteers, and Interested Members

From: Kevin Langdon, Regent, P.O. Box 795, Berkeley, CA 94701
        (510) 524-0345; [old e-mail address omitted]


Dale Adams, Ombudsman
John Cooper, Financial Officer
Bob Kopp, Editor
Jacquelinne White, Membership Officer
Jennifer Foster, Member-at-Large
Larry Jess, Member-at-Large
Wilson Ogg, Member-at-Large

Jim Grzegorowicz, Correspondence Group
John Kormes, Legal Officer
Ray Suttles, Elections Officer, Monitor, Greeter
Matt Urnezis, Archivist

Verlin Allbritton Travis Houser Henry Milligan Patrick A. Thomas
Lee Arhelger Adelaide Jaffe Ulric Neisser Grady M. Towers
Cyd Bergdorf Barry Kington David Powers Robert G. Trbovitch
Julia Cybele Cachia Bill and Mitzi Kuehl Kenneth Rogers Michael Vendetti
B.B. Crawford Laura Lansberry   Steve Schuessler Clint Williams
Billy R. Fox Michael Madow Daviel J. Schultz Kerry Williams
Wally Gannon Celia Manolesco   Gary H. Schultz Dennis Wilson
Greg Grove Paul Maxim Kevin Schwartz Cal Woodruff
Bob Gulley Daniel B. McElwain Michael J. Scordan
Loren L. Harris   Pat McGrath Kent Shultz

Memos Included

Author Date Page
Paul Maxim Late June 5
Kevin Langdon (reply to Paul Maxim) October 5 7
Paul Maxim July 9
Bob Kopp (reply to Paul Maxim) October 5 10
Kevin Langdon (reply to Paul Maxim) October 5 11
Paul Maxim July 12
Jacquelinne White (reply to Paul Maxim)    Undated 14
Kevin Langdon (reply to Paul Maxim) October 5 15
Paul Maxim (letter to Ulric Neisser) August 6 16
Jacquelinne White August 27 18
Paul Maxim (letter to Dale Adams) September 20 20
Dale Adams (reply to Paul Maxim) September 24 23
Dale Adams (reply to Paul Maxim) September 24 24
Dale Adams (letter to Kevin Langdon) September 25 26
Kevin Langdon (reply to Paul Maxim) October 5 27
Paul Maxim (``Renorming R.H.'s Mega Test'') Undated   29
Kevin Langdon (reply to Paul Maxim) October 5 34
[The material by others listed above (except Bob Kopp's e-mail) has not yet been prepared for Web publication.]

This Memo

It's been a slow summer and over three months between Memos, but things have heated up lately. This Memo, the largest ever published, is dominated by submissions from Paul Maxim and responses to them from Dale Adams, Bob Kopp, Jacquelinne White, and me. As I am the principal target of Mr. Maxim's many accusations, I do not want to raise the spectre of censorship by refusing to publish any of them, but I'm getting very tired of his groundless charges.

I felt no urgency to publish the ExCom Memo as long as there was no pressing business and the only submissions on hand were Mr. Maxim's screeds. As I am the subject of Mr. Maxim's many personal attacks, I have appended replies to all of his writings included here except his letter to Dr. Ulric Neisser of Emory (not ``Emery'') University. I'm sorry to have to burden you with such a large amount of reading material all at once.

New Executive Committee

As reported on the inside front cover of Vidya #155/156, the TNS election has been completed, with the following results:

I have been elected Regent; Dale Adams has been elected Ombudsman. No other candidates ran for either position. The weighted results of the balloting for Member-at-Large, as reported to me verbally by Elections Officer Ray Suttles, are:

Jennifer Foster  


Hal Darancette  


Larry Jess  


Wilson Ogg  


Laura Lansberry  


Paul Maxim  


Jennifer Foster, Hal Darancette, Larry Jess, and Wilson Ogg are elected Members-at-Large.

On behalf of the Triple Nine Society, I'd like to thank outgoing Ombudsman Kerry Williams for his service to the Society and to thank all candidates in this election for their willingness to serve TNS.

In Memoriam: Hal Darancette

It is my sad duty to report that Hal Darancette died on September 8. Hal was a good friend of mine and a long-time member of TNS who served the Society well as Member-at-Large and contributed to the development of TNS in many ways. He will be missed by many friends in TNS. He leaves a vacancy which will be difficult to fill.

Appointment of Laura Lansberry As Member-at-Large

* (9) We must continue. Threfore, I move that Laura Lansberry, the candidate who received the next-highest number of votes after the four who were elected, be appointed to serve the remainder of Hal Darancette's term as Member-at-Large.

Results of Voting on Motions

As I reported in my Regent's Report in Vidya #155/156, the following motions have passed by a vote of 6-0 (of the outgoing ExCom, with two vacant Member-at-Large positions; I did not hear from Kerry Williams):

* (7) Julia Cybele Cachia, Greg Grove, Robert Kopp, Kevin Langdon, and Henry Milligan are appointed to serve on the TNS Psychometrics Committee. Michael Madow shall be an alternate member of the Committe, to vote when a member disqualifies himself on a particular issue (as I intend to do in the case of any vote on my own tests) and to become a full member of the Committee in the event of a vacancy. The Committee shall elect its own Chairman. The Committee shall be responsible for revising TNS' admission standards.

* (8) Applicants furnishing proof of membership in the ISPE shall be accepted into the Triple Nine Society without providing additional evidence of qualification for membership.

Psychometrics Committee

As mentioned above, a new Psychometrics Committee has been appointed by vote of the Executive Committee.

I published the first issue of the TNS Psychometrics Committee Newsletter on August 25; I expect to publish the second issue within the next few days. I will add any TNS member to the distribution list for the Newsletter on request. I'll publish the first three issues of the newsletter, after which I expect to turn over operation of the Committee to an elected Chairman.

Purchase of a Computer for the Use of the Membership Officer

The duties of the Membership Officer include a considerable amount of work with the TNS mailing list and much correspondence. Our current Membership Officer, Jacquelinne White, does not have a computer.

John Cooper has offered to sell the society an old but still serviceable XT-class portable computer for $100 to solve this problem. I therefore make the following motion:

* (10) The sum of $150.00 is appropriated: $100.00 for the purchase of a portable IBM-compatible XT computer from John Cooper and $50.00 for shipping and incidental expenses connected with transporting this computer to Jacquelinne White and making it operational.

As John Cooper will receive the proceeds of the sale, I believe that he is ineligible to vote on this motion. However, as Jacquelinne White will only be using a computer that will be the property of the Triple Nine Society, she is eligible to vote on thiis motion, in my opinion.

I will help Jacquelinne set up the machine at her house and provide support as she familiarizes herself with the computer and the software installed on it.

Unauthorized Use of the TNS Logo

Paul Maxim's letter to Dr. Ulric Neisser on page 15, with the society's logo prominently displayed at the top of the first page, disparages the authors of some of the tests used by Triple Nine for admission, mentioning me and one of my tests by name, and states that our admission standards are compromised. Dr. Neisser is a well-known cognitive psychologist and critic of I.Q. testing. Mr. Maxim's use of our logo in this manner conveys the misleading impression that he is speaking for the Triple Nine Society.

This has never come up before, but the potential for further abuse is obvious. Therefore I propose the following motion:

* (11) Use of the Triple Nine Society logo for purposes other than official business of the society is prohibited.

This motion is submitted to clarify our policy in this matter, but Ir, but I that Mr. Maxim's actions are inimical to thal to thal to the Triple Nine Society, tend to damage the society's reputation, and are highly reprehensible, even in then in the of.

Constitutional Amendments

We are just a few signatures short of being able to bring my Constitutional amendment proposals printed in Vidya #151/152 to a vote of the membership. The Constitution is badly in need of revision to remedy known defects. If you have not done so already, please complete the petition form in that issue and mail it to the Editor.

Outstanding Motions

Please submit your comments on my motions ##9-11, above, and the motion submitted for a vote of this Committee by Paul Maxim in his memo on page 5, in accordance with the motion passed by this Committee permitting members of TNS to make one motion per calendar quarter to be voted on by the ExCom. We'll vote on the motions following publication of these comments in the next ExCom Memo, which I intend to publish around November 5.

Reply to Paul Maxim (#1)

Kevin Langdon

In the memo above, Mr. Maxim referred to Article I, Section 1 of the TNS Constitution, which specifies that ``Membership in the Triple Nine Society shall be open to anyone who can produce satisfactory evidence of a score at or above the 99.9th percentile of the general population on a standardized intelligence test . . .''

Mr. Maxim wrote:

``Standardized intelligence test,'' or ``standard IQ test,'' is understood by us to mean a test . . . authored by professional psychometricians, normed on a significant segment of the population at large, distributed by an authorized publisher, and administered on a timed and supervised basis by a Registered Psychologist or testing service.

While the definition provided above is reasonably accurate for the term ``standard IQ test,'' this term is not synonymous with the term ``standardized intelligence test.'' ``Standarized'' is, instead, a synonym for ``normed.'' My tests have been normed using standard statistical methods, with certain adaptations appropriate to the right tail of the normal curve. Full reports on the norming of the tests have been published here and elsewhere.

Mr. Maxim asserted that ``take-at-home'' tests are inaccurate, without providing evidence for this assertion. He claims that these tests are not properly normed--but he has not taken the trouble to learn the fundamentals of psychometric statistics, so how would he know? He claims that there are no safeguards against cheating or collusion--but there is no evidence of widespread problems in this area. Questionable psychometric credentials on both ``standard'' and ``take-at-home'' tests have been submitted with applications to the various high-I.Q. societies, but such irregularities are rare. Mr. Maxim claims that the ``take-at-home'' tests are not administered under standard conditions--but, because there is no time pressure and each testee is free to take the test when and where he chooses, the conditions are identical for everyone.

Mr. Maxim repeated his irrelevant remarks about the norming of the LAIT being ``five points too high (at the 4-sigma level),'' which I have refuted several times. The first norming of the LAIT, completed on a sample of 147 data points, produced scores that were five points higher, at the four-sigma level, than those on the second norming (with a sample of 553). 98% of LAIT testees received only second-norming score reports and all those who had received first-norming score reports received second-norming reports as well.

Mr. Maxim wrote, ``In the computerized LAIT score reports he distributed to his testees, Mr. Langdon carefully concealed the date of testing and the date of scoring, so as to obscure [the] reliability factor . . .'' Every LAIT score report includes the date of testing; the date of scoring is irrelevant.

In Paul Maxim's twisted mind, anyone who gets in the way of his naked ambition is fair game. Mr. Maxim wrote:

The LAIT was extensively praised by Grady Towers, in several articles he published in VIDYA and elsewhere, but Towers carefully avoided the question of reliability or score inflation. The reason for this can clearly be seen in the fact that Towers was himself a ``Langdonoid''--i.e., his membership in the Four Sigma Society was based on an aggregate LAIT score of ``165 I.Q.'' which Mr. Langdon awarded him. Hence, if Mr. Towers was aware that all the LAIT assessments were ``five points too high,'' he would have had a powerful incentive not to reveal this, since it would have meant his automatic disqualification as a Four Sigma member. By failing to addresss the reliability issue, which comes first and foremost in the mind of any professional psychometrician, Mr. Towers demonstrated just how flimsy was his grasp of this subject, and also the extent to which he had allowed himself to be seduced by Mr. Langdon's brand of ``psychometric politics.''

Grady Towers has hardly accepted my work in psychometrics uncritically; he has written extensively on the question of reliability. The LAIT's split-half correlation of .89 is well within accepted standards. Paul Maxim does not understand what the word ``reliability'' means. It is ludicrous for him to speak of Grady Towers' grasp of psychometric statistics as ``flimsy.''

I don't know how Mr. Maxim obtained Grady's score on the LAIT, but it's a second-norming score and thus is not ``five points too high.'' So much for Mr. Maxim's speculation about Grady's motives.

This is only the latest example of Mr. Maxim's willingness to speculate about others' motives. This kind of speculation is a form of ad hominem argument. It is unfortunate that Mr. Maxim does not adhere to minimum standards of civilized behavior as he pursues his vendetta against those he perceives as enemies.

Mr. Maxim wrote:

The extent of the damage done by Mr. Langdon's systematic overassessments can clearly be seen in the list of ``650 Qualifiers'' he published in his Four Sigma Bulletin No. 2 (Summer 1989). Langdon now admits that only about ``one in three'' of his original Four Sigma Society recruits had ``4-sigma'' IQs . . .

Only about 30 members were admitted to Four Sigma prior to the second norming. While only about one-third of these people were above the four-sigma level on the second norming, there is no way to avoid the fact that a preliminary norming with a few data points tends to be less accurate than a later norming with more data. It was obviously not feasible to keep testees waiting indefinitely; I had to issue score reports based on the data I had.

If 20 members were slightly below the four-sigma level, 630 of the 650 ``qualifiers'' mentioned above were above the four-sigma mark (I never required anyone to formally join Four Sigma to be regarded as a member--anyone who made a qualifying score was automatically in the club--but I didn't want to give a misleading impression regarding how many active members there were, so I used the term ``qualifiers''). The alternative to carrying these 20 people would have been to kick them out of a society they had joined in good faith, which would have been a highly unethical act.

Despite all this, Mr. Maxim's motion to instruct the Membership Officer not to accept scores on ``non-standard'' tests for admission to TNS is in order. Readers of this Memo are invited to submit their comments on this motion.

E-mail message from Bob Kopp [snail mail and e-mail addresses omitted], dated October 5, 1996:

I wish that my personal correspondence would not be submitted for publication in the ExCom memo without my permission, for it sometimes contains conjectures of a type which I would not wish to defend in a public forum. At the time I made these remarks in a letter to Paul Maxim, I assumed for some reason that the ceiling of the Cattell B was somewhere near the four-sigma level; and that if Mr. Langdon was attacking a competitor's test without good reason, this would probably reflect a conflict of interest.

Mr. Langdon subsequently stated to me that the ceiling of the Cattell B is far lower than I had assumed, so that errors of measurement would be appreciable around TNS' lower limit of acceptance. I have not been able to verify Mr. Langdon's claim independently, though I have no reason to dispute it; so I conclude that conflict of interest in this matter is not established.

Reply to Paul Maxim (#2)

Kevin Langdon

When Bob Kopp wrote the paragraph quoted in Mr. Maxim's letter, he was not aware that the person who raised the question regarding the suitability of the Cattell Verbal for admission to TNS was Julia Cachia and not me. Julia pointed out that the ceiling of the Cattell Verbal for adults is below TNS' qualifying score. When I apprised Bob of this fact, he agreed that this is ample reason to reconsider our acceptance of this test.

Bob wrote, ``I have no idea why, except to reduce the number of low-cost alternatives to LAIT.'' The LAIT is no longer scored and is therefore no longer generating revenue, but I continue to be in the testing business. The scoring fee for The Mobius Test is $12; I expect that the fee for my next scheduled release, the Stratospheric Test of Attention in Reasoning (STAR) will also be $12. Mensa currently charges $25 for administration of the Cattell Verbal and the CTMM (the same price Dr. Hoeflin charges for scoring his tests), and the testee can expect to incur other costs connected with physical travel to the testing center. This is only ``low-cost'' relative to the prices charged by ETS for the SAT and GRE and by psychologists to administer individual I.Q. tests.

Mr. Maxim wrote:

The readers of this Memo are also aware of Mr. Langdon's recent action in removing me from the TNS Psychometrics Committee, to which I had been appointed by Cyd Bergdorf. While I acknowledge that I do not have a degree in psychometrics, I have nonetheless done some research on high-IQ psychometrics, and have written some cogent articles which helped expose the systematic score inflation produced by Mr. Langdon's LAIT testing program (please see my 2-page article attached entitled ``How Inflationary Is LAIT?'').

I was a member of TNS' original Psychometrics Committee. When the Committee of which Mr. Maxim was a member was appointed, I made no objection--because the original Committee had been inactive for several years. Similarly, the current Committee was appointed after the Committee of which Mr. Maxim was a member had completely failed to get off the ground and transact any business and had not been heard from for at least several months. Furthermore, the TNS ExCom (not the Regent) can appoint anyone it likes to the Psychometrics Committee; it does not owe anyone a seat on the Committee. Mr. Maxim was offered the opportunity to submit his credentials for evaluation and did not respond--and now he's whining about it. I demonstrated that Mr. Maxim's article was anything but cogent in my response published along with his article in Vidya #155/156.

Mr. Maxim's arguments regarding a supposed conflict of interest are completely without foundation. I have already pledged to disqualify myself from any vote on my own tests. As for other tests, TNS will clearly continue to accept a number of tests for admission. It makes no difference to my testing business (which generates minuscule revenues) which tests other than my own are accepted.

Finally, Mr. Maxim questioned ``whether Mr. Langdon was authorized to unilaterally oust anyone from the PsyCom, without first obtaining ExCom approval.'' The point here is that the action taken was taken by the ExCom, not by me.

Reply to Paul Maxim (#3)

Kevin Langdon

Both the current Membership Officer and Cyd Bergdorf, who has been active in TNS organizational affairs for many years (most recently as Regent) and is universally trusted and respected, have assured me that TNS has accepted ISPE membership as evidence of qualification for TNS all along since its inception.

I know of my own knowledge that TNS membership was offered to all members of ISPE in 1978, when the society was founded.

Kjeld Hvatum failed to perform the duties of his office when he was Membership Officer. Inquiries went unanswered for many months. It wouldn't surprise me if he hadn't bothered to inform himself of TNS procedures and had therefore misinformed Paul Maxim as to our requirements. It also may be that Mr. Maxim didn't bring up his ISPE membership in this context.

I am quite aware of the fact that the automatic acceptance of ISPE members is not in the TNS Constitution and that it had never been formally enacted by the Executive Committee. That's why I proposed the motion that formally approved this practice.

As for the performance of ISPE members on my tests and Dr. Hoeflin's, TNS accepts members based on these tests, while the ISPE does not. What a surprise that TNS members outperform ISPE members on these measures!

The absolute level of ability recorded is also not surprising. Tests like mine and Dr. Hoeflin's do not correlate 1.0 with the standard tests; therefore some regression toward the mean is to be expected when populations accepted at the 99.9th-percentile level on the standard tests are tested using the newer, unsupervised and untimed, take-at-home tests.

ISPE's qualifying scores on most of the tests accepted by both societies are identical to TNS'. Their qualifying score on the SAT is actually higher than ours (1500 vs. 1470).

Mr. Maxim's assertion that ISPE has admitted members ``without any evidence whatsoever'' is absurd. These are not ``members'' but ``honorary members'' and ``mentors,'' distinguished scholars who have accepted an affiliation with the ISPE intended to enrich the society intellectually and provide links to the academic community. As readers of Vidya and this Memo are aware, I'm no great fan of the ISPE, but Mr. Maxim's remarks here are unfair and irrelevant.

The ISPE's entrance requirements are substantially the same as those of the Triple Nine Society. The differences are quite minor.

We are engaged in an experiment here. We have attempted to organize a society according to democratic principles. The ISPE is organized on diametrically opposite lines. It is an authoritarian organization run by a small clique who think they know what's good for ISPE members better than they know themselves, in which there is no democracy and members have no rights. Offering members of the ISPE membership in TNS provides them with an alternative to oppression.

Reply to Paul Maxim (#4)

Kevin Langdon

In Paul Maxim's letter to the Ombudsman of September 20, he made a number of wild charges and made no less than eleven demands for all sorts of information from me.

The TNS Psychometrics Committee Newsletter is not the same thing as the Journal of Rat-Tail Psychometrics (which I refer to, for some reason, as the Journal of Right Tail Psychometrics). The second issue of the PsyCom Newletter and the first issue of the JRTP will be published shortly.

[The journal project has been delayed but I still intend to publish it.]

I expect that the PsyCom will evalute the norming of the LAIT, along with statistical information on various other tests, as part of a comprehensive reevaluation of TNS admission standards.

The TNS Ombudsman is not empowered to direct any other officer to make materials available to anyone other than the Ombudsman. Certain records are confidential; the Ombudsman has no right to make confidential data available to anyone other than the officers making use of this information to perform the duties of their respective offices. Nevertheless, I have no problem with answering most of Mr. Maxim's inquiries. My responses to his various demands for information follow:

1. A ``clear and understandable, step-by-step account of how the LAIT was normed'' is contained in the LAIT Statistical Report, already in Mr. Maxim's possession.

2. The formula exhibited by Mr. Maxim is slightly inaccurate and is not expressed in lowest terms. The actual formula used is I.Q. = .062224 * scaled_score + 113.783 (which I now regard as half a point too generous). This formula is easily derived from information contained in the statistical report--as should be clear from the fact that Mr. Maxim was able to approximate it.

3. I am not the only one to notice that scores on the CTMM do not align well with scores on other tests. The 18-point figure is a very rough estimate of the standard deviation of the CTMM, based on data submitted by people who have taken my tests. Further study of the CTMM is needed, as there are several other problems with this test, including poor face validity, poor correlation with certain other tests, and the fact that I.Q. scores are derived according to the suspiciously simple formula I.Q. = raw_score + 38.

4. Four-sigma credentials based on standard tests are questionable because the few such tests which reach the four-sigma level just barely do so and no test can be considered accurate very close to its ceiling. This is a fact of statistics and has nothing to do with my ``commercial interests'' or those of Dr. Hoeflin.

5. This is the first and last information request on Mr. Maxim's list that is actually reasonable. The mean score on each reported previously-taken test and the mean of corresponding scaled scores on the object test are, in fact, generated as part of my current norming procedure, though this data is not routinely reported on statistical reports, because data from these tests is not used individually in norming my tests. Rather, data derived from previously reported scores which correlate well (usually above .7) with the object test are taken together and overall means and average deviations of previous scores and scaled scores are calculated and equated. The reason for this is that the sample size for any one test is very small.

6. I did not ``extend automatic eligibility for TNS membership to all ISPE members.'' This was done by vote of the Executive Committee. I have addressed this request in my ``Reply to Paul Maxim (#3),'' above.

7. Most members of TNS are not interested in a debate over ratification of a long-standing policy of the society. The vote on this policy was a formality. If Mr. Maxim would care to bring this matter to the attention of the membership he is free to do so.

8. I did not ``unilaterally appoint [myself] to the PsyCom.'' The appointment was made by vote of the Executive Committee. As the vote on the appointments to the Committee was 6-0, my appointment did not depend on my own vote, nor did Bob Kopp's depend on his.

9. I absolutely intend to respect all articles and sections of the TNS Constitu-tion in performing my duties as Regent, including Article I, Section 1. TNS has always accepted members only on the basis of standardized tests, though not all of the tests we accept are ``standard'' (commercially-published) tests. As the ISPE also accepts members only on the basis of standardized tests, our acceptance of ISPE members does not violate this provision.

10. I do not intend to violate the privacy of members of TNS who have scored at or above the three-sigma level on the LAIT. Mr. Maxim's suggestion that this be done is unethical; those who take my tests are promised confidentiality.

11. I am not currently receiving copies of any of Dr. Hoeflin's publications except The Puzzler. This is because I haven't paid for them recently. Now that Mr. Maxim has reminded me of this, I intend to rectify this omission. I have provided Dr. Hoeflin with the names of people who have made scores on my tests which would qualify them for his groups and have sometimes received free copies of his publications in return. This is a legitimate business arrangement and none of Mr. Maxim's damn business.

I am publishing Mr. Maxim's ``Renorming Ron Hoeflin's Mega Test'' in this issue of the ExCom Memo, which will be received by all members of the Psychometrics Committee. I do not intend to publish Mr. Maxim's material in either the PsyCom Newsletter or the Journal of Right Tail Psychometrics, as both of these publications are devoted to the science of psychometrics and Mr. Maxim has demonstrated his incompetence in this field. No editor of a learned journal would give Mr. Maxim's amateurish productions a second look. For the same reason, I am not interested in Mr. Maxim's offer to ``audit'' the norming of the LAIT. Other people, who are competent in psychometrics, have been afforded access to names-removed LAIT data sets, including Grady Towers and former PsyCom Chairman Fred Britton.

The tests used by PsyCom members to enter TNS are entirely irrelevant to their task of reevaluating TNS qualifying scores and the Ombudsman does not have the power to ``mandate'' the disclosure of such information.

Five members, not six, were expelled from the ISPE for founding TNS. The list provided by Mr. Maxim is complete.

Reply to Paul Maxim (#5)

Kevin Langdon

Paul Maxim's article, ``Renorming Ron Hoeflin's Mega Test,'' is, of course, not a norming of the test in the correct meaning of the term. Mr. Maxim has not even attempted a norming, but sought only to estimate the four-sigma and mega (4.75-sigma) levels on the test.

Why Mr. Maxim has sought to ephasize these levels is anyone's guess. It couldn't have anything to do with Mr. Maxim's fixation on gaining admittance to the Prometheus Society and the Mega Society, coincidentally four- and 4.75-sigma-cutoff organizations, respectively, on the basis of his score on the California Test of Mental Maturity, which Prometheus and Mega don't accept, and it is surely mere happenstance that Prometheus and Mega do accept the Mega Test.

Mr. Maxim leaned heavily in his analysis on data from the Scholastic Aptitude Test, while ignoring the fact that the four-sigma level on the SAT is well above the test ceiling. While a relatively small number of testees actually achieve perfect 1600's on the test, or scores very close to 1600, the rarity of these scores is due to the well-known psychometric effect known as ``ceiling-bumping,'' which may be thought of as a corollary of Murphy's Law, and not to superlative ability on the part of those earning such scores. To put it another way, the SAT fails to discriminate among approximately the top .02 percent of the general population.

Furthermore, Mr. Maxim is drawing conclusions based on only ten Mega data points, too small a sample to be statistically meaningful, and the discrepancy between the score Mr. Maxim believes should represent the four-sigma level and the score used by Dr. Hoeflin is trivial, amounting to only 1.5% of the test range.

Mr. Maxim concluded that there were too many four-sigma scores among those reporting LAIT scores to Dr. Hoeflin, without taking into account the fact that a significant fraction of Dr. Hoeflin's sample consisted of members of the Four Sigma Society and the Prometheus Society--who were selected due to having qualified at this level on the LAIT.

Mr. Maxim failed in this instance, as he has in his other writings, to consider the self-selection factor involved when people submit answer sheets for very difficult I.Q. tests. Someone with an I.Q. of 100 is very unlikely to submit his answers to questions he can't answer. The likelihood of submitting answers for scoring continues to increase with I.Q.

On page 3 of his article, Mr. Maxim wrote, ``Dr. Hoeflin's data indicates that 17 LAIT scores at the 4-sigma level and above were, on average, eight IQ points higher than Mega test scores attained by the same testees . . .'' As I pointed out in my reply to Mr. Maxim's ``How Inflationary Is the LAIT?'' in Vidya #155/156, five testees in this same sample with Mega scores above four sigma, averaging 38.6 raw score, earned a mean LAIT score of 163.4, approximately 3.5 I.Q. points lower.

If the highest scores in the sample are selected on one test, the corresponding scores on the other test will naturally tend to be lower, assuming that the correlation between the two tests is less than 1.0.

In considering the CTMM sample, Mr. Maxim again failed to take into account ceiling limitations. The ceiling of the CTMM for adults is 158, far below the four-sigma level.

The Stanford-Binet is known to yield too many high scores by a large factor, reaching an order of magnitude at the four-sigma level. In this case, Mr. Maxim's ignorance worked in the opposite direction and he place the four-sigma level too low.

After all of this, Mr. Maxim placed the four-sigma level on the Mega Test three raw score points higher than Dr. Hoeflin. This is not a huge difference; the errors I have enumerated above could equally account for this discrepancy.

It should be noted that Mr. Maxim did not calculate means, standard deviations, or average deviations of Mega raw scores and previous scores, did not calculate a measure of reliability for the test, did not estimate the standard error of test scores, and did not provide a formula for converting raw scores to I.Q.'s, despite his objection in his September 20 letter to Dale Adams (page 20) to my failure to explicitly state the conversion formula for calculating LAIT I.Q.'s from scaled scores.

Mr. Maxim has demonstrated no command of the basic principles of psychometric statistics. His argument in this article is entirely self-serving and without scientific merit.


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