E-mail on the Mega List at Yahoo!Groups Regarding
Brian Schwartz' Application for Admission to the Mega Society

From: "ferdlilac" <ferdlilac@yahoo.com>
Date: Mon, 14 Jul 2003 18:08:25 -0000
Subject: [mega] Application For Mega Membership From Brian Schwartz (*not humor*)

Dear Sirs:

I believe that my test scores make me eligible for consideration for membership in your society.

In 1967, at the age of fourteen, I took the S.A.T. My score was 1593 -- 793 in English (Verbal) and 800 in Math. According to Ron Hoeflin's Fifth Norming of the Mega Test, see also the Prometheus Society's 1998/99 Membership Committee Report,section 8.5.6, in an average year only six people achieved a score of 1590 or higher. And, according to Ron Hoeflin's Sixth Norming, see also the Prometheus report, section 8.5.4, virtually all high school seniors in the 99th IQ percentile or higher took the S.A.T. Since there were three million seniors (aged 17) in 1967, a seventeen-year-old with a score of 1593 would have scored in the 99.9998th percentile.

But since I was 14, and a junior, my percentile rank would be higher. A 14 year old who does as well as a normal. average 17 year old has a ratio IQ of slightly over 120. At that level ratio IQs are more or less equivalent to deviation IQs. See:

http://www.geocities.com/ultrahiiq/Deviation_IQs.html

And a deviation IQ of 120 is about the 90th percentile (for both 15 and 16 SD) See:

http://members.shaw.ca/delajara/Qtable.html

This would put my score far above the 99.9999 level, eligible for Mega. But is the SAT an acceptable test for admission purposes? I believe it is.

The SAT has been given every year since 1926. Over a million people take the test every year. It is possibly the most carefully studied, normed, and scrutinized test in history.

The SAT correlates highly with g. (See A. Jensen, "The g-factor", N. Lemann, "The Great Sorting"(Atlantic Monthly,Sep.95), Prometheus Society Membership Committee Report, section 8.5) The hundreds of questions on the SAT all test mental ability (fluid g) and do not rely on learned knowledge (crystallized g)

Because of this high g-loading, Ron Hoeflin relied on SAT scores to norm his Mega test. Indeed, he believed that the SAT was valid at the 99.9999 level, but could not use it because he didnt have enough data: "I had hoped that with data on over 5 million SAT test subjects I would be enabled to refine my norms for the upper end of the Mega Test scale, in particular permitting me to pinpoint the one-in-a-million level more accurately. Unfortunately, this goal could not be achieved by means of this extra data since the number of SAT scores reported to me by Mega Test participants, 222, remains inadequate." (Sixth Norming)

I hope the above helps you with my application. I am honored to be considered for membership in your society.

Brian Schwartz
Treasurer, Prometheus Society

From: "Chris Cole" <chris@questrel.com>
Date: Mon, 14 Jul 2003 14:46:36 -0400
Subject: RE: [mega] Application For Mega Membership From Brian Schwartz (*not humor*)

The constitution of the Mega Society states that anyone will be admitted who has "scored at the one-in-a-million level on a test of general intelligence which is credibly claimed by its authors to be able to discriminate at this level." I don't believe the authors of the SAT (the Educational Testing Service) make this claim.

Although it would not be relevant for admissions to the Mega Society, Ron Hoeflin in his fifth and sixth normings of the Mega Test does not claim that the SAT discriminates at this level. He uses the SAT scores to estimate the sample bias of the Mega Test, and then extrapolates this bias to find the raw scores corresponding to true population rarity.

This is a controversial argument, but it is not the same as stating that the SAT can discriminate at the one-in-a-million level.

Here is a reductio argument explaining why the test authors must credibly claim that the test discriminate at the one-in-a-million level.

Suppose ten million people flip fair coins 100 times. Ten of these people will flip heads more often than anyone else. Is the intelligence of these ten people therefore at the one-in-a-million level? Obviously not; it was random chance that selected them.

Admittedly coin flipping has no g-loading. But the point is that the amount of g-loading matters. And that leads to the idea of the range of a test. Ron Hoeflin estimated the Mega range using some statistical bootstrapping, which is how the SAT was involved. That the SAT has some g-loading and that it was taken by millions of people is not enough to prove that it discriminates at the one-in-a-million level.

At the moment the members have voted that the Titan Test is the only test accepted for admissions to the Mega Society.

From: richard may <ferdlilac@yahoo.com>
Date: Mon, 14 Jul 2003 11:57:46 -0700 (PDT)
Subject: [mega] RE:Application For Mega Membership From Brian Schwartz (*not humor*)

Thank you for your well reasoned response, Chris Cole.

Richard May

From: "ferdlilac" <ferdlilac@yahoo.com>
Date: Mon, 14 Jul 2003 19:59:04 -0000
Subject: [mega] More From Brian Schwartz Regarding SAT

The [following] was written [by Brian Schwartz] before I was made aware of Chris Cole's reply...but I think it's relevant:

In case anyone raises this point... the SAT people put a lot of effort each year into re-evaluating and revising their test. They could have saved themselves a good deal of work each year by "dumbing the test down" to have a 99.9 ceiling...which they finally did in 1994. By putting in all that extra work (every year for over 50 years) to keep the ceiling at one in half a million, they were implicitly claiming that their test did discriminate at (or near) the 99.9999 level. And colleges knew this. When I applied to go to Oxford at age 16, their attitude was one of condescending if politely incredulous humor. But as soon as they learned my SAT scores, I was suddenly a serious candidate! (And was admitted...)

Chris Cole writes: "Ron Hoeflin in his fifth and sixth normings of the Mega Test does not claim that the SAT discriminates at this level. He uses the SAT scores to estimate the sample bias of the Mega Test, and then extrapolates this bias "

The reason Ron Hoeflin did not use SAT scores to discriminate at the Mega level was simply that he had too few of them. Of 222 people reporting SAT scores to him, only 4 had scores of 1570 or higher (the 1 in 150,000 level). Incidentally, of the 222 people who reported SAT scores to Ron, 4 had scores at the one in 150,000 level (1570) ...and 4 had Mega scores of 40...exactly what you'd expect if the SAT worked at that level. But the sample was too small.

From: "Chris Cole" <chris@questrel.com>
Date: Mon, 14 Jul 2003 17:51:27 -0400
Subject: RE: [mega] More From Brian Schwartz Regarding SAT

For admission to the Mega Society the constitution states that it is necessary to show that the ETS (the author of the SAT) claims that the SAT discriminates at the one-in-a-million level. We presume that the members would agree that any such claim by the ETS is credible. So in order to be admitted Mr. Schwartz simply has to document that the ETS claims that his score is at the one-in-a-million level.We've already thoroughly discussed in Noesis why it is unlikely ETS will ever make such a claim. I think the members understand the concept of test range, and why it is not feasible with a test composed of fixed questions to both spread out the mean and the tails. You can have one or the other, but not both. Since the market is near the mean, for economic reasons that is what the SAT does. Spreading out the tails is not something the ETS can afford to worry about.

From: "ferdlilac" <ferdlilac@yahoo.com>
Date: Tue, 15 Jul 2003 18:57:45 -0000
Subject: [mega] Re: More From Brian Schwartz Regarding SAT

Thank you for your response, Chris Cole.

From: Kevin Langdon <kevin.langdon@polymath-systems.com>
Date: Tue, 15 Jul 2003 19:41:54 -0700
Subject: Re: [mega] More From Brian Schwartz Regarding SAT

At 07:59 PM 7/14/03 +0000, Brian Schwartz wrote:

> This paragraph was written before I was made aware of Chris Cole's reply...but
> I think it's relevant:

> In case anyone raises this point... the SAT people put a lot of effort each year into
> re-evaluating and revising their test. They could have saved themselves a good deal
> of work each year by "dumbing the test down" to have a 99.9 ceiling...which they
> finally did in 1994.

> Even after 1994, the ceiling is somewhat higher than that, about one in 3000 or so.
> By putting in all that extra work (every year for over 50 years) to keep the ceiling
> at one in half a million, they were implicitly claiming that their test did discriminate
> at (or near) the 99.9999 level.

A more realistic figure for the ceiling of the old SAT is something like one in 150,000. They weren't interested in discriminating at that level; they wanted to leave some headroom so they could discriminate up to about the one in five or ten thousand level.

> And colleges knew this. When I applied to go to Oxford at age 16, their attitude was
> one of condescending if politely incredulous humor. But as soon as they learned my
> SAT scores, I was suddenly a serious candidate! (And was admitted...)

Those are very good scores. I'm not surprised.

> Chris Cole writes:

>> Ron Hoeflin in his fifth and sixth normings of the Mega Test does not claim that the
>> SAT discriminates at this level. He uses the SAT scores to estimate the sample bias
>> of the Mega Test, and then extrapolates this bias.

> The reason Ron Hoeflin did not use SAT  scores to discriminate at the Mega level was
> simply that he had too few of them. Of 222 people reporting SAT scores to him, only 4
> had scores of 1570 or higher (the 1 in 150,000 level).

More like one in 100,000.

> Incidentally, of the 222 people who reported SAT scores to Ron, 4 had scores at the
> one in 150,000 level (1570) ...and 4 had Mega scores of 40...exactly what you'd
> expect if the SAT worked at that level.

Nope. The fiifth and sixth normings put the ceiling of the Mega Test way too high. 40 is about at the one in 100,000 level, too.

> But the sample was too small.

That's just one problem.

At 05:51 PM 7/14/03 -0400, Chris Cole wrote:

> For admission to the Mega Society the constitution states that it is necessary to show
> that the ETS (the author of the SAT) claims that the SAT discriminates at the one-in-
> a-million level.

I don't think we need to be quite so literal. If *anyone* claimed that *credibly* it would be enough for me.

> We presume that the members would agree that any such claim by the ETS is credible.

The SAT folks are usually at least in the right ballpark.

> So in order to be admitted Mr. Schwartz simply has to document that the ETS claims
> that his score is at the one-in-a-million level.

It would be necessary for the members of Mega to vote to accept the SAT.

> We've already thoroughly discussed in Noesis why it is unlikely ETS will ever make
> such a claim. I think the members understand the concept of test range, and why it
> is not feasible with a test composed of fixed questions to both spread out the mean
> and the tails. You can have one or the other, but not both.

> Since the market is near the mean, for economic reasons that is what the SAT does.
> Spreading out the tails is not something the ETS can afford to worry about.

Yes. That's a very good point. The SAT can't and doesn't try to discriminate at very high levels. No test discriminates well very close to the extremes of its range.

There are two other problems with Brian's application:

1. We should survey the available tests and decide what to accept *first*, then consider individual applications in the light of the standards we've established. I dislike seeing anyone's credentials debated publicly.

2. We don't accept age-corrected scores, nor should we. We want people who are actually smart, not those who've shown the potential to be smart when they're older.

(My estimates of the rarity level of various scores on the SAT are rough but I doubt that they're off by much.)

If Brian wants to join Mega he should take the Titan Test.

This brings up a question regarding our qualifying scores. The true one-in-a-million level on the LAIT would be 176, discounting ceiling-bumping effects; on the Mega it would be 46 and on the Titan 45. I think it's reasonable to allow one point on each test to compensate for ceiling effects (as we already do for the LAIT), so I think that our qualifying scores should be:

LAIT 175

Mega 45

Titan 44

That would mean raising our qualifying score on the Mega by two points and on the Titan by one.

What do others think?

Kevin Langdon

[After examining the summary of IQ's corresponding to scores on the Mega and Titan tests in Dr. Hoeflin's norms in OATH #23 (see Table 1) and the data contained in Darryl Miyaguchi's "Generic I.Q. Chart" at

http://www.eskimo.com/~miyaguch/combnorm.html

it has become apparent to me that the Mega and Titan tests are more closely comparable at the high end than I'd been led to believe, and therefore I now recommend 45 as our qualifying score on the Titan Test as well as the Mega Test.

We must adjust our qualifying scores if we are to continue to claim to discriminate at the one-per-million level.  --KL]

Table 1. Mega and Titan Test Norms

(From Dr. Hoeflin's tables on pp. 2-3, OATH #23, 9/94)

Mega Test Norms                             Titan Test Norms

Raw Score             I.Q.           Percentile           Raw Score             I.Q.           Percentile

1                      100                50                              1                      120                90

2                      111                75                              2                      123                92

3                      116                84                              3                      126                94

4                      120                89                              4                      128                95

5                      124                93                              5                      130                96

6                      127                95                              6                      132                97

7                      129                96                              7                      134                98

8                      130                97                              8                      135                98.6

9                      132                97.6                           9                      136                98.8

10                      133                98                            10                      137                99

11                      134                98.3                         11                      138                99.2

12                      135                98.6                         12                      139                99.3

13                      136                98.8                         13                      140                99.4

14                      138                99                            14                      141                99.5

15                      139                99.2                         15                      142                99.57

16                      140                99.4                         16                      143                99.6

17                      141                99.5                        17                      143                99.67

18                      142                99.6                         18                      144                99.7

19                      144                99.7                         19                      145                99.75

20                      145                99.75                       20                      146                99.8

21                      146                99.8                         21                      147                99.84

22                      147                99.84                       22                      148                99.87

23                      148                99.87                       23                      149                99.89

24                      150                99.9                         24                      150                99.9

25                      151                99.92                       25                      151                99.92

26                      152                99.94                       26                      152                99.94

27                      153                99.95                       27                      153                99.95

28                      154                99.97                       28                      154                99.97

29                      156                99.975                     29                      156                99.975

30                      157                99.98                       30                      157                99.98

31                      158                99.986                     31                      158                99.986

32                      159                99.989                     32                      159                99.989

33                      160                99.992                     33                      160                99.99

34                      162                99.994                     34                      162                99.994

35                      163                99.996                     35                      163                99.996

36                      164                99.997                     36                      164                99.997

37                      165                99.998                     37                      165                99.998

38                      166                99.9983                   38                      166                99.9987

39                      168                99.999                     39                      168                99.999

40                      169                99.9994                   40                      170                99.9994

41                      172                99.9997                   41                      172                99.9997

42                      174                99.9998                   42                      174                99.9998

43                      177                99.9999                   43                      176                99.9999

44                      180                99.99997                 44                      180                99.99997

45                      183                99.99999                 45                      180                99.99999

46                      186                99.999997               46                      186                99.999997

47                      190                99.999999               47                      190                99.999999

48                      190+              99.999999+             48                      190+              99.999999+

[I disagree with Dr. Hoeflin's norms. I don't believe that it's possible to get enough more discrimination per item from the very small number of items that make the difference among near-ceiling scores to spread out scores in the far right tail this way. But there's no doubt that the Mega and Titan norms are closely comparable at the high end. --KL]

From: "Chris Cole" <chris@questrel.com>
Date: Wed, 16 Jul 2003 06:56:10 -0400
Subject: [mega] re-norming the tests

I would love to see an analysis of this point, essentially a debate on the proper way to bootstrap the norms on these tests. I admit that I think the arguments have all been made before somewhere, but it's my impression that they have been spread out in space and time. Maybe I'm just getting old, but I can't remember the details. So I'd like to see them all made in one coherent fashion. If you submit your analysis for Noesis, I'm sure Ron would be motivated to defend his analysis. Maybe we'd have a couple of rounds of exchange, members who'd contribute their views, and then we'd have a vote and settle the matter.

From: richard may <ferdlilac@yahoo.com>
Date: Wed, 23 Jul 2003 23:24:18 -0700 (PDT)
Subject: [mega] No More From Brian Schwartz Regarding SAT

[From Brian Schwartz:]

Thank you all for the polite and serious consideration with which you received my application. I'm not wholly convinced by your rebuttals, but I think it would not be appropriate for me to drag the debate on and on and on. I'm an outsider to your society, and I shouldn't presume to tell you how to run it.

From: "Chris Cole" <chris@questrel.com>
Date: Thu, 24 Jul 2003 07:04:58 -0700
Subject: [mega] the range of the SAT

Brian,

I think the issue here is about the range of the SAT, not how the Mega Society is run. The range of a test is a matter of science, which means it is mostly an objective fact. I agree that this discussion may be of limited interest to the general membership, but I'm happy to continue discussing the issue with you directly.

-Chris