The Newsletter of the Philosophical Discussion Group
Of British Mensa

Number 100 : March 2000

14th February 2000 : Alan Edmonds


If you read the Mensa International Journal you may find advertisements for two societies : the International Society for Philosophical Enquiry (ISPE) and the Glia Society. Both of them require for membership that the candidate should have passed a test which shows that he/she belongs to the top one in 1000 with respect to IQ; ie that he/she is more 'intelligent' than 99.9 % of the population. The International Mensa website ( also gives addresses etc of a number of similar societies which have high requirements on IQ . We have to thank Darryl Miyaguchi in the US whose web site ( contains much additional information on such societies. He gives the following table: you will see that the demands of some of these societies are extraordinarily high. Apart from the Glia Society, based in Lieshout (near Eindhoven) they all have addresses in the US.








High Five












Sinistral SIG












Triple Nine












Mega Society




Editorial Note : The ISPE membership figure is that which appears on Myaguchi’s Web-site. The actual membership is of the order of 800. I cannot comment on the accuracy of the other membership levels (not that they are particularly critical to the argument).

In what I have to say below, the term 'high-IQ society' does not usually refer to Mensa but to societies with a percentile requirement greater than 99. Note also that different tests - eg Cattell B, WAIS, Culture-fair,.......give an individual different numbers for IQ. This is one reason why percentile figures or sigma numbers are frequently used since they do not vary in this way.

Now the British Mensa web site ( states that the Cattell B test used by British Mensa has a limit : "A middle aged adult can only get a maximum IQ of 161 on the Cattell "B" test", (ie. 99.54 % as a percentile). Thus the high-IQ societies have to use tests which are far more refined than Cattell B. On his web site mentioned above Miyaguchi gives a list of 'Uncommonly Difficult IQ Tests', some of which are used by these societies.

The Mega Test, originated by Ron Hoeflin, is particularly interesting; the full details of the test are given on the web ( I invite readers to try their hands at it - some of the items are intriguing puzzles. It claims to cope with extremely high IQs, and the procedure by which it is 'normed' (a verb unknown to Chambers Dictionary) is discussed in It is used by a number of high-IQ societies, though not currently by ISPE; they have their own test which I am not familiar with.

Let us consider briefly what is involved in constructing an ordinary IQ test; the psychometrist decides on a set of items to be submitted to the subjects; he then puts together a correlation matrix the elements of which give the correlations between pairs of items. These correlation coefficients are obtained by summing over a sample from the target population. To be meaningful the sample is usually of the order of a thousand subjects. The correlation matrix (often consisting of thousands of numbers) is then submitted to factor analysis. The ways in which factor analysis may be used are discussed by Kline and Mackintosh (see references below) and many others.

If on the other hand one is trying to test the abilities of what is necessarily a very small subset of the population it is impossible to construct a correlation matrix for the test items; there will simply not be enough subjects easily available. Other methods must be used to attempt to validate the test, and one approach is described by Hoeflin (see above) which depends on extrapolation from known data. The difficulties are vividly described by Mackintosh (p 341) :

[The author has been discussing the difficulty of determining whether a very high IQ is associated with exceptional success.]

"There is one plausible, but widely ignored, explanation for this, namely that, above a certain level, IQ scores simply cease to be reliable or valid. ......When special tests have been constructed for groups of supposedly above-average intelligence, the construction of items is usually based on further extrapolation from already difficult items in existing tests. Here one can reasonably question the validity of the new test: by what criterion is one justified in concluding that such extrapolation poses sensible questions that succeed in measuring differences in the same set of skills as are measured by normal tests ? The answer is by no means obvious........Just as there are not enough generally accepted geniuses in the world to undertake a proper study of intelligence and genius, so it has proved difficult to find enough people of very high intelligence to permit the standardization and validation of tests measuring IQ above 140." [Here he means WAIS]

There are other difficulties : one is that most of the tests used by the high IQ societies are self-administered, and although restrictions are imposed on the candidates (for example, they may be forbidden to use a computer to facilitate the production of answers) observation of the restrictions seems to be left to the honesty of the candidates.

Another problem is that many of the target population are likely to be mature individuals who have been through higher education and professional experience. For example I am a chartered mathematician with some knowledge of discrete mathematics, including finite groups and graph theory, though I am not a specialist in these fields. Thus I can, consciously or unconsciously, apply procedures which would make solution of many of the items in say the Mega Test relatively easy. This sort of situation is familiar to the psychometrists and a solution is described by Kline (p. 4, he is talking about g rather than IQ, but the argument is the same) :

"Modern factor analysis ........ has broken the g factor into two: fluid and crystallized intelligence. Fluid intelligence is the basic reasoning ability of an individual dependent, to a large extent, on the neurology of her brain. Crystallized intelligence represents this ability as it is evinced in the skills valued by the culture in which the individual lives. In the West, therefore, fluid ability is invested in science and technology and not at all in hunting and tracking, to give a cross-cultural example. Factor analysis......has revealed the extent to which these g factors are implicated in different tasks and occupations."

Mackintosh covers the same points in more detail - see chapters 6, 8 and 9.

I have not yet approached any of the experts in the field (for example Paul Kline, who is Professor of Psychometrics at the University of Exeter) to get their opinion of the tests used by the high-IQ societies; but I feel fairly confident that Mackintosh's comments above would represent a general view.

What conclusions can we draw from the arguments just outlined ? I think we should view the people who construct tests purporting to measure very high IQ in the same way as we view the constructors of very difficult crossword puzzles - they furnish products which give a minority a lot of innocent amusement but which should not be taken too seriously. A mature adult who boasts of an extraordinarily high IQ without being able to show any other significant achievement should expect the same sort of response as that of the fabled New York taxi-driver : 'If you're so smart vy ain't you rich ?'.

The societies for the allegedly extremely intelligent, particularly the ones with vanishingly small memberships should be treated with the same tolerance as other groups of cranks.

I must thank Theo Todman for introducing me to the subject of high-IQ societies; until a few weeks ago I was quite ignorant of the existence of such bodies other than Mensa.


(I have chosen the following relatively brief works rather than the massive and intimidating tomes of Cattell, Jensen and others. Kline's work is a pocket-book - 166 pages - which covers concisely the techniques of intelligence testing and their consequences. Mackintosh gives a dispassionate review of many of the issues arising from intelligence testing).

Kline P (1992) Intelligence : The Psychometric View, Routledge

Mackintosh N J (1998) IQ and Human Intelligence, Oxford U P

Alan Edmonds

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