Robert Israel wrote, in reply to silly assertions about IQ scores supposedly attributable to historical personages:
> Estimated how? By picking numbers out of a hat?
The thoroughly discredited study by Cox (1926) used the number of lines devoted to the biography of each person in a standard reference book to estimate each person's IQ. This methodology is not replicable on current populations, and has been completely abandoned. See
Shurkin, Joel N. (1992). Terman's Kids: The Groundbreaking Study of How the Gifted Grow Up. Boston: Little, Brown.
for full details.
> Of all the silly things I've seen written about IQ's, this list has to be one > of the silliest.
Silly ideas about IQ, alas, are more commonplace than sound ideas. I'd appreciate comments from sci.math readers to what I have drafting about IQ tests for a forthcoming publication below:
IQ scores are not a measure of anything.
Psychologists have consistently conceived of IQ tests as ?measures.? For example, the classic article by Spearman (1904) was titled ??General Intelligence,? Objectively Determined and Measured.? Lewis Terman (1916) wrote the first edition of his manual for the Stanford-Binet scale under the title The Measurement of Intelligence (a title used by more recent authors for their books on IQ testing) later making his title slightly less definite by changing it to (1937) Measuring Intelligence. Even the authors who have noted the Flynn effect, including James R. Flynn himself, have adopted this terminology and written under such titles as ?Massive IQ Gains in 14 Nations: What IQ Tests Really Measure? (Flynn 1987) or The Rising Curve: Long-Term Gains in IQ and Related Measures (Neisser 1998). All these titles assume that IQ tests ?measure? something, and some amateur writers on psychology specifically invite readers to analogize IQ scores to measurements on a yardstick (Shaine 2001). But professor of psychology Joel Michell points out that it took hundreds of years of scientific and philosophical development of the concept of measurement to establish the foundations of such simple measurements as length and weight, much more conjoint measurements such as density, and none of that work has been done for most psychological test scales (Michell 1999). Indeed, tests of mental ability are based on an untested theory of ?measurement? unrelated to any view of measurement used outside the field of psychology (Michell 1999). The best considered view is that IQ tests and other mental ability tests are not measures at all. Certainly they should not be analogized to rulers.
An IQ score, despite the analogies appealed to by some authors, is not like a marking on a ruler related to an absolute scale but is on an ordinal scale (Mackintosh 1998, pp. 30-31). Psychologists, in a terminology that is largely confined to the field of psychology, speak of four kinds of scales that test scores can be reported on:
interval scales, and
A nominal scale labels results according to distinct categories--the common example is distinguishing male and female test-takers. An ordinal scale sorts test-takers into a rank order, and it is conclusion of this article that IQ tests are ordinal scales. An interval scale has a measurement unit that is comparable in extent along all parts of the scale--many psychologists assume, without proof, that IQ scales are interval scales. A ratio scale, in psychological terminology, is a scale with a meaningful zero point such that any two scores can be compared by multiplication or division. The physical scales of length or of temperature are ratio scales, and one can meaningfully speak of an object being twice as long as another, or a temperature reading being twice as hot as another. IQ cannot be referred to an ?absolute zero,? and thus is surely not a ratio scale. (It is very unfortunate that one large group of authors on gifted education refer to ?conventional IQs? as ?ratio IQs,? which is a mistaken usage in this context.) Therefore, although authors of articles on childhood giftedness quote statements such as that ?a profoundly gifted child of IQ 190 differs from his or her moderately gifted classmate of IQ 130 to the same degree that the latter differs from an intellectually handicapped child of IQ 70? (Gross 2000), such a statement is simply an incorrect inference caused by a misunderstanding of the mathematical nature of the IQ scale (Mackintosh 1998, pp. 30-31; Truch 1993, p. 35; Eysenck 1998, pp. 24-25; see also
for more discussion of IQ scores as scores from an ordinal scale). Alfred Binet warned against this error early on, writing, ?This scale properly speaking does not permit the measure of the intelligence,  because intellectual qualities are not superposable, and therefore cannot be measured as linear surfaces are measured, but are on the contrary, a classification, a hierarchy among diverse intelligences;? (Binet 1905, English translation 1916).
Lewis Terman (designer of the Stanford-Binet IQ test) was well aware of the arbitrary nature of IQ scoring and denied that IQ scores had interval characteristics.
> The expression of a test result in terms of age norms is simple and > unambiguous, resting upon no statistical assumptions. A test so scaled does not > pretend to measure intelligence as a linear distance is measured by the equal > units of a foot-rule, but tells us merely that the ability of a given subject > corresponds to the average ability of children of such and such an age. This was > all that Binet claimed to accomplish, and one can well doubt whether the > voluminous output of psychometric literature since his day has enabled us to > accomplish more. We have accordingly chosen to retain this least pretentious of > units for the estimation of mental level. (Terman & Merrill 1937, p. 25)
> Finally, the reader should understand that the mental levels we have added > beyond fifteen, where mental ability as measured by this scale practically > ceases to improve, are not true ?mental ages,? but purely arbitrary scores > designed to permit the computation of I.Q.'s for adult subjects of superior > ability. The magnitude of these units in score points has been adjusted in > such a way as to give approximately the same distribution of I.Q.'s for adult > subjects as is found for children. The adjustment assumes that in terms of an > absolute scale (if we had one), the distribution of brightness of adult > subjects would follow the same curve as the distribution for unselected > children of a given age. (Terman & Merrill 1937, p. 26) > > In this connection it should be noted that mental ages above thirteen years > cease to have the same significance as at lower levels, since they are no > longer equivalent to the median performances of unselected populations of the > corresponding chronological ages. . . . Beyond fifteen, of course, mental > ages are artificial and are to be thought of as simply numerical scores. > (page 31)
A very thorough critique of the approach that psychologists have taken in rewriting the standards for ?measurement? in science can be found in Michell (1999). An application of Michell?s critique to IQ testing can be found in Barrett (2000).
As usual, James Flynn expressed the matter very thoughtfully. He thinks, as is clear from his writings, that IQ tests are fairly reliable in sorting people into rank orders on the basis of a correlate of intelligence that is tapped by the tests. In other words, he agrees with most psychologists that the rank orderings produced by IQ tests are reasonable, and that they reflect a genuine rank ordering of real-world differences in intelligence. But Flynn points out that when you try to treat IQ scores as magnitude ?measures? rather than as ordinal rankings, they may not correlate well with intelligence. In his elegant phrasing (Flynn 1987),
> Imagine that we could not directly measure the population of cities but had > to take aerial photographs, which gave a pretty good estimate of area. In > 1952, ranking the major cities of New Zealand by area correlated almost > perfectly with ranking them by population, and in 1982, the same was true. > Yet anyone who found that the area of cities had doubled between 1952 and > 1982 would go far astray by assuming that the population had doubled. The > causal link between population and its correlate is too weak, thanks to other > factors that intervene, such as central city decay, affluent creation of > suburbs, and more private transport, all of which can expand the city's area > without the help of increased population.
Barrett, Paul (2000). Intelligence, Psychometrics, Iq, G, and Mental Abilities: Quantitative Methodology Dressed as Science. Psycoloquy, 11, No. 46. Received May 12, 2006 from
Binet, Alfred. (1916). New methods for the diagnosis of the intellectual level of subnormals. In E. S. Kite (Trans.), The Development of Intelligence in Children. Vineland, NJ: Publications of the Training School at Vineland. (Originally published 1905 in L'Année Psychologique, 12, 191-244.) (Available on the Web at Classics in the History of Psychology site)
Eysenck, Hans (1998). Intelligence: A New Look. New Brunswick: Transaction Publishers.
Flynn, James R. (1984). The Mean IQ of Americans: Massive Gains 1932 to 1978. Psychological Bulletin vol. 95, pages 29-51.
Gross, Miraca U. M. (2000) Exceptionally and Profoundly Gifted Students: An Underserved Population. Understanding Our Gifted, 12, (2) pp. 3-9, (Winter 2000). Available on the Web at the Hoagies Gifted Web site