Is the Bell Curve Statistically Sound? (James Case, 01/95) Reprinted from SIAM News Volume
Is the Bell Curve Statistically Sound? (James Case, 01/95)
Reprinted from SIAM News
Volume 28-01, January 1995
(C) 1995 by Society for Industrial and Applied Mathematics
All rights reserved.
Is The Bell Curve Statistically Sound?
By James Case
The Bell Curve: Intelligence and Class Structure in American
Life. By R.J. Herrnstein and Charles Murray, The Free Press, New
York, 1994, 845 +xxvi pages, $30.
R.J. Herrnstein (now deceased) and Charles Murray knew very well
that the mere mention of race in The Bell Curve: Intelligence
and Class Structure in American Life would expose their work
(and themselves) to severe criticism. They were not prepared,
however, for the verdict of "guilt by association" rendered by
(among others) ABC News, which likened The Bell Curve to the
work of the "Professors of Hate" profiled in the oft quoted
Rolling Stone article of October 24. Nor were they prepared to
hear no fewer than three respected commentators on the MacNeil
Lehrer NewsHour of October 28 denounce the book as a "political
tract," rather than a scientific treatise, despite its strict
conformance with accepted guidelines for the conduct of
scientific inquiry.* Right or wrong, The Bell Curve is hardly
the compendium of neo-nazi pseudoscience some make it out to be.
Despite the clarity of its exposition, the book's contents are
only partially accessible to technically unsophisticated
readers, since the claims made and the evidence adduced are both
statistical in nature. The claim is made, in particular, that
intelligence is an effectively scalar quantity, measurable by
standard IQ tests administered (sometimes in as little as 12
minutes) by trained examiners, and that scores so obtained
during the high school or even junior high school years are
unexcelled predictors of adult employment status and earning
The authors express great confidence in the abstract measure of
"general intelligence" proposed in 1904 by a former British Army
officer named Charles Spearman, using the then still new concept
of a correlation coefficient. As data from would-be intelligence
tests began to accumulate, Spearman noticed that people who did
well on one such test tended to do well on others, while those
who did poorly on one tended to do poorly on all. Even when two
tests were purposely designed to measure radically different
cognitive skills, the correlation between scores remained
positive. Although the correlations varied considerably in
strength from one pair of tests to the next, they were (and
continue to be) consistently positive. This convinced Spearman
that differences between one intelligence and another are
differences of degree, but not of kind, and motivated him to
develop a scalar measure (and call it "g", for general
intelligence) to quantify such differences.
An analogy from the world of boxing might shed some light on the
nature of g. All the measurements included in the "tale of the
tape" before a prize fight of any consequence -- such as height,
weight, and reach, along with circumferences at the chest
(expanded and normal), neck, waist, thigh, wrist, ankle, fist,
and bicep -- correlate positively with one another, at least to
the extent that heavyweights tend to be larger in each dimension
than middleweights, who tend to be larger in every way than
lightweights. In consequence, Spearman's algorithm can be
employed to determine an abstract scalar measure $b$ of "boxer
size." Perhaps the fight game should replace its traditional
weight classes with $b$-classes: Maybe young fighters could be
better protected from injury that way. That still doesn't mean,
however, that boxer size is a scalar quantity, or that the
differences between two boxers of equal $b$ are unimportant.
Spearman's method applies equally well to measurements of
intelligence and boxer size and reveals no more about the one
than about the other. Nevertheless, Herrnstein and Murray cite
an extensive literature purportedly placing the essential
correctness of Spearman's conclusions beyond reasonable doubt.
They also point out that the current tests have largely been
purged of the "cultural bias" once alleged to invalidate them:
Twenty-five years have passed since the appearance of the report
that made bias a sensitive issue (Arthur Jensen, 1969), and the
problem never was as grave as advertised, say Herrnstein and
Murray, nor, given time and good will, as hard to correct.
For these and other reasons, Herrnstein and Murray tend to
ignore the distinctions between g, IQ, and intelligence. Because
others refuse to concede that those distinctions are
unimportant, however, the abbreviation "IQtelligence" is used in
place of "intelligence as measured by $g$" in the remainder of
this review. The extent to which intelligence and IQtelligence
are one and the same thing may never be known. Although $g$ is
easily measured, attempts to define it and to observe it
directly have never succeeded.
Because even the most efficient intelligence tests include many
questions, a high degree of "data compression" is undoubtedly
possible without significant information loss. The Educational
Testing Service achieves it by reporting just two scores (for
verbal and quantitative abilities) on its oft defamed SAT test
and three (for verbal, quantitative, and analytical skills) on
its Graduate Record Examination. Both sets of scores are
expressed on the familiar SAT scale, with its standard deviation
of 100 about a mean of 500. Spearmanites further simplify the
reporting process by combining scores from the different
segments of a given intelligence test into a weighted average
representing $g$, typically expressed on the IQ scale, where the
standard deviation is 15 about a mean score of 100.
Herrnstein and Murray justify (in part) their acceptance of g as
a measure of intelligence by observing that little, if any, of
the predictive power of intelligence testing seems to be lost by
so doing. Although teenage IQ is not by itself a reliable
predictor of success in engineering and other quantitative
curricula, it does seem to predict adult employment status and
earning power in today's increasingly complex world.
The first of the four parts of The Bell Curve summarizes
extensive evidence indicating that IQtelligence is (at least
statistically) predictive. Part II explores the extent to which
low IQ appears to predispose an individual toward poverty,
failure in school, unemployment, illness, injury in the
workplace, family problems, welfare dependency, and ineffective
parenting, or a life of crime, incivility, and poor citizenship.
Although these and other social ills have been studied
extensively, IQ and its equivalents have often been omitted from
the list of potential explanators, seriously compromising (at
least in the opinion of Herrnstein and Murray) the validity of
the conclusions reached. They stress that "years in school" and
"highest degree earned" are inadequate proxies for IQtelligence.
Part III digresses on racial issues, and a short Part IV
discusses conclusions and policy prescriptions.
Resting as it does on the still controversial statistical
technique known as meta-analysis, the evidence with which the
authors seek to establish the correlation between teenage
IQtelligence and adult status and earning power demands
scrutiny. In use since 1904, when Karl Pearson grouped data from
the British military to conclude that the then current practice
of vaccination against intestinal fever was ineffective, the
technique did not become commonplace until the 1980s. Today,
meta-analysis is prominent in medical research and is becoming
more so in the social sciences, due in part to its 1992
endorsement by the National Research Council. It is designed to
illuminate the not uncommon situation in which scores or even
hundreds of costly studies of a given issue have already been
made, by a host of different investigators, using a variety of
different approaches, without achieving actionable consensus.
Meta-analysis represents an attempt to replace the blue ribbon
committee approach to building such consensus with something
more scientific. The idea is to treat the existing studies as
data to which the tools of statistical inference may be applied.
Yet meta-analysis remains a controversial method of inference
which has sparked controversy in every field to which it has
been applied: Few investigators, it has been suggested ,
possesses the statistical expertise to conduct and interpret
That said, it does appear that postadolescent IQ has indeed
become an excellent predictor of adult "employment status"
and/or earning power. The authors of The Bell Curve point out,
in summarizing the findings on which that conclusion presently
rests, that whereas the year 1900 found the top 10% of American
IQs scattered almost uniformly throughout the workforce (if not
on the farms where half the population still lived, then in
stores, churches, factories, bicycle shops, and the like), the
second millennium will find them highly concentrated in science,
medicine, the law, top management, and a handful of other more
or less prestigious occupations. As the social and financial
barriers that once restricted entry into the more desirable
occupations have fallen, members of what Herrnstein and Murray
term the "cognitive elite" have come to all but monopolize them.
Readers of The Bell Curve will, of necessity, learn much about
this cognitive elite. In addition to spending more years in
school than most, and receiving better grades, say the authors,
members "watch far less television than the average American.
Their movie-going tends to be highly selective. They seldom read
the national tabloids that have the nation's highest circulation
figures or listen to the talk radio that has become a major form
of national communication for other parts of America." They are
also, even at an early age, more politically inclined than
average. None of this means that "the cognitive elite spend
their lives at the ballet and reading Proust. Theirs is not a
high culture, but it is distinctive enough to set them off from
the rest of the country in many important ways."
Members tend, in particular, to live in virtual isolation from
nonmembers. As columnist Mickey Kaus puts it, "I entered a good
Ivy League college in 1969. I doubt I've had a friend or regular
social acquaintance since who scored less than 1100 on his or
her SAT boards." Isolated or not, members of the cognitive elite
tend to earn substantially more than other Americans. The figure
shown here, which appears on page 516 of The Bell Curve,
provides historical perspective.
As shown in the figure, whereas median family income rose rather
steadily to a 1973 peak, then leveled off at a somewhat lower
level, the fraction of American families with income in excess
of a hundred thousand 1990 dollars has continued to climb (with
some irregularities). Their new-found riches, Herrnstein and
Murray allege, tend to bring the political interests of the
cognitive elite into alignment with those of the already
affluent. The following established tendencies seem likely, say
the authors, to persist and to aggravate existing social
- An increasingly wealthy and isolated cognitive elite.
- A merging of the cognitive and the affluent elites.
- A deteriorating quality of life for people excluded from the
upper reaches of the cognitive ability distribution.
The latter effect, which is partially documented by the figure,
is a direct consequence of the other two. Unchecked, say
Herrnstein and Murray, "these trends will lead the US toward
something resembling a caste society, with the underclass mired
ever more firmly at the bottom and the cognitive elite ever more
firmly anchored at the top, restructuring the rules of society
[italics added] so that it becomes harder and harder for them to
lose. . . . Like other apocalyptic visions, this one is
pessimistic, perhaps too much so. On the other hand, there is
much to be pessimistic about."
The last remark would seem to explain why The Bell Curve was
written in the first place. Herrnstein and Murray knew full
well that they would be accused of racism, bigotry, and
intellectual dishonesty, just as Arthur Jensen was some 25 years
ago, for saying many of the same things. Yet as they (and
apparently the electorate) interpret current events, the nation
is in an alarming decline, due in large part to inadequate
leadership and public policy. The forces of darkness are
advancing on every front, and the authors genuinely believe that
the measures they propose will help stem the tide.
Many of the policy reforms proposed by the authors have to do
with education. They think it extraordinarily unwise, for
instance, that "only one tenth of 1 percent of all the federal
funds spent on elementary and secondary education go to programs
for the gifted." After all, they say, "The people who run the
United States -- create its jobs, expand its technologies, cure
its sick, teach in its universities, administer its cultural and
political institutions_are drawn mainly from a thin layer of
cognitive ability at the top." Since the 1960s, however, "while
a cognitive elite has become increasingly segregated from the
rest of the country, the quality of the education they receive
has been degraded." Would they not run things better if they
were better educated? Would they not become the philosopher
kings Plato sought to train?
The Bell Curve has more to say about the nature and causes of
the nation's current decline, and contains more food for
thought, than even a lengthy synopsis can hope to convey. At a
guess, the book's most lasting contribution will be its
documentation of the nation's increasing stratification
according to IQtelligence and/or wealth, and its shrill warning
against any alliance of the cognitive and affluent elites. The
individual agendas of these groups transcend traditional party
lines, and together they constitute an even greater menace than
Herrnstein and Murray seem to realize: Each group reinforces the
other's instinctive arrogance by lending its prestige to the
never-ending quest of every elite to "restructure the rules of
society" to its own advantage.
 Charles C. Mann, Can meta-analysis make policy?, Science,
266 (November 11, 1994), 960-962.
 William Overton, Creationism in schools: the decision in
McLean versus the Arkansas Board of Education, Science,
215(February 19, 1982), 934-943.
James Case is an independent consultant who lives in Baltimore,
E-Mail Fredric L. Rice / The Skeptic Tank