The Bell Curve : Lousy Charts

Arun Gupta (
Sun, 2 Apr 1995 13:47:55 GMT

In an essay "Lies, Damned Lies, and Statistics", in "The Bell Curve
Debate : History, Documents, Opinions", Leon Kamin points out the
following misuse of statistics :

"The confidence that Hernnstein and Murray appear to place in the
ability of logistic regressions to interpret the social world seems
excessive. To many readers that statistical procedure will be unknown,
and thus beyond the reach of critical evaluation. That in turn will
lead many to misunderstand the apparently simple charts scattered
through the volume.

The problem can be illustrated by a chart on page 322, captioned:
"After controlling for IQ, blacks and Latinos have substantially
higher probabilities than whites of being in a high-IQ occupation."

The top panel of the chart indicates that for a person of average
age (29) before controlling for IQ", the probability of being in
such an occupation is 5% for whites, 3% for blacks and 3% for
Latinos. The surface appearance, that blacks and Latinos are
discriminated against, is misleading; logistic regression will
demonstrate that.

The bottom panel of the chart shows that "for a person of average age
and average IQ for people in high-IQ occupations (117)," the
probability of being in such an occupation is 10% for whites, 26%
for blacks, and 16% for Latinos. These adjusted probabilities arise
from using regression to "hold IQ constant", statistically, at
the average value of NLSY respondents in high-IQ occupations (lawyers,
doctors, et cetera.)

The insight afforded by the regression analysis is powerful.
Those relatively rare blacks and Latinos who have IQs of 117, far
from being discriminated against, are more likely than whites with
the same high IQ to be in the high-income professions. Maybe
affirmative action has degenerated into reverse racism.

The chart does not tell us the actual number, or actual proportions,
of NLSY whites, blacks and Latinos in the professions. The regression
analysis has fitted a smooth curve through the cloud of actual data
points. The probabilities in the chart have been read off from that
idealized ("best-fitting") curve. We do not know how closely the
curve fits the real data.

We do know that since IQs as high as 117 are relatively rare, the
curve at that point is based largely on extrapolating from the much
more numerous data points at lower IQ levels. That extrapolation is
pretty much an act of faith. How much so can be illustrated by a
few simple and rough calculations.

There were 3022 blacks in the total NLSY sample. The respondents
wehre about equally distributed across eight different ages, with
the same racial mix at all age levels. We can thus calculate that
the sample of 29-year olds (the top panel of the chart) contained
about 378 blacks. The regression analysis predicts that 3 percent
of them (about 11 people) should be in the professions. But it
also tells us (the bottom panel) that among 29-year-old blacks with
the necessary IQ (117 or higher), the probability of being in a
profession skyrocketes to 26%.

We know that the average IQ of blacks in the NLSY sample was 86.7
with a standard deviation of 12.4. That enables us to calculate
(the bell curve again) that 2.78 of the black 29-year-olds in the
sample should have IQs of 117 or higher. The regression analysis
informs us that fully 26% of those 2.78 blacks (0.72 of a black)
are predicted to be in the professions.

Murray is right; we are losing ground. Before the days of affirmative
action, an entire token black was par for the course.


Any comments, anybody ?
arun gupta