On Sun, 11 Nov 2007 20:09:36 -0800, Beliavsky
wrote:

The book "The Bell Curve" (1994) by Herrnstein and Murray

The book and it's statistical analyses are flawed. Hernstein and
Murray start with a theory, then *lie* with statistics to support
their theory.

http://epaa.asu.edu/epaa/v4n20.html

The correlation between the AFQT scores and parental SES in the
NLSY data is .55. After reporting this correlation, H&M summarize:
"Being brought up in a conspicuously high-status or low-status family
from birth probably has a significant effect on IQ, independent of the
genetic endowment of the parent" (p. 589). Although the magnitude of
these effects or their explanation are debatable, the IQ scores used
in The Bell Curve to demonstrate the independent role of a cognitive
endowment are caused to an important degree by parent's SES. This
means, to rephrase H&M argument about ignoring years of education in
their regressions, that when IQ is used as an independent variable, it
is to some extent expressing the effects of SES in another form. Can
this be solved by the machinery of multiple regression? It is too
often believed that regression analysis provides the proper
statistical control, "accounting for" is the usual term, which
mathematically remedies the confounding of effects imposed by the
realities of the investigated phenomenon or by the study design. The
answer is an unequivocal "No." Neter, Wasserman, and Kutner (1990)
explain:

"Sometimes the standardized regression coefficients, b1 and
b2, are interpreted as showing that X1 has a greater impact on the
[outcome variable] than X2 because b1 is much larger than b2. However,
....one must be cautious about interpreting regression coefficients,
whether standardized or not. The reason is that when the independent
variables are correlated among themselves, as here, the regression
coefficients are affected by the other independent variables in the
model." (By a happy circumstance, the correlation alluded to in this
section is .569, almost exactly the correlation between IQ and SES!)
"Hence, it is ordinarily not wise to interpret the magnitudes of
standardized regression coefficients as reflecting the comparative
importance of the independent variables" (p.294).

For a detailed discussion of these issues, the reader is invited
to consult Chapter 13 of Mosteller & Tukey's Data Analysis and
Regression (1977). They masterfully demonstrate the problems of
interpreting regression coefficients, and sound very clear warnings
concerning the comparison of regression coefficients even for fully
deterministic systems under tight experimental control.


--
Dorothy

There is no sound, no cry in all the world
that can be heard unless someone listens ..

The Outer Limits