IQs and The Bell Curve . The Bell Curve (Free Press,1994),

QUESTION:

Problem 170SE

IQs and The Bell Curve . The Bell Curve (Free Press,1994), written by Richard Herrnstein and Charles Murray(H&M), is a controversial book about race, genes, IQ,and economic mobility. The book heavily employs statistics and statistical methodology in an attempt to supportthe authors’ positions on the relationships among thesevariables and their social consequences. The main themeof The Bell Curve can be summarized as follows:

(1) Measured intelligence (IQ) is largely geneticallyinherited.

(2) IQ is correlated positively with a variety of socioeconomic status success measures, such as prestigious job, high annual income, and high educationalattainment.

(3) From 1 and 2, it follows that socioeconomic successes are largely genetically caused and thereforeresistant to educational and environmental interventions (such as affirmative action).

The statistical methodology (regression) employedby the authors and the inferences derived from thestatistics were critiqued in Chance (Summer 1995) andThe Journal of the American Statistical Association (Dec.1995). The following are just a few of the problems withH&M’s use of regression that are identified:

Problem 1 H&M consistently use a trio of independent variables—IQ, socioeconomic status, and age—in a series of first-order models designed to predictdependent social outcome variables such as income and unemployment. (Only on a single occasion are interaction terms incorporated.) Consider, for example, themodel

E(y) = β0 + β1x1 + β2x2 + β3x3

where y = income, x1 = IQ, x2 = socioeconomic status,and x3 = age. H&M employ t-tests on the individual bparameters to assess the importance of the independentvariables. As with most of the models considered in TheBell Curve, the estimate of β1 in the income model ispositive and statistically significant at α = .05, and theassociated t-value is larger (in absolute value) than thet-values associated with the other independent variables.Consequently, H&M claim that IQ is a better predictorof income than the other two independent variables. Noattempt was made to determine whether the model wasproperly specified or whether the model provides an adequate fit to the data.

Problem 2 In an appendix, the authors describemultiple regression as a “mathematical procedure thatyields coefficients for each of [the independent variables],indicating how much of a change in [the dependentvariable] can be anticipated for a given change in anyparticular [independent] variable, with all the others heldconstant.” Armed with this information and the fact thatthe estimate of β1 in the model above is positive, H&Minfer that a high IQ necessarily implies (or causes) a highincome, and a low IQ inevitably leads to a low income.(Cause-and-effect inferences like this are made repeatedly throughout the book.)

Problem 3 The title of the book refers to the normal distribution and its well-known “bell-shaped” curve.There is a misconception among the general public thatscores on intelligence tests (IQ) are normally distributed. In fact, most IQ scores have distributions thatare decidedly skewed. Traditionally, psychologists andpsychometricians have transformed these scores so thatthe resulting numbers have a precise normal distribution.H&M make a special point to do this. Consequently, themeasure of IQ used in all the regression models is normalized (i.e., transformed so that the resulting distributionis normal), despite the fact that regression methodologydoes not require predictor (independent) variables to benormally distributed.

Problem 4 A variable that is not used as a predictor of social outcome in any of the models in The BellCurve is level of education. H&M purposely omit education from the models, arguing that IQ causes education,not the other way around. Other researchers who haveexamined H&M’s data report that when education isincluded as an independent variable in the model, theeffect of IQ on the dependent variable (say, income) isdiminished.

a. Co/mment on each of the problems identified. Whydo each of these problems cast a shadow on the inferences made by the authors?

b. Using the variables specified in the model above,describe how you would conduct the multiple regression analysis. (Propose a more complex modeland describe the appropriate model tests, including aresidual analysis.)