IQ Controversy

Note: numbers in brackets refer to Publications list.

IQ Controversy

(a) Problem of defining "intelligence":

In his controversial revival  of the eugenic  traditions of the 20s, Arthur Jensen (1969) appealed explicitly to Spearman's factor model  as a vehicle for defining "intelligence".  However, in view of the factor indetermincay problem (see above, factor analysis), these high hopes are doomed to failure [40, 47, 52, 57, 83] . Recourse to concrete IQ tests is equally unsatisfactory, because different tests are often quite poorly correlated. In fact , this was the reason why Spearman had postulated his factor model in the first place. From a purely pragmatic point of view one further finds that, contrary to what some authors who should know better have claimed, conventional IQ tests  are surprisingly poor predictors of  most criteria of practical interest, including scholastic achievement. For example, the SAT - a descendent of conventional "verbal" IQ tests such as the Army Alpha - consistently performs worse  than easily available  previous grades as a predictor of subsequent grades. This was known, though not advertised, since the 20s. For long range criteria (such as graduation or GPA at graduation), the SAT usually accounts for less than 5% of the criterion variance (Humphreys, 1967, Donlon, 1984). As one might expect, the picture dims further for the GRE: In two recent, large scale, validity studies, Horn and Hofer (undated) and Sternberg (1998 ) found that the validities of the GRE for predicting successful completion of graduate training were effectively zero.

(b) Spearman's Hypothesis

In the early 80s, Jensen (in Bias in Mental Testing, 1980) revived a casual observation Spearman had made in 1927:  He had reported that subtests most highly loaded on  his  general intelligence factor g showed the largest Black/White contrasts (Spearman Hypothesis). Jensen, after substituting the largest principal component (PC1) for g, interpreted this as new, compelling evidence for the existence of g which seemed to corroborate his central claim that Blacks, on average, are deficient in g compared to Whites,  and that these differences are primarily genetic rather than not cultural, in origin.

In [43]  I drew attention to the fact that this result can be explained as an artifact which has nothing to do with Blacks or g. Rather it arises with any data, including randomly generated data, if they exhibit a sufficiently large mean difference vector.  William Shockley subsequently challenged this interpretation. He correctly pointed out that it was limited to a positive relation between the mean differences and the weights of the PC1 of the pooled group, while  most of Jensen's data showed such  positive correlationswithineachgroup. I, therefore, extended  my results to this more general situation by invoking joint  multinormality as an additional condition. I then showed mathematically, geometrically, empirically, and by random simulation, the following result:

Publication [83] is a Target Article on this topic, followed by  numerous  commentaries. Most of them endorse the stringency of the above reasoning. For a chronicle of the incredibly protracted history of this paper, see [86].

(c) Hit-Rate Bias

 In  view of the severe implications  of a mistaken interpretation of discrepancies in IQ performance of various ethnic groups, much attention has been focused on the question whether these discrepancies might conceivably  be the result of  a bias  favoring some groups over others (perhaps also, males over females). A. Jensen (1980)  devoted a whole book to this issue, befittingly entitled Bias in Mental Testing. He concluded that such worries are unwarranted so far as the Black/White discrepancy is concerned because, if anything, conventional IQ tests overpredict Black criterion performance.

With this reasoning Jensen followed tradition in adopting an institutional point of view (e.g. that of universities) over that of the applicants, by focussing on  regression equations and  validity coefficients. From an institutional point of view, a test is useful if it improves the composition of the subgroup that is eventually hired or admitted on the basis of superior test performance.  From this point of view, one can  show that even a test with low validity has some merit, as long as the hiring institution employs a sufficiently stringent admission quota (by raising the test cut-off).

However, this narrow perspective ignores two important aspects of the bias problem:

Finally, we review a number of data sets to evaluate the  hit-rates of the SAT and ACT for different ethnic groups. We also assess the hit-rate bias, i.e., the extent to which conventional tests favor or discriminate against subgroups in terms of the chances that a qualified student  passes the test. We found that conventional admission tests discriminate against Blacks, and  further, that this bias increases as the admission quotas are tightened. In [82] these results are further refined and extendend to include formulae for estimating the minimum validity needed for given quota and base rate, so that use of the test improves the percentage of correct decisions over random admissions. The bottom line is that, in the realistic validity range (.3 - .4)  for longrange criteria of practical interest, no test improves over random admission in terms of overall percent of correct decisions if one of the two base rates exceeds .7.