In "The g Factor," Jensen (1998, 1999) fails to establish his claim of the existence of an 18 point lag between the average IQ score for American blacks compared to American whites. The populations upon which he tested his hypothesis are constructed in a faulty manner, leading to an invalid treatment of data. The gap he discovers may therefore be a statistical artifact. He emphasises that no cultural bias is present in IQ testing, but the criterion through which his test groups are defined is supported only by cultural usage and falls within his own classification under the category "Wrong Conceptions of Race".
2. The test groups are defined as "persons of European ancestry who are socially identified as 'white' and persons of some African ancestry who are socially identified as 'black' or African-American" (p. 350). Notice the use of "some" in the previous sentence. The cultural basis of this so-called "social identification" is immediately apparent when one realises how differently the sentence would read if the "social definitions" for white and black were simply reversed, and the test populations defined as "persons of African ancestry who are socially identified as 'black' and persons of some European ancestry who are socially identified as 'white'". The statistical flaw that mars the entire research becomes even clearer when the author states that
"all of the descriptive statistics and studies referred to here are based on the social classification of individuals into racial groups as black and white, although virtually all American blacks have some degree of European Caucasian ancestry. American blacks are socially defined simply as persons who have some degree of sub-Saharan African ancestry and who identify themselves (or, in the case of children, are defined by their parents) as black or African American. Persons of European Caucasoid ancestry are classified as whites." (p. 353)
Notice how this classification supposedly rests entirely on how "persons who have some degree of sub-Saharan African ancestry [...] identify themselves" and how black children depend on their parents' "definition" to be regarded as such. Let us analyse carefully how such a crucial flaw has developed. Since Jensen is a fastidious methodologist I will need no further support than what is to be found in his own writings. Here, in the author's own terms, is an account of the "wrong conception of race":
"The root of most wrong conceptions of race is the Platonic view of human races as distinct types, that is, discrete, mutually exclusive categories. According to this view, any observed variation among the members of a particular racial category merely represents individual deviations from the archetype, or ideal type, for that 'race'". (p. 421)
The accurate conception he subsumes under the heading of "Races as Breeding Populations with Fuzzy Boundaries", and insofar as the white-black or black-white continuum is concerned, provides some figures on "the proportion of Caucasoid genes [in] the black gene pool" (p. 432), such as: "M [intermixing index; FOOTNOTE 1] varies across different regions of the United States, being as low as 4 percent to 10 percent in some southeastern States and spreading out in a fan-shaped gradient toward the north and the west to reach over 40 percent in some northeastern and northwestern states" (ibid).
3. How do these two conceptions of race, the false and the true, apply to the test populations of black and white? The definition of black derives from the accurate view of a "breeding population with fuzzy boundaries", as it regards as black anyone with "some African ancestry". The definition for white however derives from the wrongheaded one of "human races as distinct types, that is, discrete, mutually exclusive categories". Jensen writes that "persons of European Caucasoid ancestry are classified as whites", but this he understands as a necessary condition, not as a sufficient one: indeed if such persons can at the same time trace any amount of African ancestry, they cease automatically to be white and become black. It is clear that as much as he regards being black as being located on a spectrum, being white rests in his mind on an all-or-nothing condition, i.e., exactly what his "wrong conception of race" assumes. What invalidates Jensen's testing of his hypothesis is not so much that for his two sample populations he sometimes relies on an accurate definition of race, sometimes on an inaccurate one, but that their definition depends on two separate senses of the same word.
4. Elsewhere in his book Jensen explains that a "culture-biased test" "shows signs of not measuring the same thing in different individuals" (p. 361). His construction of test populations is culture-biased because he does not use the same criterion in accordingly defining them, seeking comprehensive reasons for inclusion when dealing with blacks, and restrictive reasons for exclusion when dealing with whites. Jensen pays lip-service to the notion of "fuzzy boundaries" between races but faced with the black-white spectrum, he assigns anybody who can be located to any degree along such a continuum to his "black" sample, reserving "white" for whoever cannot be located on it through lack of evidence of any African ancestry. Candidly, he betrays some annoyance at the fact that such restrictive determination of whites is not foolproof when he writes: "In every generation there has been a small percentage of persons who have some African ancestry but whose ancestry is predominantly Caucasian and who permanently 'pass as white'. The white American gene pool therefore contains some genes that can be traced to Africans who were brought over as slaves (estimated by analyses of genetic polymorphisms to be less than 1 percent)" (p. 432).
5. Does this invalidate Jensen's work? Yes, completely. His two test populations are not statistically comparable: one comprises a sub- group which is confined at the very end of the black-white spectrum, the other covers its remaining part, i.e., the entire range from 100% black to 98.99% white. How, under these circumstances, could any statistical comparison of "whites" and "blacks" be of any pertinence? Jensen is too astute a statistician not to be fully aware of the methodological implications. How can he possibly claim that central values or dispersion indices for any of the features he aims at measuring can be validly contrasted when he writes of the proportion of European genes in his 'black' population that "the largest studies, which yield estimates with the greatest precision, give mean values of M [FOOTNOTE 2] close to 25 percent, with a standard error of about 3 percent" (p. 432), while at the same time M for whites as defined by him must be in the region of 99 percent (from the figure mentioned for his "pass as white" test)?
6. What should Jensen have done instead? He should in any case have applied a single criterion in defining his test populations. He could, for instance, have worked from "blacks" defined in a way symmetrical, i.e., as persons "who cannot trace any European ancestry". Alternatively, he could have accepted in earnest his own definition of race and distinguished his samples as falling on one side or the other of the midpoint in the white-black continuum. Instead, he has simply condoned and regarded as having scientific validity a culturally biased definition of blacks which, as in his quote, is so pervasive in the social fabric that only 1 percent of persons with "some African ancestry" manage to "pass as white".
7. Statistics are apparently lacking as to how many whites manage to "pass as black", and here lies the core of Jensen's misguided science: the social environment is constrained in such manner that no one attempts and fails to "pass as black". The social reason for this is provided in his statement that African genes are "genes that can be traced to Africans who were brought over as slaves" (p. 432). In other words, Jensen's definition of blacks was coined in the times of slavery and remains embedded in these dark ages. Sticking to it -- or much worse, naively assuming that work of scientific significance can be based upon it -- betrays a deep-seated belief that sharing an African ancestry is a taint (the antiquated notion of "atavism") which grounds an individual within a particular type whose features obfuscate any other, such as being in reality 98.99% white. What cultural attitude might counter such a stifling legacy? Perhaps nothing more than changing some linguistic habits rooted in historical prejudice. Like having an identity for anybody who does not happen to be located at either of the ends of the black-white or white-black range: a name like "mulatto", for instance. Or even better, no names at all for something as trivial as what mix one has been assigned from the single gene pool of one species.
 "For any given allele, the estimated proportion (M) of white European ancestry in American blacks is obtained by the formula M = (qB - qAf) / (qW - qAf), where qB is the given allele's frequency in the black American population, qAf is its frequency in the African population, and qW is its frequency in the white European population" (p. 432).
 M is clearly defined here as an index measuring a person's degree of intermixing, i.e., differently than in the previous footnote.
Jensen, A. R. (1998) The g factor: The science of mental ability. Westport, Connecticut: Praeger.
Jensen, A. (1999) Precis of: "The g Factor: The Science of Mental Ability" PSYCOLOQUY 10 (23). ftp://ftp.princeton.edu/pub/harnad/Psycoloquy/1999.volume.10/ psyc.99.10.023.intelligence-g-factor.1.jensen http://www.cogsci.soton.ac.uk/cgi/psyc/newpsy?10.023