Gould, Richardson et al. v. Spearman (2018)

Judge: Order, order in the court, settle down, everyone! Today, November 3, 2018, I wish to formally begin deliberations in the case of Stephen Jay Gould, Ken Richardson, et al. v. Charles Spearman.  Spearman, the defendant, has been charged with one count of reification, one count of conflating correlation and causation, and one count of attempting the pointless task of accurately reducing a complex entity - namely, human intelligence - to a single number. The plaintiffs include Gould, Richardson, Henry Schlinger, and a number of others  from whom we shall soon be hearing. The plaintiffs will now be allowed to call their first witness to the stand. Mr. Lawyername, who do the plaintiffs want to present as their first expert witness?

John Lawyername, the lawyer for the plaintiffs: Your honor, we wish to present Henry Schlinger, professor at California State University, Los Angeles, as our first witness today.

Judge: Very well. Mr. Schlinger, please take the stand.

Schlinger: Thank you for allowing me to testify today. Ladies and gentlemen of the jury, I believe that Spearman "took an abstract mathematical correlation and reified it as the general intelligence that someone possesses" (Schlinger 2003, p. 17). In addition, "Spearman saw what he wanted to see in his data...Once the error of reification is committed, it is easy to commit another logical error, circular reasoning...In Spearman's case, the only evidence for g, or general intelligence, were the positive correlations, even though it was those positive correlations he was trying to explain in the first place" (ibid.). Lastly, Spearman portrays the results of factor analyses of IQ test scores as synonymous with intelligence, even though "The positive intercorrelations that result from factor analysis of their test scores are themselves far removed from the behavior of any individual in the test-taking situation or, for that matter, in any other context" (ibid.).

Judge: Mr. Spearman, who do you wish to call as your first expert witness?

Spearman: Next, I would like to call Charlie Reeve and Milton Hakel to the stand.
Reeve & Hakel: "All constructs are abstractions, purposely invoked to describe coherent classes of phenomena that co-occur in nature. For instance, gravity is a mathematical construct that describes one of the four classes of forces associated with matter. Similarly, g is a psychometric and psychological construct that describes a class of phenomena associated with results of human mental functioning. Both of these constructs are abstract ideas; both are latent. However, because the phenomena ascribed to these constructs can be observed, the constructs are subject to conceptual refinement, measurement, and verification" (Reeve & Hakel 2002, pp. 48-49).

The plaintiffs wish to call Stephen Jay Gould to the stand.
Gould: "The misuse of mental tests is not inherent in the idea of testing itself. It arises primarily from two fallacies, eagerly (so it seems) endorsed by those who wish to use tests for the maintenance of social ranks and distinctions: reification and hereditarianism" (Gould 1981, p. 155; cited in Carroll 1995). Also, "many factorists have...tried to define factors as causal entities. This error of reification has plagued the technique since its inception. It was "present at the creation" since Spearman invented factor analysis to study the correlation matrix of mental tests and then reified his principal component as g or innate, general intelligence" (Gould 1996, p. 284).

Judge: Who do you want to call  to respond to these accusations that you are guilty of reification?

Spearman: Your honor, I wish to call John Carroll as my first witness.

Carroll: Gould's criticisms of Spearman, and of research on IQ tests as a whole, are mistaken. This is because, contrary to Gould's assertions, "...factor analysis implies no "deep conceptual error" of "reification."...Merely because it is convenient to refer to a factor (like g) by use of a noun does not make it a physical thing. At the most, factors should be regarded as sources of variance, dimensions, intervening variables, or "latent traits" that are useful in explaining manifest phenomena, much as abstractions such as gravity, mass, distance, and force are useful in describing physical events. Gould's far-reaching condemnation of factor analysis as a device for producing reifications is one of his own deepest conceptual errors; it stands factor analysis on its head" (Carroll 1995).

And Jensen & Weng as my second witness.
"...Gould’s strawman [sic] issue of the reification of g was dealt with satisfactorily by the pioneers of factor analysis, including Spearman (1927) Burt (1940) and Thurstone (1947)...the consensus of experts is that g need not be a “thing”-a “single, ” “hard,” “object’‘-for it to be considered a reality in the scientific sense. The g factor is a construct. Its status as such is comparable to other constructs in science: mass, force, gravitation, potential energy, magnetic field, Mendelian genes, and evolution, to name a few. But none of these constructs is a "thing"" (Jensen & Weng 1994, p. 232).

The plaintiffs call Joseph L. Graves and Amanda Johnson to the stand.

Graves & Johnson: Spearman has clearly confused correlation with causation in positing the existence of a g factor based on positive correlations between IQ test scores. The fact is, "...such variables may be statistically correlated without necessarily having any functional relationship... Science recognizes this fact and demands the implementation of experimental techniques to establish causal relationships. Pseudoscience, on the other hand, is content with the bald assertion that, given a correlation, a causal relationship must exist" (Graves & Johnson 1995, p. 281).

Next we will deliberate the charge that the g factor identified by Spearman is inconsistent and unstable. 

The plaintiffs once again call Joseph L. Graves and Amanda Johnson to the stand.

Graves & Johnson: "...g can vary widely, depending on how it is calculated. Such admissions explain why batteries of tests applied to individuals and groups return different values of correlation; certainly, one would not expect a fundamental underlying mechanism to behave so capriciously. Similarly, a physicist would not expect to get different values for the speed of light depending on the technique used to measure it. Thus, the mutability of g significantly hinders the scientific legitimacy of psychometric theory" (Graves & Johnson 1995, p. 281).

The defendants call Johnson, te Nijenhuis, and Bouchard to the stand.
Johnson, te Nijenhuis, & Bouchard: "...the g factors identified by the batteries were completely correlated (correlations were .99, .99, and 1.00). This provides further evidence for the existence of a higher-level g factor and suggests that its measurement is not dependent on the use of specific mental ability tasks...Our analyses indicate that g factors from three independently developed batteries of mental ability tests are virtually interchangeable" (Johnson et al. 2004, p. 104) In a subsequent replication of this study, it was again found that "...the g factors were effectively interchangeable" (Johnson, te Nijenhuis, & Bouchard 2008, p. 89)

I also wish to  call Jensen & Weng to the stand again.
Jensen & Weng: "...g is remarkably robust and almost invariant across different methods of analysis, both in agreement between the estimated g and the true g in simulated data and in similarity among the g factors extracted from empirical data by different methods" (Jensen & Weng 1994, p. 231).

Judge: So, Dr. Spearman, what is the main point that your witnesses wish to make regarding the plaintiffs' claims that your g factor is so inconsistent as to be scientifically invalid?

Spearman: The main point, your honor, is that these accusations, such as those by Graves & Johnson, are simply false. On the contrary, the evidence that has just been presented shows that the g factor is highly consistent no matter what method is used to calculate it.

Judge: This is a difficult case. It seems like the assumption that correlations between test scores prove the existence of a single dimension of intelligence is unwarranted, but referring to the existence of this correlation, which is not controversial, is not necessarily problematic. What is problematic is when researchers talk out of one side of their mouths and say "We never thought factors were actual things! We refer to them as constructs! The g factor is a construct, not a thing!" while, at other times and other places, talking about individual and group differences in g, the heritability of g, whether it is possible to boost g with Head Start programs, etc. None of these latter descriptions would make sense if these scholars did not believe that g were an actual human quality, rather than an abstract theoretical construct. Clearly, g theorists do treat the g factor as "a real property in the head" (Gould 1994), despite their frequent insistence.

References
Carroll. Reflections on Stephen Jay Gould's The Mismeasure of Man (1981). Intelligence. 1995.
Gould. The Mismeasure of Man (1st edition). 1981.
Gould 1994
Gould. The Mismeasure of Man (2nd edition). 1996.
Graves & Johnson 1995.
Jensen & Weng 1994.
Johnson et al. 2004.
Johnson, te Nijenhuis & Bouchard 2008.
Reeve & Hakel 2002.