Cognitive Assessment, Principles of assessment of aptitude and achievement

Mean-spirited Mono-g-ists vs. Muddleheaded Poly-G-ists

I hate the impudence of a claim that in fifty minutes you can judge and classify a human being’s predestined fitness in life. I hate the pretentiousness of the claim. I hate the abuse of scientific method which it involves. I hate the sense of superiority which it creates, and the sense of inferiority which it imposes.

– Walter Lippmann, in a 1923 essay on Lewis Terman and the IQ testers

Most of us have uncritically taken it for granted that children who attend school eight or ten years without passing the fourth grade or surmounting long division, are probably stupider than children who lead their classes into high school at twelve years and into college at sixteen. Mr. Lippmann contends that we can’t tell anything about how intelligent either one of these children is until he has lived out his life. Therefore, for a lifetime at least, Mr. Lippmann considers his position impregnable!

– Lewis Terman, in response to Walter Lippmann

Spearman’s (1904) little g caused a big stir when it was first proposed and has, for over a century now, been disrupting the natural state of harmony that would otherwise prevail amongst academics. Many a collegial tie has been severed, many a friendship has soured, perhaps even engagements broken off and marriages turned into dismal, loveless unions because of the rancor this topic provokes. I have seen otherwise mild-mannered professors in tweed jackets come to blows in bars over disagreements about g.1

It all began when Spearman observed that mental abilities that he measured were all positively correlated. This observation has been replicated by thousands of studies. No one who is familiar with this gigantic body of evidence doubts that essentially all cognitive abilities are positively correlated. This statistical regularity is typically referred to as the positive manifold.2 You could become an academic superstar (i.e., admired by six or seven other academics) if you were to find a pair of cognitive abilities that are negatively correlated with each other. So far, no one has.3 Thus, everyone in the know agrees with Spearman on this point. What some people hate is his explanation for it.

Spearman believed (and invented some very fancy statistical procedures to support his argument)4 that abilities are correlated because all abilities are influenced by a common cause, g (general intelligence). Spearman was careful to note that he did not know for certain what g was but was not shy about speculating about its nature. He thought that it might be a kind of mental energy and that some people had a lot of it and some had very little.

The essential points of contention in the byzantine quarrels between Spearmanian mono-g-ists and anti-Spearmanian poly-G-ists5 have not changed much over the decades. There is some diversity within both groups but the lines between them are fairly clear. Not only do the mono-g-ists insist that g be acknowledged as an ability, but they believe that it should be esteemed above all others. Some appear to believe that no ability other than g even matters. Some poly-G-ists will grant that g exists but deem it inconsequential compared to the myriad other abilities that influence the course of a human life. Other poly-G-ists deny that g exists and are disgusted by the very idea of it.

It turns out that these two groups are not merely on opposite sides of an intellectual debate—they are members of different tribes. They speak different dialects, vote for different candidates, and pray to different gods. Their heroic tales emphasize different virtues and their foundation myths offer radically different but still internally consistent explanations of how the world works. If you think that the matter will be settled by accumulating more data, you have not been paying attention for the last hundred years.

Poly-G-ists do not merely believe that mono-g-ists are mistaken but that they are mean-spirited, perhaps evil, or at the very least, Republicans. In their view, the course of human history can be summed up in this manner:

Since the dawn of time up to the beginning of the twentieth century, humans lived in a paradise of loving harmony and high self esteem. Then Spearman invented g and ruined everything. Previously, Live White Males (for back then they were not yet dead) had been content to be equal to everyone else and were really rather decent fellows. However, many of them were corrupted by Spearman’s flattery and convinced themselves they had more g than other people. The deceived began to call themselves Fascists and went around disempowering people with nasty labels. Though eventually defeated by George Lincoln King, Jr. in the Civil Liberties War, Fascists still wield influence via college aptitude tests. If we rid the world of all standardized tests, people will no longer label one another, low self esteem will be eradicated, and a new Utopia will be established.

On the other side, mono-g-ists know that poly-G-ists have seen the same data and read the same studies as they have. They believe that the poly-G-ists are simply too muddled-headed to understand the data, too blinded by their ideological wishes to see the world as it is, or too fearful of social consequences to proclaim publically that the emperor has no clothes. In the short epic tragedy, the Spearmaniad, mono-g-ists find this account of how things came to be:

In the dark mists of prehistory, life was nasty, brutish, and short. Worse, it was almost impossible to tell the common folk from their betters and some very mediocre presidents were elected. When the goddess of mathematics looked upon the chaos of the world, she cried crystal tears of pure correlation coefficients. Now Spearman was a mighty statistician and he gathered the correlations up and arranged them in matrices. From these matrices he invented factor analysis, from which flowed new knowledge: first IQ tests, then writing, then the wheel. All that was done with factor analysis was beautiful, virtuous, and true. But the brief flowering of civilization that followed was ended when a cabal of ignorant do-gooders objected to the use of IQ tests, presumably because they (or their ugly, talentless children) performed poorly on them. We now stand on the brink of disaster. Giving up IQ tests will be followed immediately by a rapid descent into barbarism. College aptitude tests may postpone or soften the impact of this catastrophe for a little while but cannot avert it entirely.

The theoretical status of g will not cease to be controversial until something extraordinary happens to the field. I do not pretend to know what this might be. Maybe a breakthrough from biology will resolve the matter. Maybe divine intervention. Until then, I feel no need to join either tribe. I will remain agnostic and I will not get too excited the next time really smart people eagerly announce that finally, once and for all, they have proof that the other side is wrong. This has happened too many times before.

1 Okay…not really…but I have seen some very sarcastic emails exchanged on professional listservs!

2 The term positive manifold at one time had a precise meaning drawn from mathematics, meaning that the correlation matrix of all tests was nearly a rank 1 matrix (i.e., a correlation matrix implied by Spearman’s Two-Factor Theory). As it is currently used, the term simply means that the correlation matrix consists entirely of positive correlations.

3 Not, at least, in more than one large representative sample. From time to time, someone gets an occasional negative correlation but other researchers have trouble replicating the finding.

4 Hence, the intense controversy is not merely a result of lies and damned lies.

5 So named because in perhaps the most important theory to deny the existence of g (Horn & Cattell, 1964), the most important abilities all have names that begin with a capital letter G (Gf, Gc, Gv, and so forth).

This post is an excerpt from:

Schneider, W. J. (2013). Principles of assessment of aptitude and achievement. In D. Saklofske, C. Reynolds, & V. Schwean (Eds.), Oxford handbook of psychological assessment of children and adolescents (pp. 286–330). New York: Oxford University Press.


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