The Mismeasure of Man | Study Guide

Stephen Jay Gould

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The Mismeasure of Man | Chapter 6 : The Real Error of Cyril Burt: Factor Analysis and the Reification of Intelligence | Summary



The Case of Sir Cyril Burt

Sir Cyril Burt was a British educational psychologist and for 20 years was in charge of intelligence testing for London schools. He then became the chair of the psychology department at the University of London. After he retired from there, he published several papers on intelligence in identical twins. Burt claimed to have found that the IQ scores of twins were very similar, even when they were raised in different environments. This added a great deal of support to the hereditarian position that intelligence is inherited, not shaped by any factors after birth such as nutrition, environment, or education.

However, Burt's claims do not stand up. When other psychologists looked at his data, they discovered that he was a fraud—Burt had made up a lot of his data. Beyond that he falsely claimed to be the inventor of a statistical technique called factor analysis. He stole credit from a man named Charles Spearman in a series of actions that Gould concludes show that Burt was not just lying but mentally ill. Why retell this story? Because factor analysis is essential to the proper interpretation of intelligence test results. Gould trained in the difficult mathematics of factor analysis early in his career as an evolutionary biologist. His skill with this is one of the unique strengths that he believes he brings to the whole topic of intelligence testing.

Correlation, Cause, and Factor Analysis

In this section Gould explains the difference between correlation and causation. "Correlation assesses the tendency of one measure to vary in concert with another." He cites the example of how both legs and arms grow in length as a child gets older. This has a strong correlation that can be expressed mathematically by a factor called r, the correlation coefficient. The more perfect the correlation, the closer r gets to 1. If r equals zero, on the other hand, this shows that there is absolutely no relationship at all between two separate things.

But just because two things can be correlated does not mean that one of them is causing the other. Gould gives the example of how both his age and the price of gasoline have increased over 10 years. Yet no one would claim that his birthdays are causing a hike in the cost of gas.

Comparisons are simple to understand when it comes to just two measurements, but it rapidly gets more complex when three or more items are being correlated. It's possible to draw a line for two items, and a cube for three, but what if you want to study 100 different correlations at once? It's not possible for three-dimensional creatures to envision a graph that exists in a hundred of them. This is where factor analysis comes in. It is a mathematical technique to simplify dozens of correlations into just a handful in order to more clearly understand them.

Gould's talk of matrices, vectors, coefficients, sines, and cosines is difficult to follow even when he attempts to simplify it. He uses many graphs and charts to attempt to illustrate what he is saying. The bottom line is this: The more closely two measures are correlated, the closer together their lines, or vectors, will be on a graph. If they are separated from each other by 90 degrees, they have no relationship or correlation at all. It is also important to note how close each vector lies to a central line, or axis. This represents how much of the original information—before it was simplified—is still retained in the chart.

Although factor analysis can help those trained in it to better understand a large collection of data, it is important to remember that the math is just numbers. It does not describe anything physical that exists in the real world. It is a kind of shorthand, or mathematical label, that helps scientists talk about measurements. When someone forgets this and starts to talk as if factor analysis is describing a real, physical thing, it is called reification. Gould says that factor analysis on the results of IQ tests has lured many a scientist into making this error.

This is what Charles Spearman did in 1904. He reified the data from his factor analysis of mental tests, giving it the label g, for general intelligence. Spearman believed that g pointed to a single mental capability called intelligence that lay at the foundation of all cognitive skills. But it is possible to look at the same data in legitimately different ways using factor analysis. When you do this, you get different values for Spearman's g. It is even possible to do it in a way that g completely disappears. Does this mean that general intelligence doesn't even exist?

Charles Spearman and General Intelligence

Gould explains yet another statistical technique, tetrad difference, with the example of mice. Imagine that you measure the growth of four different mouse parts: leg length, leg width, tail length, and tail width. The correlation is unsurprisingly positive for all four measures because as mice grow, so do all their parts. But is there just one rate of growth, or does length increase at a different rate than width? Do legs grow at a different rate than tails? Spearman's mathematical formula attempts to answer this. If a single growth factor is at work, the tetrad difference should be zero. In addition, in order to prove that a single factor is at work, the measures need to "load on," or approach the value of g. This means that the more strongly "loaded" g is for a mental test, the better it proves that something called general intelligence actually exists. Spearman claimed that this was precisely what he found in his factor analysis of IQ tests. In other words, Spearman said that a person who was smart at one kind of mental activity would be smart at all others as well.

Spearman modified his theories about intelligence over the course of his career. Although he did think that general intelligence was inherited and immutable, Spearman also believed that specific abilities could be improved through training and education. The application of IQ scores to the real world was never Spearman's primary interest, however. He was motivated by a strong desire to simply understand intelligence and the brain. It was Burt who took it further.

Cyril Burt and the Hereditarian Synthesis

Among psychologists, Sir Cyril Burt is best remembered for his work with factor analysis. He refined the process invented by Spearman and extended it to include the notion that subsidiary special abilities were part of general intelligence. But in the process, Burt contradicted himself, often within the same paper. He would rail against reifying the results of IQ tests and thinking that intelligence was a real thing. Rather, they were "convenient mathematical abstractions, not ... concrete mental 'faculties,' lodged in separate 'organs' of the brain." Then he would say that reification of intelligence was fine, but scientists like Spearman were locating intelligence in the wrong portions of the brain.

Burt used factor analysis to support his unshakeable conviction that intelligence was an inborn and inherited "general factor" of the mind. But g only speaks to the notion of general intelligence, not that it is inherited. Factor analysis says nothing about that. So where did Burt's strong belief in hereditarianism come from? Gould refuses to psychoanalyze Burt, but he promises to prove that this was a preexisting belief of Burt's, not a conclusion he could reach scientifically through his data. And in the long run, this belief led Burt to commit outright fraud.

Gould looks at Burt's earliest study in 1909 of English school boys and points out its defects. The most glaring error was his conclusion that intelligence is inherited because the boys' test scores were similar to that of their parents. But he never measured the parents' intelligence; he just assumed it based on their social rank or occupation. He also "corrected" scores that seemed inaccurate to him by talking to the boys' teachers and adjusting test results based solely on what the teacher said about the student.

In 1937 Burt did take a look at the home environment of London students who were a year or more behind in school, and he did find a strong correlation between poverty and poor academic performance. But rather than see this as an indication that maybe intelligence wasn't completely inherited, Burt said the exact opposite. "Burt ... opted for innate stupidity as the primary cause of poverty," Gould writes. Burt was so blinded by his obsessive belief in the innate nature of intelligence that he refused to see connections that he did see in other areas. For example, Burt acknowledged how poverty could increase juvenile delinquency. He saw how powerful an influence environment could be on human behavior but refused to admit that it could have the same effect on mental performance.

Burt's belief that students' innate intelligence could be measured and ranked by IQ tests had real-world consequences for generations of British students. Students were tested at the age of 10 or 11, and their scores determined what kind of secondary school they could attend. Only 20 percent were deemed suitable for college preparatory schools. The rest were funneled to technical schools and were blocked from attending university. Gould laments the anguish felt by so many children whose dreams were crushed by these tests.

L.L. Thurstone and the Vectors of Mind

L.L. Thurstone was a professor of psychology at the University of Chicago from 1924 to 1955. Gould calls him the "exterminating angel" of Spearman's g. According to Gould, Thurstone did not do this because he thought g failed to represent something real, rather "Thurstone disliked g because he felt it was not real enough."

Thurstone invented the vector method Gould uses earlier in the chapter to show factor analysis. In the process Thurstone claimed that both Spearman and Burt had placed their factors in the wrong place and thus failed to correctly identify general intelligence. His reasons for this were mathematical, and Gould admires the solution Thurstone devised to correct it. However, Thurstone's correction was not based on any new evidence or test data. It was simply a decision he made based on his preexisting belief that IQ tests do indeed measure some real mental ability. It is not that Thurstone's analysis of the data is better than Spearman's; it is simply different. "If the same data can be fit into two such different mathematical schemes," Gould says, "perhaps both ... are wrong."

Using his system Thurstone believed he had discovered proof for seven kinds of mental abilities, including verbal, numerical, spatial, and memory skills, but when he did so, Spearman's g completely disappeared from the results. In other words, Thurstone's analysis of IQ test results made the notion of general intelligence disappear.

The field of psychology erupted into furious debate, with one side defending the Spearman-Burt theory of general intelligence and the other championing Thurstone's multiple mental abilities. Thurstone worked hard to get psychologists and schools to stop using a single IQ score to rank children. Like Spearman and Burt, however, Thurstone did believe that whether you called it general intelligence or multiple abilities, mental performance was largely inherited. "The accusation of being undemocratic must not be hurled at the biologists," Thurstone said. "If anyone is undemocratic on this issue, it must be Mother Nature."

Later Thurstone did more analysis and had to acknowledge that he hadn't made g disappear entirely after all, although in his view his multiple abilities still existed.

Epilogue: Arthur Jensen and the Resurrection of Spearman's g

This is a section was added in 1996 to the second edition of The Mismeasure of Man when the notion of g, or general intelligence, was resurrected both in The Bell Curve and in the work of American psychologist Arthur Jensen. Jensen uses factor analysis and comes to the same conclusion as Spearman: The g factor represents a real thing called intelligence. Gould is highly critical of Jensen's reasoning, which he says is flat-out wrong when Jensen is talking about evolution and circular when he is talking about factor analysis and g.

Gould also accuses Jensen of scientific racism due to Jensen's claim that the difference in IQ test scores between white and black people reflects a true different in intelligence, not a flaw in test design.

A Final Thought

This section is a single paragraph reprinting a quote from the 19th-century English philosopher John Stuart Mill: "The tendency has always been strong to believe that whatever received a name must be an entity or being, having an independent existence of its own."


In the introduction to the second edition of The Mismeasure of Man, Gould states how proud he is of this chapter. He admits that he struggled to explain the complex mathematics of factor analysis in a way that would make sense to lay readers. He believes that using Thurstone's vectors, which can be shown in geometric diagrams, makes factor analysis understandable. However, not everyone who reads this chapter will agree that Gould succeeded. It remains difficult to sift through the math and even more difficult to tease out what it means. Does the statistical analysis of IQ test data prove that something called general intelligence exists or not? Does it decide one way or the other a scientific debate about intelligence and IQ tests that is still raging today?

In this chapter Gould claims that it does. Although he has respect for some of the work that these men did, Gould winds up demolishing the conclusions reached by Charles Spearman, Cyril Burt, L.L. Thurstone, and Arthur Jensen. Each one of them made the same fundamental mistake, in Gould's view. They each made the cardinal error of thinking that the mathematical tool they used to study their IQ data gave them a clear and accurate window into the physical structure of the brain. This is what Gould means when he repeatedly talks about the fallacy of reifying intelligence. As powerful as factor analysis can be in understanding patterns in nature, scientists need additional information from biology in order to tie the math to the real world. This is Gould's point in this chapter.

Spearman, Burt, and Thurstone were long dead when Gould published The Mismeasure of Man. But Jensen was still alive, and he defended himself strongly against Gould's claims. Jensen says that Gould quoted him out of context and thus misrepresented his views. He also thinks that Gould has misrepresented Spearman, Burt, and Thurstone. Jensen claims that these three men knew that their statistical analysis in and of itself didn't prove the "real" existence of g, or general intelligence and were not reifying anything. They were simply doing what scientists always do—constructing a hypothesis to tentatively explain data.

It is difficult for the lay reader to decide the outcome of a debate between experts in a scientific field, but Jensen was not the only psychologist to dispute Gould's charges of reification. In fact, even one of Jensen's most constant critics in the field of intelligence, New Zealand researcher James R. Flynn, agrees with Jensen in this case. Although Flynn thinks Gould got some things right, he has also stated that in this chapter at least, Gould "evades all of Jensen's best arguments."

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