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THE CATTELL CONTROVERSY
RACE, SCIENCE, AND IDEOLOGY
By WILLIAM H. TUCKER
UNIVERSITY OF ILLINOIS PRESS
Copyright © 2009 Board of Trustees of the University of Illinois
All right reserved.
ISBN: 978-0-252-03400-8
Chapter One
FACTOR ANALYSIS AND ITS DISCONTENTS CATTELLIAN SCIENCE
Harold Bloom, the well-known literary critic and staunch defender of the traditional canon, maintains that Shakespeare invented human personality. More than three centuries would pass from the Bard's time, however, before science—more specifically, the newly created field concerned with human behavior—began systematic attempts to understand how his invention worked. Indeed, although psychology became a recognized science in the late nineteenth century, decades were still to elapse before researchers in the field turned their attention to the study of personality. Even as late as 1919 a speaker, commenting to an audience of social workers on the difficulty of finding a textbook on the topic, declared, "The study of personality does not exist, either as a science or an art, written down."
One reason that it took so long for psychologists to discover personality was their initial focus on its predecessor as the core element of human nature: character. As historian of science Ian Nicholson points out in Inventing Personality: Gordon Allport and the Science of Selfhood—his aptly titled book on the role of the "patron saint of personality" in the development of the field—the Victorian era's focus on character was appropriate to a cultural landscape that emphasized "hard work over leisure, courage over popularity, self-sacrifice over self-aggrandizement, and moral conviction over intellectual ability." But as the predominantly agrarian American society experienced the relatively sudden and dramatic changes of industrialization and urbanization, a different psychological discourse more appropriate to this new context emerged, replacing the morally freighted construct of character with the more modernist conception of personality. In the former approach selfhood was achieved through surrender to an ethical standard informed by an external framework, whereas in the latter it was achieved through realization of a set of characteristics emanating from within the self. The new approach was thus consistent with the priorities of an increasingly industrialized society, in which employers and administrators were interested in personality traits such as dominance, sociability, and aggressiveness, rather than the qualities of character.
Yet even after its establishment as a recognized field of study, personality did not assume the central focus that it would appear to merit. Although psychology tends to be a highly fragmented discipline, subdivided into a host of specialties often isolated from each other, personality is arguably its broadest single topic. Only the study of personality stands at the intersection of clinical psychology, abnormal behavior, human development, motivation, emotions, learning, social relations, and the relationship between genetic and environmental influences, overlapping with each of these behavioral areas and having significant implications for a thorough understanding of any of them. To say that personality is truly at the heart of psychology is no exaggeration. It is thus particularly puzzling that, through its many editions from 1957 to 1997, the most widely used text on the topic has called personality the "dissident" in the development of the discipline, "never ... deeply embedded in the mainstream of academic psychology." This is a strange paradox: the core subject matter of the field—what should be its substantive mainstream—lies perhaps not outside its scholarly mainstream but certainly far from its center.
The explanation for this apparent contradiction can be found in what Lee Cronbach, in his 1957 presidential address to the American Psychological Association, famously called "the two disciplines of scientific psychology." "Experimental psychology" seeks to discover general laws—to identify the variables that make different people behave alike. Supposedly patterned after the approach that has proved so effective in the physical sciences, this discipline of psychology attempts to study behavior under controlled conditions, in which one or sometimes more so-called independent variables are systematically manipulated in order to observe the effect on some "dependent" variable. Such tight control of the experimental situation allows the researcher to conduct rigorous tests and draw conclusions about causation, determining, for example, whether an appeal based on fear is more effective in attempting to change behavior than an appeal based on reason, whether one lengthy period of practice or a number of shorter periods are more effective in learning some skill, or whether children act more aggressively after viewing a violent movie than after a nonviolent one. This method regards the differences from one person to another in the same condition of the study as "noise"—what statisticians call "error variance"—obscuring the effect of the independent variable in much the same way as static can obscure the signal on a radio, and researchers purposely design experiments in ways that will minimize such individual difference variation; the only variation of interest to experimentalists is that created by the different conditions to which subjects have been exposed.
In contrast, "correlational" or "differential" psychology seeks to understand why in the same situation people behave differently from each other, viewing these individual differences not as an annoyance blurring the effect under investigation but as the principal object of interest. Instead of studying the factors that, say, affect learning for people in general, the differential approach seeks to explain why some people learn faster than others. In place of the rigid control afforded by the experimental approach, this discipline of psychology substitutes the naturalism of more lifelike situations, gathering data of much greater complexity and using multivariate statistical techniques to make sense of the results. Where experimental psychology focuses on the variation among conditions—or, as they are often called, "treatments"—differential psychology focuses on the variation among persons. Although it is possible to investigate questions about personality through the experimental method, naturally the field is much more firmly anchored in the correlational techniques appropriate to the investigation of individual differences.
Both these approaches to studying behavior were developed around the dawn of the twentieth century. Whereas experimental psychology was expanding at the time to include more and more substantive areas, the differential approach focused almost exclusively on intellectual ability and was often referred to as "genetic" psychology—an allusion not to the latest subfield of biology but to use of the "genetic method," which traced the development of the individual. Almost from the moment of its introduction in the mid-1910s, the "mental test"—in the sense of an instrument for measuring intellectual ability—became differential psychology's principal method as well as its major substance. (Actually, the term mental test had been coined twenty years earlier by James McKeen Cattell—one of the first American research psychologists and no relation to Raymond Cattell—who used it to refer to such psychophysical measurements as tests of reaction time and sensory discrimination.) Although lip service was paid to the importance of assessing other personal traits, researchers focused obsessively on intelligence, no doubt gratified by the public recognition, influence, and prestige they suddenly enjoyed, as their conclusions played a prominent role in the nation's discussions over immigration and the putative threat of the "feebleminded." After spending the first ten pages of a twelve-page article in a popular magazine in 1923 discussing intelligence, well-known Harvard psychologist Robert M. Yerkes acknowledged the significance of "temperamental traits" but observed that "little progress has been made" toward assessing them. This neglect of other characteristics by scientists did not mean, however, that the human personality was still being ignored by psychology at the time. But it did leave professional interest in the topic mainly in the hands of clinicians and psychoanalysts, whose conclusions were based not on empirical assessments but on their experience and intuitions working with patients, leading Gordon Allport to complain that "the bulk of all literature on the psychology of personality is written from this one [Freudian] point of view." Paul R. McHugh, occupant of a named chair and director of the Department of Psychiatry and Behavioral Medicine at the Johns Hopkins University School of Medicine, refers to this "tendency ... to rely upon feelings for evidence" and to claim knowledge without proof as "romanticism," and although McHugh was concerned with the conflict between "romanticists" and "empiricists" that took place in psychotherapy in the 1970s and '80s, his description of the former is an equally appropriate characterization of the pronouncements made by their forerunners half a century earlier, many of them having been trained in the Freudian tradition. It was not until the latter half of the 1930s that academic theorists formalized the study of personality in classic works by researchers such as Allport, Ross Stagner, and Henry Murray and his associates. But having attracted the attention of academic researchers late in the discipline's scientific development and relying mainly on nonexperimental techniques, personality remained peripheral to the mainstream for some time.
Just around the time that Allport and Murray were defining the field, Cattell began his own interest in the study of personality, after being mentored in London by Charles Spearman and Cyril Burt. These prominent researchers were two of the three most important scientists—Louis Leon Thurstone at the University of Chicago was the third—in the development of the multivariate statistical procedure called "factor analysis." Factor analysis is a data reduction technique: it begins with a large number of variables and attempts to account for the relations between them by postulating a smaller number of underlying hypothetical constructs or factors; Cattell often called them "functional unities." Although the method is now used in many different fields, most of the technical details involved in factor analysis were developed by psychologists studying the structure of intelligence. In fact, there are some important results in matrix algebra, the mathematical field on which the technique is based, that were first published in psychological journals.
The concept behind factor analysis is straightforward, involving the identification of groups of variables that tend to cluster together; if some variables tend to appear and disappear as a group, it suggests that they are not independent of each other but may be manifestations of some more basic construct. The cornerstone of the process is the correlation coefficient, a statistic describing the degree of relationship between two variables on a scale from 0.0 to 1.0 or 0.0 to -1.0, depending on whether they both tend to increase at the same time or one tends to increase as the other decreases; the larger the value of the correlation coefficient (either positive or negative), the stronger the relationship between the two variables. Height and weight, for example, have a correlation of approximately +.5, meaning that taller persons tend to be heavier, although the medium size of this correlation suggests that there are many exceptions to this general trend—people who are short and heavy or tall and thin. All the correlations between every possible pair of variables can be displayed in a correlation matrix, an example of which appears in table 1. Each of the seven letters denotes a variable, and each numerical entry indicates the correlation between that cell's row and column variables. It is not necessary to complete the lower left half of the table, which would be a mirror image of the upper right; that is, the correlation between, say, variables p and r is the same, whether p is the row and r the column or vice versa. Although there are seven variables in the table, the correlations between them clearly form two distinct groups: variables p, q, r, and s all have very high correlations with each other, as do variables t, u, and v with each other, but none of the former has a sizable correlation with any of the latter. This pattern suggests that the correlations might be "explained" by two underlying factors, the nature of which could be determined by seeing what the variables in each group had in common with each other. If, for example, the first four variables were all tests involving reading and vocabulary, then a factor involving verbal ability would be an obvious interpretation.
The technical details of this procedure are somewhat more complex. The underlying assumption of the factor analysis model is that an individual's score on any particular variable can be expressed as a linear combination of the factors in what Cattell referred to as the "specification equation": [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. In other words, presuming that the variables are all ability tests of some type, a person's score on test j is determined by a sum of products: the extent to which performance on that test requires the first factor (aj1), multiplied by the person's ability on the first factor (F1i); plus the extent to which performance on test j requires the second factor (aj2), multiplied by the person's ability on the second factor (F2i); plus a similar product for each additional "common" factor; plus a final component consisting of the extent to which test j requires a specific factor (ajs), one required only by that test and no other, multiplied by the person's ability on that "unique" factor (Usi). Thus, the specification equation is like a recipe: it indicates how much to weight (the a coefficients) each of the "ingredients" (the factors), which then combine to produce the exact performance or behavior. Suppose, for example, that the events in the Olympic decathlon have three common factors—speed, strength, and endurance. Then the score for competitor i on, say, the pole vault (test j) might be determined by the sum of four products: a measure of his ability to run fast (F1i), weighted by the degree to which the pole vault requires speed (aj1); a measure of his strength (F2i), weighted by the degree to which the pole vault requires strength (aj2); a measure of his endurance (F3i), weighted by the degree to which the pole vault requires endurance (aj3); and a measure of his ability at the unique skill involved in the pole vault but in none of the other events (Usi), weighted by the degree to which the pole vault requires that skill (ajs).
At the start of a factor analysis, however, the number and nature of these underlying constructs are unknown, and the problem is to take the observed data—scores on the variables and the resulting correlation matrix that indicates the relationship between every possible pair—and from this information "extract" the factors and decide on their meaning. The "solution" to a factor analysis—that is, the numerical result of the procedure—is itself a matrix like the one in table 2, in which the rows are the variables or tests and the columns are the hypothetical factors. Each entry in this matrix, called a factor "loading," is the a coefficient in the specification equation and indicates the degree to which a specific test requires or depends on a particular factor; like a correlation, a factor loading takes on a value between 0.0 and plus or minus 1.0. The mathematics of the procedure produces this factor matrix but does not identify the name or nature of the factors, a task that requires an interpretation based on the pattern of loadings—that is, by deciding what the variables with large loadings on a specific factor have in common. In table 2, for example, variables p, r, and s have high loadings on factor I. If those three variables are cognitive measures involving verbal tasks, then the factor might plausibly be defined as verbal ability. Similarly, the interpretation of factor II would depend on the content of variables q and t, and the interpretation of factor III on the content of variables u and v. Of course, the values in table 2 are hypothetical examples, constructed to illustrate the logic of factor analysis; real data are never so clear and simple.
An additional complexity in the process of factor analysis is the fact that the solution—that is, the matrix of factor loadings—is not unique; like a single equation with two unknowns, an infinite number of factor matrices can provide an equally acceptable solution from a purely mathematical point of view. The reason for these multiple possible solutions is that the factor loadings for each variable are formally identical to the coordinates in a space whose dimensionality is equal to the number of factors but whose axes can be placed arbitrarily. Thus, although the relationship of the points to each other is fixed, each possible "rotation" of the axes produces a different set of coordinates or loadings. (It is as if the hands of a clock were fixed at a particular angle to each other—for example, 45°, with the minute hand behind the hour hand—but the clock face with the numbers on it could be rotated to any possible position, making it impossible to know whether it was reading 3:00, or approximately 11:44, or one of the many other possibilities.) Researchers must decide which of the resulting orientations is the "correct" one—obviously not in a mathematical sense, which provides no basis for preferring one possibility over another, but in the sense that it yields some psychologically meaningful interpretation of the factors.
(Continues...)
Excerpted from THE CATTELL CONTROVERSY by WILLIAM H. TUCKER Copyright © 2009 by Board of Trustees of the University of Illinois. Excerpted by permission of UNIVERSITY OF ILLINOIS PRESS. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.
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