Bell Curve

2 Introduction Introduction 3Hereditary Genius, published just a decade after the appearance of Originof Species in 1859. So began a long and deeply controversial associationbetween intelligence and heredity that remains with us today.'Galton realized that he needed a precise, quantitative measure of themental qualities he was trying to analyze, and thus he was led to put informal terms what most people had always taken for granted: Peoplevary in their intellectual abilities and the differences matter, to thempersonally and to society.' Not only are some people smarter than others,said Galton, but each person's pattern of intellectual abilities isunique. People differ in their talents, their intellectual strengths andweaknesses, their preferred forms of imagery, their mental vigor.Working from these observations, Galton tried to devise an intelligencetest as we understand the term today: a set of items probing in*tellectual capacities that could be graded objectively. Galton had theidea that intelligence would surface in the form of sensitivity of perceptions,so he constructed tests that relied on measures of acuity ofsight and hearing, sensitivity to slight pressures on the skin, and speedof reaction to simple stimuli. His tests failed, but others followed whereGalton had led. His most influential immediate successor, a French psychologist,Alfred Binet, soon developed questions that attempted tomeasure intelligence by measuring a person's ability to reason, drawanalogies, and identify pattems."T'hese tests, crude as they were by modemstandards, met the key criterion that Galton's tests could not: Theirresults generally accorded with common understandings of high and lowintelligence.By the end of the nineteenth century, mental tests in a form thatwe would recognize today were already in use throughout the BritishCommonwealth, the United States, much of continental Europe, andJapan.M Then, in 1904, a former British Army officer named CharlesSpearman made a conceptual and statistical breakthrough that hasshaped both the development and much of the methodological controversyabout mental tests ever sincea5By that time, considerable progress had been made in statistics. Un.like Galton in his early years, investigators in the early twentieth cenetury had available to them an invaluable number, the correhtioncoefficient first devised by Galton himself in 1888 and elaborated by hisdisciple, Karl Pears~n.~ Before the correlation coefficient was available,scientists could observe that two variables, such as height and weight,seemed to vary together (the taller the heavier, by and large), but theyhad no way of saying exactly how much they were related. With Pearson'sr, as the coefficient was labeled, they now could specify "how much"of a relationship existed, on a scale ranging from a minimum of -1 (forperfectly inverse relationships) to + 1 (for perfectly direct relationships).Spearman noted that as the data from many different mental testswere accumulating, a curious result kept turning up: If the same groupof people took two different mental tests, anyone who did well (orpoorly) on one test tended to do similarly well (or poorly) on the other.In statistical terms, the scores on the two tests were positively correlated.This outcome did not seem to depend on the specific content ofthe tests. As long as the tests involved cognitive skills of one sort or another,the positive correlations appeared. Furthermore, individual itemswithin tests showed positive correlations as well. If there was any correlationat all between a pair of items, a person who got one of themright tended to get the other one right, and vice versa for those who gotit wrong. In fact, the pattern was stronger than that. It turned out to benearly impossible to devise items that plausibly measured some cognitiveskill and were not positively correlated with other items that plau.sibly measured some cognitive skill, however disparate the pair of skillsmight appear to be.The size of the positive correlations among the pairs of items in a testdid vary a lot, however, and it was this combination-positive correlationsthroughout the correlation matrix, but of varying magnitudesthatinspired Spearman's insight.17] Why are almost all the correlationspositive? Spearman asked. Because, he answered, they are tapping intothe same general trait. Why are the magnitudes different? Because someitems are more closely related to this general trait than others.'81Spearman's statistical method, an early example of what has since becomeknown as factor analysis, is complex, and we will explore some ofthose complexities. But, for now, the basis for factor analysis can be readilyunderstood. Insofar as two items tap into the same trait, they sharesomething in common. Spearman developed a method for estimatinghow much sharing was going on in a given set of data. From almost anysuch collection of mental or academic test scores, Spearman's methodof analysis uncovered evidence for a unitary mental factor, which henamed g, for "general intelligence." The evidence for a general factor inintelligence was pervasive but circumstantial, based on statistical analysisrather than direct observation. Its reality therefore was, and remains,arguable.