Factor Analysis and the Idea of General Intelligence
What do we find when we apply this logic to real test data? Both the WAIS and the WISC (the adult and child tests, respectively) rely, as we’ve said, on numerous subtests. This arrangement allows us to compare each person’s scores on one of the subtests to their scores on all the other subtests. When we make these comparisons, we find an impressive level of consistency from one subtest to the next. People who do well on one portion of the test tend to do well across the board; people who do poorly on one sub-test tend to do poorly on the other subtests as well. In other words, we find substantial correlations among all the subtests’ scores. The correlations aren’t perfect—and so we know, by the logic we’ve developed, that the subtests don’t overlap completely in what they measure. Even so, the correlations are telling us that the subtests are far from inde-pendent of each other; instead, they all overlap in what they’re measuring.
To document and measure this overlap, psychologists rely on a statistical technique known as factor analysis, developed by Charles Spearman (1863–1945). This technique distills from the pattern of correlations a broad summary of how all the scores are related to each other. Specifically, factor analysis (as its name implies) looks for com-mon factors—“ingredients” that are shared by several scores. The analysis detects these shared factors by using the logic we’ve already developed: If the scores on two separate tasks are correlated with each other, this suggests the tasks are influenced by the same factor. If scores on three tasks are all correlated with each other, then all the tasks, it seems, are influenced by the same factor. And so on.
Factor analyses confirm that there’s a common element shared by all the compo-nents of the IQ test; indeed, in children’s data, this single common element seems to account for roughly half of the overall data pattern (Watkins, Wilson, Kotz, Carbone, & Babula, 2006); a single common factor seems just as important in data drawn from testing of adults (e.g., Arnau & Thompson, 2000). The various subtests differ in how strongly they rely on this common element, and so some subtests (e.g., someone’s com-prehension of a simple story) depend heavily on this general factor; other tests (e.g., someone’s ability to recall a string of digits) depend less on the factor. Nonetheless, this general factor seems to matter across the board, and that’s why all the subtests end up correlated with each other.
But what is this common element? If the subtests overlap in some way, what is the nature of the overlap? More than 50 years ago, Charles Spearman offered the obvious hypothesis—namely, that the common element is general intelligence, usually abbreviated with the single letter g. Spearman proposed that g is a mental attribute called on for virtually any intellectual task. It follows, therefore, that any individuals with a lot of g have an advantage in every intellectual endeavor; if g is in short supply, the individual will do poorly on a wide range of tasks.