# The G Factor: The Science of Mental Ability

By Arthur R. Jensen | Go to book overview

differences that enters into many aspects of human behavior besides those narrowly conceived of as scholastic or intellectual.

NOTES
1.
Jensen, 1980a (Chapter 8); Jensen, 1993a. The most detailed and advanced treatments of validity are by Cronbach ( 1971) and Messick ( 1989).
2.
Another way of conceptualizing the meaning of a validity coefficient (rxc) is in terms of the following formula: rxc = (T - R) / (P - R), where T is the average level of performance on the criterion for persons selected with the test, R is the mean level of criterion performance for persons selected at random, and P is the mean criterion performance for perfectly selected persons, as if rxc = 1. Hence rxc is a direct measure of the proportional gain in the mean criterion performance that results from the use of the test for selection as compared to what the mean level of criterion performance would be with random selection. In other words, the validity coefficient is a direct indicator of the effectiveness of the test's predictive accuracy, such that, for example, a validity coefficient of .50 provides just half as accurate prediction as a validity coefficient of 1.00, which indicates perfect prediction. Even a quite modest validity coefficient has considerable practical value when a great many binary (i.e., yes- no, pass-fail, win-lose) decisions are made. For example, the casino at Monte Carlo reaps large sums of money every day from its roulette games, because of course the house always has better odds for not losing than the gamblers have for winning, yet the house advantage is, in fact, equivalent to a predictive validity coefficient of only +.027! The practical value of a validity coefficient of +.27, therefore, is certainly not of negligible value where a large number of selection decisions must be made.
3.
The standard error of estimate (SEest) is related to the validity coefficient (rxc) as follows: SEest = sc (1 - rxc2)½, where sc is the standard deviation of the criterion measure. The ratio SEest/sc measures the proportional error of predicting individuals' point values on the criterion. The percentage gain in accuracy of point predictions as compared with purely random selection is equal to 100(1 - SEest/sc), which is termed the index of forecasting efficiency. The use of this index is now in disfavor when the overall value of test-based selection is being considered, because the index of forecasting efficiency is not directly related to the overall mean gain in criterion performance afforded by test- based selection. The validity coefficient itself, however, is a direct indicator of the proportional gain in mean criterion performance of individuals who were selected by means of a test with a certain validity coefficient (see Note 2). The common habit of squaring the validity coefficient to obtain the proportion of variance in the criterion accounted for by the linear regression of criterion measures on test scores, although not statistically incorrect, is an uninformative and misleading way of interpreting a validity coefficient for any practical purpose.
4.
There are several types, definitions, and statistical criteria of test bias. For a comprehensive discussion, see Jensen, 1980a, Chapter 9.
5.
Some psychologists distinguish between two types of knowledge: declarative knowledge, which is knowing about something (e.g., Fe stands for iron in the periodic table of elements; Plato wrote The Republic; yeast is used in making bread), and procedural knowledge, which is knowing how to go about doing something (e.g., trouble

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