Certainly, like any other statistic, a g factor based on a limited number of mental tests and a limited number of subjects will contain error. There are three main sources of such error: (1) subject sampling error, because a sample does not perfectly represent the population; (2) psychometric sampling error, because a limited number of diverse mental tests does not perfectly represent the total population of mental tests, actual or conceivable; and (3) all factor scores in a common factor analysis, including g factor scores, by any method of derivation, are only estimates of the true factor scores, which remain unknown, in the same sense that obtained scores are estimates of true scores, with some determinable margin of probable error, in classical measurement theory. It has been deter- mined mathematically that the average minimum correlation between estimated factor scores and their corresponding hypothetical true factor scores rapidly increases as a function of the ratio of the number of tests to the number of first- order factors (Gorsuch, 1983, p. 259). With 11 tests and two first-order factors, as in this psychometric battery, the minimum correlation between estimated and true factor scores would be + .84, and the actual correlation could be well above this value.

Just as we can think statistically in terms of the sampling error of a statistic, when we randomly select a limited group of subjects from a population, or of measurement error, when we obtain a limited number of measurements of a particular variable, so too we can think in terms of a psychometric sampling error. In making up any collection of cognitive tests, we do not have a perfectly representative sample of the entire population of cognitive tests or of all possible cognitive tests, and so any one limited sample of tests will not yield exactly the same g as another limited sample. The sample values of g are affected by subject sampling error, measurement error, and psychometric sampling error. But the fact that g is very substantially correlated across different test batteries means that the variable values of g can all be interpreted as estimates of some true (but unknown) g, in the same sense that, in classical test theory, an obtained score is viewed as an estimate of a true score.

The deviation from perfect construct validity in g attenuates the values of r(g× d). In making up any collection of cognitive tests, we do not have a perfectly representative sample of the entire universe of all possible cognitive tests. Therefore any one limited sample of tests will not yield exactly the same gas another such sample. The sample values of g are affected by psychometric sampling error, but the fact thatgis very substantially correlated across different test batteries implies that the differing obtained values of g can all be interpreted as estimates of a “true” g. The values of r (g× d) are attenuated by psychometric sampling error in each of the batteries from which a gfactor has been extracted. We carried out a separate study to empirically estimate the values for this correction.