IX. MEASUREMENT OF GENERAL INTELLIGENCE: THE IQ
We now see that the “general” factor in intelligence may be defined simply as the positive coherence which exists among the multitudinous abilities of an individual, as respects their amounts. The first to obtain a quantitative measure of general intelligence, for the practical purpose of classifying school children, was Binet. Binet concluded from reflection on the research done, that failure or success in one mental function may be of slight significance for the classification of an individual, because correlation is imperfect; but that failure or success in a score of different functions must be of very great significance, because correlation among mental functions tends strongly to be highly positive. Working on this basis, he devised a large number of mental tests, intended to sample the individual’s performance in many different functions.
A mental test may be defined as a standard stimulus, which provokes a response capable of quantitative interpretation. Binet devised numerous standard stimuli, and a method of interpreting the responses elicited, in terms of a context of scores made by children of various ages, throughout the period of immaturity. His measurements were thus in terms of “mental age,” a phrase now somewhat familiar in education.
The science of mental measurement is rapidly progressing to more exact usage. The concept of “mental age” when applied to persons who vary in birthday age is in some respects misleading, and in other respects quite inapplicable (as with superior adults). General intelligence is at present usually scored in terms of points achieved, percentile attained in total distribution, or of mental ratio. The most reliable scales now available for the measurement of general intelligence in school children, score in terms of mental age and intelligence quotient (IQ). This measure (IQ) signifies the ratio borne by the intellectual level attained by a given child in tests, to the level attained by the typical child of his birthday age. For instance, a child 9 years 6 months old has an IQ of 100, if his score in tests equals that made by the average child of 9 years 6 months. If he is inferior to the average child of his age, the amount of such inferiority will be expressed by a ratio less than 100. Thus, if his performance equals only that of the average child of 5 years 2 months, his IQ will be 62 months ÷ 114 months, or 54 (dropping fractions less than .5). On the other hand, if he is superior to the average, attaining, let us say, the performance of the average child of 14 years 0 months, his IQ will be 168 months ÷ 114 months, or 147. An IQ of 100 may thus be thought of as “par” in general intelligence for a school child, while anything less may be thought of as “below par” to the extent indicated; and anything greater than 100 may be thought of as “above par.” The IQ shows the point of focus, for amounts of performance in a variety of mental functions. It derives its value for educational procedure from the positive correlation, which has been demonstrated to exist among performances in mental operations.
Scales at present available will measure general intelligence, in terms of IQ, about as low as IQ 10, and about as high as IQ 190, at certain periods of development. No doubt human intelligence ranges somewhat below and above these limits, but adequate methods of establishing the two extremes have not yet been devised. It is by no means usually realized that the range of individual differences in general ability is so wide that it is extremely difficult to invent methods of discovering its full extent. However, for practical purposes, available scales are adequate to cover the range for young school children, because intelligences that fall below IQ 25 or above IQ 175 are so rare as to be dealt with very seldom.
Within the limitations named, the general intelligence of school children can now be determined by a competent examiner, with a very small margin of error. The average error made by such an examiner will not exceed ± 5 IQ.
Not all scales for the measurement of general intelligence are scorable in terms of IQ. Some have been standardized in terms of “raw” points achieved, and some in terms of percentile status. There is at present much variety of usage in scoring, the ideal being to find units of measurement. It does not lie within the scope of this volume to treat the problem of establishing units for the measurement of mental traits. The general intelligence of the children to be discussed here has usually been determined in terms of IQ, which will be comprehended from the brief description given.
An ideal of students of mental measurement is to devise a scale which will measure any intelligence, from the lowest to the highest existing, after maturity, in units every one of which is equal to every other; and to devise a scale fulfilling the same requirements for each 12-months interval of the period of immaturity. This ideal is far from being realized at the present time, but the future will see it achieved.
In the meantime scales for the measurement of special talents, which are not measured by the scales for measuring general ability, are being worked out. What these special talents are we shall now consider.