Chapter 4. What Is The IQ

It is generally known that the I Q is a number, that the number measures level of intelligence, and that the level of intelligence is determined by the individual's performance on an intelligence test. Beyond that the average person knows little about the I Q.

The letters I Q stand, of course, for Intelligence Quotient. This quotient is obtained by dividing mental age by chronological age and multiplying the result by 100. It is Mental Age that is supposedly measured by the test. For example, if a child's test score indicates a mental age of nine years and the child is actually aged eight years and six months, his IQ would be computed as follows.

Another child who makes the identical score but whose chronological age is ten years would score this way:

What, then, is Mental Age? It is the average score made by children of a particular age group. Mental Age is arrived at by a process known as "standardiz-ing" a test. The test is given to a large number of children of all ages and of presumably representative backgrounds. When the results are averaged for each age group, norms are established. The score for the average ten year-old is, let us say, 120. If a ten year-Did taking the test scores 120, his I Q is:

If he scores more than 120 his IQ will be over 100, or above average; if he scores below 120 his I Q will be under 100, or below average.

General categories of intelligence have been set up, based on the I Q and what is considered the normal distribution of intelligence. While there are differences among psychologists* concerning these classifications, a typical one, based on one particular test, would look like this:

Notice that although a particular test may be standardized so that a score of 100 is established as normal, there is leeway of up to fifteen points on either side of 100 in forming the normal category. This leeway is the result of what is known as a standard deviation, a statistician's phrase used to describe the extent to which a score may be influenced by numerous factors that have nothing to do with intelligence. In this instance, it would mean that a child scoring 85 might well have scored 100 if other extraneous factors were not involved; therefore a score of 85 would be considered average.

Standard deviations are arrived at by a mathematical process and are different for each I Q test. It is one of the unfortunate realities of life that the people who use the I Q most-teachers, guidance counselors, and personnel workers-practically never take the standard deviation into account. In fact, many of them are not even aware of its existence!

There is little doubt that if everyone realized and remembered that any I Q is at best a crude approximation rather than an absolute index to intelligence, few people would be unduly impressed or intimidated by the I Q. And, what is more important, few children would find opportunities denied them because of this single factor.

While the IQ is a crude measure, only the psychologists and the statisticians really understand how crude it is, and some of them seem to have lost sight of its great limitations. Not only is the I Q score an approximate measure, but it is also subject to changes and variations that can be startling.

There are two ways of considering the reliability of the I Q. One is from the mathematical or statistical point of view, which sees the problem in relation to large numbers of children. The statistician feels there is enough evidence to support the reliability of the I Q. Why? Because his statistics show that for about half of the individuals tested the scores will vary from a gain of six points to a loss of four points when they are given a second test. For the other half, however, the scores will vary more!

Lewis M. Terman, who devised the famous Stan-ford-Binet intelligence test and who is a leading defender of the reliability of the I Q, explains:

"Roughly speaking, the chances that an I Q will either increase as much as six points or decrease as much as four points are one in two; that it will either increase as much as twelve points or decrease as much as eight points, one in five; that it will either increase as much as eighteen points or decrease as much as twelve points, one in twenty; that it will either increase as much as twenty-four points or decrease as much as sixteen points, one in a hundred and forty."1

In applying Terman's figures to an average elementary school with a population of 500 children, Florence L. Goodenough presented the following supposition:

". . . it is apparent that under the best conditions of individual testing, at least 100 children may be expected to show changes in I Q upon retest of as much as 10 points. In approximately 25 of these cases, the change will amount to as much as 15 points, and in 4 or 5 instances, as much as 20 points. If, in place of the highly trained examiners and careful checking of the scores for arithmetical errors that is presupposed in the foregoing figures, the tests are given by persons with only a moderate amount of training and skill, the frequency of such changes will be correspondingly greater. If the ordinary group test is used in place of an individual test, and particularly if the test is used at the time of the later examination is not the same one as that used at the earlier examination, the frequency and magnitude of the discrepancies between first test and later test may be greater still."2

An individual test is one which is given to one child by an examiner who asks the child to perform certain tasks and answer certain questions. A group test is one which is administered to a large number of children simultaneously. Each child is given a printed booklet of questions. Answers are marked in this booklet or on a special answer sheet which can be scored mechanically. Since most children are given group tests, administered by teachers who have had no special training in this field, the unreliability of the I Q becomes even more apparent.

In relation to the way the IQ is used in the schools, Prof. Goodenough also points out:

"A rather remarkable example of 'wishful thinking' is apparent in the almost universal tendency of school people to ignore the 50 per cent last mentioned [those whose I Qs will vary by more than 5 points in either direction when retested] and to utilize the results of single tests in educational classification and guidance with a degree of assurance that would be warranted only if the entire range of variation were no greater than that shown in the middle 50 per cent [those whose I Qs will vary by less than 5 points in either direction when retested.]"

If the scores of half the children will vary so much when retested, why do statisticians and psychologists speak of the "constancy" of the I Q? Because there is no other single method of measuring intelligence that approaches the reliability or relative constancy of the I Q.

But with relevance to the individual child-the second way of considering the I Q-the reliability of the I Q takes on an entirely different aspect. For, as we have seen, changes of twelve, eighteen, and twenty points are not uncommon, and for the individual child such changes can be tremendously significant.

Finally, in addition to the standard deviation factor and the relative unreliability of the I Q, another condition justifies downgrading the importance of the I Q. There is an enormous number of tests, each one constructed by a different psychologist, each one different from the others, and each one claiming to measure intelligence better than all the rest. Later we shall go into the differences among these tests, but for the moment it is important only to understand hat no single test enjoys universal acceptance in the schools; that many different tests are used by each school system and even within each school; and, most important of all, that no two tests give the same results for the same child.

So this is the I Q. When Kathy is six years old she is given Test A and scores 95. Taking into account the standard deviation, this means that her IQ might be 110 or it might be 80; the score indicates only that it is most probably somewhere in between. Then there is one chance in two that if she were retested, even immediately, her actual score would be over 100 or below 90. If she had been given Test B instead, she might have scored 120-or perhaps 70. At eight years of age she may be tested again, this time with Test C. It would not be at all extraordinary if her score resulted in an I Q of 132. The chances of such a sequence of scores are probably almost as good as her chances of scoring 95 in each of these three tests.

Kathy's 95 I Q would land her squarely in the middle of an average class, where she would get an average education. But Kathy's 95 I Q does not conclusively prove that she is of average ability or potential. It is at best a poor indication of what she might be capable of achieving. If she has great potential, it might show itself no matter what kind of class she is in. But for every child who develops his potential satisfactorily, there are many other children whose potentials are never realized. Certainly one of the prime forces that help a child realize his potential is a stimulating, challenging, and enriched education. The I Q should not play the important role that it does in keeping some children from that kind of education.