The definition of IQ that I've posted here for the past ten years needs to be
drastically modified on the basis of new (to me) official information that I'm
only now obtaining. I'm rewriting what's on this website, but this tectonic
shift is subject to correction until it can be vetted by experts.
(An expanded discussion of IQ may be found here.)
What Is "IQ" ?
"IQ" stands for " Intelligence Quotient".
As originally defined, someone's IQ is equal to 100 times their Mental Age (MA) divided by their Chronological Age (CA).
IQ = 100 X Mental Age/Age in Years
The mental-age concept was invented to aid in the grade placement of children.
"IQs" are no longer the ratios of mental ages/chronological ages (ratio-IQs)!
For the past 50 years (and in a sense, right from the beginning, with the 1918 Army Alpha and Army Beta tests), there has been a trend toward defining intelligence in terms of percentile rankings, and then looking up the IQ that would correspond to that percentile ranking if intelligence were Gaussian-distributed. (In fact, mental age/chronological age scores aren't Gaussian distributed.)
It might be argued that these newer percentile-based "IQs" aren't actually intelligence quotients, since they no longer involve quotients.
Generally speaking, these newer "deviation-IQs" or standard score (percentile-based) "IQs", are much lower than the older ratio IQs.
Some Problems with Ratio-IQs
A key problem with ratio IQs is that both high and low ratio IQs are much more common than would be predicted if ratio IQs were distributed in accordance with a Gaussian distribution. To give specific examples (Roid, G. H. (2003). Stanford-Binet Intelligence Scales, Fifth Revision, Technical Manual. pg. 85. Itasca, IL: Riverside Publishing), a ratio IQ of 130±2 (almost Mensa-level), with a predicted frequency of occurrence of roughly 1-in-60, on the older L-M forms of the Stanford-Binet IQ tests actually occurs with a frequency of, maybe, 1-in-11(?) on the newer, percentile-based Stanford-Binet, Fifth Edition (SB5) IQ test. This corresponds to a range of percentile based IQs of 114 through 121, respectively. Similarly, a ratio IQ of 145±2, with a predicted frequency of occurrence of about 1-in-600, may be actually found in the general population with a frequency of, perhaps, something like 1-in-17(?), corresponding to a range of SB5 IQs of 122 through 133, respectively. Why does a single, older, L-M ratio IQ translate into a range of the newer SB5 IQs? I'm speculating that it may be because the newer SB5 is a completely redesigned test, constructed, like the Wechsler tests, with 10 subtests that measure 10 different cognitive abilities. Although the SB5 can provide a single number that can be used as an overall IQ, it can also (I presume) afford a more-detailed assessment of a test-taker's cognitive profile than could the older L-M ratio-IQ tests. But at the moment, this is just a fantasy on my part. I don't really know.
Also, these frequency estimations I'm listing above are based on assumptions on my part that don't reflect different weightings in the translations of ratio-IQs to SB5 IQs, and that may not be correct. I've estimated the frequency of occurrence of a norm-referenced IQ from 114 through 121 (s = 15) by adding up the frequencies of occurrence of each of the IQ intervals 114±½, 115±½,... 121±½, between 113½ and 121½ to arrive at the total frequency of occurrence for finding an IQ within that interval. The problem is that the mappings of ratio-IQs of 130±2 to norm referenced IQs in the interval between 113½ and 121½. probably aren't uniform. For example, an L-M ratio-IQ of 130±2 may be more likely to translate into an SB5 IQ pf 121 than 114.
In the near future, I hope to learn more about this.
In the SB5 Assessment Service Bulletin Number 3, Use of the SB5 in the Assessment of High Abilities, also published by Riverside Publishing Company, Dr. Deborah L. Ruf furnishes sample profiles of gifted children which I've tried to distill into comparisons between ratio IQs and "norm-referenced" (percentile-based) IQs, as sampled in the Table below.
|Age Equivalent||Ratio IQ||
* - My numbers for Melanie are
particularly questionable. I don't have her exact age, so I'm using 11½ (the
midpoint between 11 and 12) for her chronological age, as well as for the
chronological ages of Mary Ann and Adam. Then I'm supposing that Melanie's Age
Equivalent score of 19 is her mental age, although I'm not sure that this
assumption is valid for Age Equivalents above 15. Until someone knowledgeable
reviews my assumptions and calculations, the numbers in this table are meant to
be "if-then for-instances" rather than consequential results.
In this table, I've used the Age Equivalents listed in Dr. Ruf's Tables 5 and 6 as mental ages, and have divided them by the children's chronological ages to arrive at equivalent ratio IQs. I need to warn you that I'm not sure that what I've done is correct. It needs to be confirmed.
Ratio-IQs have other shortcomings. For one thing, they assume that throughout childhood, mental age is directly proportional to chronological age. In practice, it's not. As Dr. Ruf puts it, "intellectual growth has more or less predictable spurts and plateaus". For another, they run into problems with adult populations. The Terman tests, Forms L and M, used a mental age of 16 for adults of all ages older than 16. However, the Wechsler Adult Intelligence Scales (WAIS) show an increase in the maximum IQ of 150 (Standard Deviation = 15) of about 10 points between the ages of 16 and the early twenties. Similarly, the average IQ also increases about 10 points (Standard Deviation = 15) going from 16 to the early twenties. Then, too, different abilities peak at different ages in life, with vocabulary often increasing into the sixties. Beyond the early twenties, age-related cognitive decline tends to set in, slowly at first, and then with increasing rapidity as subjects segue into old age.
Advantages of Ratio IQs
At the same time, ratio-IQs and the mental age concept have their advantages. People haven't gotten any less intelligent just because the SB5 assigns them lower IQs than did the L-M forms of the Stanford-Binet. A 16-year-old child with a mental age of 26 and an SB5 IQ of 124 is still going to be 10 years ahead of the average 16-year-old ("A rose by any other name... "). What's entailed is a major shift in our interpretations of IQs, and of the cut-offs for giftedness. Any time a child's ratio IQ exceeds about 130, they should be (I should think) candidates for gifted education programs.
What these norm-referenced IQ tests are showing, I think, is that the fraction of the population that requires gifted education programs is about five times larger--about one in every 9 children--than the old L-M tests indicated.
With its Age Equivalence scores, the Stanford-Binet Intelligence Scales, Fifth Edition, has the ability to identify children with relatively high mental ages and with special educational needs.
The SB5 also introduces Rasch scores that assign absolute levels of difficulty (for a given population) to the test questions on IQ tests. This should set the stage for more meaningful adult intelligence metrics.
(To be continued)
IQs are measured with IQ tests. There are a number of IQ tests available.
Types of IQ Tests:
1. Individually administered tests
(a) Stanford Binet
The Stanford-Binet IQ test was the first US-developed IQ test, and was introduced by Dr. Lewis M. Terman in 1916. By now, there have been six editions of the Stanford-Binet.
Ratio IQs versus Deviation (Percentile) "IQs"
The 1916, 1937, 1960, and 1972 editions of the Stanford-Binet utilized the concept of mental age, while the fourth version in 1986 employs percentile rankings. These percentile rankings are then converted to an equivalent IQ score, called a "deviation IQ", by converting percentiles to IQs using a Gaussian distribution.
Examples of questions similar to those on the Stanford-Binet IQ test.
(b) Wechsler Tests
The Wechsler tests are considered today to be the standard by which other IQ tests are judged.
There has been a series of Wechsler Adult Intelligence Scales, beginning with the
The Wechsler tests consist of 10 or 11 (at the discretion of the test administrator) subtests, each of which has a ceiling that is 2.75 standard deviations above the mean. (The most recent edition of the Wechsler Adult Intelligence Scale, the WAIS-III, utilizes 13/14 subtests. Six of these tests are "verbal", meaning that these questions and their answers are transmitted verbally. The six verbal subtests are:
The other five tests (eight
subtests on the WAIS-III) are "performance" (non-verbal)
subtests in which the test-taker has to perform certain tasks
as fast as possible.
The five performance subtests are:
and the three additional subtests that have been added to the WAIS-III are,
The Wechsler tests measure
deviation IQs, with a standard deviation of 15 points
of IQ. The Wechsler tests attempt to compensate for age-related cognitive
Measuring 11 different facets of intelligence as they do, the Wechsler IQ tests are influenced by breadth of capability in various cognitive areas, as opposed to depth. They were designed as clinical evaluation instruments, and can detect various kinds of neurological problems. Dr. Wechsler warned that his tests should not be used above an IQ of 130, but they are commonly used to measure IQs considerably higher than that. One word of caution about IQ tests: they are subject to "ceiling effects" as an examinee approaches the ceilings of a test. For example, with the Wechsler tests, someone might make a perfect or almost-perfect score on several of the verbal subtests, but fail to make a perfect score on several others. Consequently, the individual in question wouldn't have bee adequately tested on those subtests for which she "hit the ceiling".
As mentioned above, Wechsler-derived IQs are adjusted for age to offset the cognitive decline that attends aging. The graph below shows how Wechsler IQs vary with age:
The Slossen tests are similar to the Stanford-Binet and correlate closely with them. The Slossen tests have a ceiling of 27 years of mental age.
Untimed tests are often called "power"
tests. Other tests are timed, proctored group tests, such as the
Raven Advanced Progressive Matrices, the California Test of Mental
Maturity (CTMM) and the Cattell Culture-Fair Test, which are easier
to administer but are narrower in scope. (Included in this group
would be the Scholastic Aptitude Test, the Graduate Record Exam,
and the Miller Analogies.) Still a third class of test is the
unproctored power test, such as the Mega Test, the Titan Test,
and the Test for Genius. These are untimed tests in which the
test-taker lays protracted siege to difficult problems that emulate
the kinds of problems encountered in actual research. These tests
are not universally recognized as true IQ tests because it is
felt that they are susceptible to cheating, and that their scores
depend upon collateral factors such as persistence and library
skills as well as sheer intelligence.
IQ's were originally measured using the MA/CA concept: IQ = MA/CA. If you were 10 years old and earned Mental Age scores on IQ tests equal to those of 16-year-olds, your IQ would be 16/10 X100, or 160. This seemed to work well enough for children, but it encountered
IQ tests have been under attack since their inception. It is, perhaps, counter-intuitive and unpopular that a test requiring an hour or two can establish the upper bounds of one's intellect for a lifetime. However, although they're not infallible, for adults, they do a remarkably good job of generating a score that will remain more or less constant throughout life.
Be Measured With a Single Number?
Yes and no. One of the most serious criticisms of using a single number to assess intelligence is that people may be stronger in certain areas such as verbal skills, logical aptitude or spatial visualization than in others. Drs. Richard Feynman and Albert Einstein would be examples of geniuses who were reputed to be extremely strong mathematically while being relatively weak verbally. More commonly, though, purely intellectual abilities tend to be uniformly high or uniformly low in a given individual, consistent with the concept of an underlying "g" or "general intelligence" that powers all the specialized intellectual aptitudes. In addition, there are several sub-factors such as verbal, spatial, Still, this doesn't happen with everyone, and the exceptions, like Richard Feynman and Albert Einstein, are very important. Tests like the Wechsler Adult Intelligence Scale (WAIS) consist of a number of subtests that are scored separately and can measure the profile for an individual. (Dr. Howard Gardner has defined seven types of intelligence, while Dr. Robert Sternberg has identified three.)
It's also easier to make an IQ score that's lower than your true IQ than it is to make a score that's higher. Taking a test on a bad day, or spending too much time on a few difficult items could artificially lower one's score. The best results are obtained when more than one test is administered.
What Does Adult
Generally, one's mental age stops rising rapidly when one reaches the latter teens--e. g., 16. Consequently, on some IQ tests, "16" was taken as the chronological-age divisor in an IQ calculation for adults. The Wechsler Adult Intelligence Scale is calibrated for all ages up to 70, with chronological-age divisors appropriate to every age 70 or below.
The average IQ is, by definition, 100. To get an idea what this means, someone with an IQ of 80 or below is considered to be marginally able to cope with the adult world. People with IQ's of 80 or below typically work as unskilled laborers such as lawn maintenance and trash pickup. They generally need help from friends or family to manage life's complications. About 10% of the population has an IQ of 80 or below.
People with IQ's of 80-90 are a little on the slow side but may be found in fast-food restaurants, day-care centers, etc. They may also be found in unskilled jobs. About 16% of the population has IQ's in this range.
People with IQ's of 90-110 generally occupy semi-skilled positions, including typists, receptionists, assembly line workers, and checkout clerks. They are able to keep up with the world, and comprise about 46% of the public.
People with IQ's in the 110 to 120 range fill the skilled trades and include some tool and die makers, teachers, and Ph. D.'s among their ranks. They also make up 16% of the population.
People with IQ's of 120 and above tend to staff the professions as doctors, dentists, lawyers, teachers, and college professors. They fall in the upper 10% of the population.
Before going any higher in the IQ scale, it's necessary to talk about ratio-IQ's versus deviation-IQ's. As mentioned above, IQ's were defined as the ratio of Mental Age to chronological age.
The average IQ of all
college professors is 130, which lies within the upper 3% of the