Intelligence quotient

An intelligence quotient, or IQ, is a score derived from one of several different standardized tests designed to assess intelligence. When modern IQ tests are constructed, the mean (average) score within an age group is set to 100 and the standard deviation to 15. Today almost all IQ tests adhere to the assignment of 15 IQ points to each standard deviation, but this has not been the case historically. Approximately 95% of the population have scores within two standard deviations of the mean. If one SD is 15 points, then 95% of the population would be expected to have an IQ within a range of 70 to 130.

IQ scores have been shown to be associated with such factors as morbidity and mortality, parental social status, and, to a substantial degree, parental IQ. While the heritability of IQ has been investigated for nearly a century, controversy remains regarding the significance of heritability estimates, and the mechanisms of inheritance are still a matter of some debate.

IQ scores are used in many contexts: as predictors of educational achievement or special needs, by social scientists who study the distribution of IQ scores in populations and the relationships between IQ score and other variables, and as predictors of job performance and income. The average IQ scores for many populations have been rising at an average rate of three points per decade since the early 20th century, a phenomenon called the Flynn effect. It is disputed whether these changes in scores reflect real changes in intellectual abilities.

Whether or not IQ tests are an accurate measure of intelligence is open to debate. It is difficult to define exactly what constitutes intelligence; it may be the case that IQ scores represent a very specific type of intelligence.

Early history
The first large scale mental test may have been the imperial examination system in China. Modern mental testing began in France in the nineteenth century. It contributed to separating mental retardation from mental illness and reducing the neglect, torture, and ridicule heaped on both groups.

Englishman Francis Galton coined the terms psychometrics and eugenics, and developed a method for measuring intelligence based on nonverbal sensory-motor tests. It was initially popular but was abandoned after the discovery that it had no relationship to outcomes such as college grades. French psychologist Alfred Binet, together with psychologists Victor Henri and Théodore Simon published the Binet-Simon test in 1905 which focused on verbal abilities. It was intended to identify mental retardation in school children. The score on the Binet-Simon scale would reveal the child's mental age. For example, a 6 year-old child who passed all the tasks usually passed by 6 year-olds—but nothing beyond—would have a mental age that exactly matched his chronological age, 6.0. (Fancher, 1985). In Binet's view there were limitations with the scale and he stressed what he saw as the remarkable diversity of intelligence and the subsequent need to study it using qualitative, as opposed to quantitative, measures (White, 2000). American psychologist Henry H. Goddard published a translation of it in 1910. The eugenics movement in the USA seized on it as a means to give them credibility in diagnosing mental retardation, and thousands of American women, most of them poor African-Americans, were forcibly sterilized based on their scores on IQ tests, often without their consent or knowledge. American psychologist Lewis Terman at Stanford University revised the Binet-Simon scale which resulted in the Stanford-Binet Intelligence Scales (1916). It became the most popular test in the United States for decades.

The general intelligence factor (g)
The psychologist Charles Spearman made the first formal factor analysis of correlations between the tests in the early 20th century. Spearman's model used a single common factor that accounted for the positive correlations across intelligence tests. His analysis is considered to be the first theory of intelligence. His statistical model of intelligence came to be known as the general intelligence theory. Using his model, Spearman argued that intelligence is largely a single global ability. For three quarters of a century, Spearman's g theory was the dominant theory of intelligence.

The g-loading of an intelligence test is the degree to the test score reflects general mental ability, as opposed to specific skills related to the test. Most highly g-loaded tests involve some form of abstract reasoning. Therefore Spearman and others have regarded g as the perhaps genetically determined real essence of intelligence. This is still a common but not proven view. Other factor analyses of the data are with different results are possible. Some psychometricians regard g as a statistical artifact. The accepted best measure of g is Raven's Progressive Matrices which is a test of visual reasoning.

The War Years
During World War I a way was needed to evaluate and assign recruits. This led to the rapid development of several mental tests. The testing generated controversy and much public debate. Nonverbal or "performance" tests were developed for those who could not speak English or were suspected of malingering. After the war, positive publicity on army psychological testing helped to make psychology a respected field. Subsequently there was an increase in jobs and funding in psychology. Group intelligence tests were developed and became widely used in schools and industry.

L.L. Thurstone argued for a model of intelligence that included seven unrelated factors (verbal comprehension, word fluency, number facility, spatial visualization, associative memory, perceptual speed, reasoning, and induction). While not widely used, it influenced later theories.

David Wechsler produced the first version of his test in 1939. It gradually became more popular and overtook the Binet in the 1960s. It has been revised several times, as is common for IQ tests in order to incorporate new research. One explanation is that psychologists and educators wanted more information than the single score from the Binet. Wechsler's 10+ subtests provided this. Another is that the Binet focused on verbal abilities while the Wechsler also included non-verbal abilities. The Binet has also been revised several times and is now similar to the Wechsler in several aspects but the Wechsler continues to be the most popular test in the United States.

Cattell-Horn-Carroll theory
Raymond Cattell (1941) proposed two types of cognitive abilities in a revision of Spearman's concept of general intelligence. Fluid intelligence (Gf) was hypothesized as the ability to solve novel problems by using reasoning and crystallized intelligence (Gc) was hypothesized as a knowledge-based ability that was very dependent on education and experience. In addition, fluid intelligence was hypothesized to decline with age while crystallized intelligence was largely resistant. The theory was almost forgotten but revived by his student John L. Horn (1966) who later argued that Gf and Gc were only two among several factors and he eventually identified 9 or 10 broad abilities. The theory continued to be called Gf-Gc theory.

John B. Carroll (1993) after a comprehensive re-analysis of earlier data proposed the Three Stratum Theory, which is a hierarchical model with three levels. At the bottom is the first stratum which consists of narrow abilities that are highly specialized (e.g., induction, spelling ability). The second stratum consists of broad abilities. Carroll identified eight second-stratum abilities. Carroll accepted Spearman's concept of general intelligence, for the most part, as a representation of the uppermost third stratum.

More recently (1999), a merging of the Gf-Gc theory of Cattell and Horn with Carroll's Three-Stratum theory has led to the Cattell-Horn-Carroll theory. It has greatly influenced many of the current IQ tests.

Many of the broad, recent IQ tests have been greatly influenced by the Cattell-Horn-Carroll theory. It is argued to reflect much of what is known about intelligence from research. A hierarchy of factors is used. g is at the top. Under it there are 10 broad abilities that in turn are subdivided into 70 narrow abilities. The broad abilities are: Modern tests do not necessarily measure of all of these broad abilities. For example, Gq and Grw may be seen as measures of school achievement and not IQ. Gt may be difficult to measure without special equipment.
 * Fluid Intelligence (Gf): includes the broad ability to reason, form concepts, and solve problems using unfamiliar information or novel procedures.
 * Crystallized Intelligence (Gc): includes the breadth and depth of a person's acquired knowledge, the ability to communicate one's knowledge, and the ability to reason using previously learned experiences or procedures.
 * Quantitative Reasoning (Gq): the ability to comprehend quantitative concepts and relationships and to manipulate numerical symbols.
 * Reading & Writing Ability (Grw): includes basic reading and writing skills.
 * Short-Term Memory (Gsm): is the ability to apprehend and hold information in immediate awareness and then use it within a few seconds.
 * Long-Term Storage and Retrieval (Glr): is the ability to store information and fluently retrieve it later in the process of thinking.
 * Visual Processing (Gv): is the ability to perceive, analyze, synthesize, and think with visual patterns, including the ability to store and recall visual representations.
 * Auditory Processing (Ga): is the ability to analyze, synthesize, and discriminate auditory stimuli, including the ability to process and discriminate speech sounds that may be presented under distorted conditions.
 * Processing Speed (Gs): is the ability to perform automatic cognitive tasks, particularly when measured under pressure to maintain focused attention.
 * Decision/Reaction Time/Speed (Gt): reflect the immediacy with which an individual can react to stimuli or a task (typically measured in seconds or fractions of seconds; not to be confused with Gs, which typically is measured in intervals of 2–3 minutes). See Mental chronometry.

g was earlier often subdivided into only Gf and Gc which were thought to correspond to the Nonverbal or Performance subtests and Verbal subtests in earlier versions of the popular Wechsler IQ test. More recent research has shown the situation to be more complex.

Modern comprehensive IQ tests no longer give a single score. Although they still give an overall score, they now also give scores for many of these more restricted abilities, identifying particular strengths and weaknesses of an individual.

Modern theories
J.P. Guilford's Structure of Intellect (1967) model used three dimensions which when combined yielded a total of 120 types of intelligence. It was popular in the 1970s and early 1980s but faded due to both practical problems and theoretical criticisms.

Alexander Luria's earlier work on neuropsychological processes lead to the PASS theory (1997). It argued that only looking at one general factor was inadequate for researchers and clinicians who worked with learning disabilities, attention disorders, mental retardation, and interventions for such disabilities. The PASS model covers four kinds of processes. The (P)lanning processes involve decision making, problem solving, and performing activities and requires goal setting and self-monitoring. The (A)ttention/arousal process involves selectively attending to a particular stimulus, ignoring distractions, and maintaining vigilance. (S)imultaneous processing involves the integration of stimuli into a group and requires the observation of relationships. (S)uccessive processing involves the integration of stimuli into serial order. The planning and attention/arousal components comes from structures located in the frontal lobe, and the simultaneous and successive processes come from structures located in the posterior region of the cortex. It has influenced some recent IQ tests and been seen as a complement to the Cattell-Horn-Carroll theory described above.

Well-known modern IQ tests include Wechsler Adult Intelligence Scale, Wechsler Intelligence Scale for Children, Stanford-Binet, Woodcock-Johnson Tests of Cognitive Abilities, Kaufman Assessment Battery for Children, and Raven's Progressive Matrices.

Approximately 95% of the population have scores within two standard deviations (SD) of the mean. If one SD is 15 points, as is common in almost all modern tests, then 95% of the population are within a range of 70 to 130. Alternatively, two-thirds of the population have IQ scores within one SD of the mean, i.e. within the range 85-115.

IQ scales are ordinally scaled. While one standard deviation is 15 points, and two SDs are 30 points, and so on, this does not imply that cognitive ability is linearly related to IQ, such that IQ 50 means half the cognitive ability of IQ 100. In particular, IQ points are not percentage points.

The correlation between IQ test results and achievement test results is about 0.7.

Mental age vs. modern method
German psychologist William Stern proposed a method of scoring children's intelligence tests in 1902. He calculated what he called a Intelligenz-Quotient score, or IQ, as the quotient of the mental age (the age group which scored such a result on average) of the test-taker and the chronological age of the test-taker, multiplied by 100. Terman used this system for the first version of the Stanford-Binet Intelligence Scales. This method has several problems such as not working for adults.

Wechsler introduced a different procedure for his test that is now used by almost all IQ tests. When an IQ test is constructed, a standardization sample representative of the general population takes the test. The median result is defined to be equivalent to 100 IQ points. In almost all modern tests, a standard deviation of the results is defined to equivalent to 15 IQ points. When a subject takes an IQ test, the result is ranked compared to the results of normalization sample and the subject is given an IQ score equal to those with the same test result in the normalization sample.

The values of 100 and 15 were chosen in order to get somewhat similar scores as in the older type of test. Likely as a part of the rivalry between the Binet and the Wechsler, the Binet until 2003 chose to have 16 for one SD, causing considerable confusion. Today almost all tests use 15 for one SD. Modern scores are sometimes referred to as "deviation IQs," while older method age-specific scores are referred to as "ratio IQs."

Reliability and validity
Psychometricians generally regard IQ tests as having high statistical reliability. A high reliability implies that while test-takers can have varying scores on differing occasions when taking the same test and can vary in scores on different IQ tests taken at the same age, the scores generally agree. A test-taker's score on any one IQ test is surrounded by an error band that shows, to a specified degree of confidence, what the test-taker's true score is likely to be. For modern tests, the standard error of measurement is about 3 points, or in other words, the odds are about 2 out of 3 that a persons true IQ is in range from 3 points above to 3 points below the test IQ. Another description is that there is a 95% chance that the true IQ is in range from 4-5 points above to 4-5 points below the test IQ, depending on the test in question. Clinical psychologists generally regard them as having sufficient statistical validity for many clinical purposes.

Flynn effect
Since the early 20th century, raw scores on IQ tests have increased in most parts of the world. When a new version of an IQ test is normed, the standard scoring is set so that performance at the population median results in a score of IQ 100. The phenomenon of rising raw score performance means that if test-takers are scored by a constant standard scoring rule, IQ test scores have been rising at an average rate of around three IQ points per decade. This phenomenon was named the Flynn effect in the book The Bell Curve after James R. Flynn, the author who did the most to bring this phenomenon to the attention of psychologists.

Researchers have been exploring the issue of whether the Flynn effect is equally strong on performance of all kinds of IQ test items, whether the effect may have ended in some developed nations, whether or not there are social subgroup differences in the effect, and what possible causes of the effect might be. Flynn's observation has prompted much new research in psychology and "demolish some long-cherished beliefs, and raise a number of other interesting issues along the way."

IQ and age
IQ can change to some degree over the course of childhood. However, in one longitudinal study, the mean IQ scores of tests at ages 17 and 18 were correlated at r=.86 with the mean scores of tests at ages 5, 6 and 7 and at r=.96 with the mean scores of tests at ages 11, 12 and 13.

IQ scores for children are relative to children of a similar age. That is, a child of a certain age does not do as well on the tests as an older child or an adult with the same IQ. But relative to persons of a similar age, or other adults in the case of adults, they do equally well if the IQ scores are the same.

For decades, it has been reported in practitioners' handbooks and textbooks on IQ testing that IQ declines with age after the beginning of adulthood. However, later researchers pointed out that this phenomenon is related to the Flynn effect and is in part a cohort effect rather than a true aging effect.

There have been a variety of studies of IQ and aging since the norming of the first Wechsler Intelligence Scale drew attention to IQ differences in different age groups of adults. Current consensus is that fluid intelligence generally declines with age after early adulthood, while crystallized intelligence remains intact. Both cohort effects (the birth year of the test-takers) and practice effects (test-takers taking the same form of IQ test more than once) must be controlled for to gain accurate data. It is unclear whether any lifestyle intervention can preserve fluid intelligence into older ages.

The peak of capacity for both fluid intelligence and crystallized intelligence occurs at age 26. This is followed by a slow decline.

Genetics and environment
Environmental and genetic factors play a role in determining IQ. Their relative importance have been the subject of much research and debate.

Heritability
Heritability is defined as the proportion of variance in a trait which is attributable to genotype within a defined population in a specific environment. There are a number of points to consider when interpreting heritability. Heritability measures the proportion of variation in a trait that can be attributed to genes, and not the proportion of a trait caused by genes. The value of heritability can change if the impact of environment (or of genes) in the population is substantially altered. A high heritability of a trait does not mean that environmental effects such as learning are not involved. Since heritability increases during childhood and adolescence, one should be cautious drawing conclusions regarding the role of genetics and environment from studies where the participants are not followed until they are adults.

Studies have found the heritability of IQ in twins to be between 0.7 and 0.8 in adults and 0.45 in childhood in the Western world. It may seem reasonable to expect that genetic influences on traits like IQ should become less important as one gains experiences with age. However, the opposite occurs. Heritability measures in infancy are as low as 0.2, around 0.4 in middle childhood, and as high as 0.8 in adulthood. One proposed explanation is that people with different genes tend to seek out different environments that reinforce the effects of those genes. There is an ongoing debate about whether these heritability estimates are too high due to not adequately considering various factors, such as that the environment may be relatively more important in families with low socio-economic status or the effect of the maternal (fetal) environment.

Shared family environment
There are aspects of environments that family members have in common (for example, characteristics of the home). This shared family environment accounts for 0.25–0.35 of the variation in IQ in childhood. By late adolescence it is quite low (zero in some studies). There is a similar effect for several other psychological traits. These studies have not looked at the effects of extreme environments such as in abusive families.

Non-shared family environment and environment outside the family
Although parents treat their children differently, such differential treatment explains only a small amount of non-shared environmental influence. One suggestion is that children react differently to the same environment due to different genes. More likely influences may be the impact of peers and other experiences outside the family.

Individual genes
A number of individual genes have been reported to be associated with IQ. Examples include CHRM2, microcephalin, and ASPM. However, Deary and colleagues (2009) argued that there are still almost no replicated evidence. About 20,000 genes are thought to have an impact on the development and functionality of the brain.

Gene-environment interaction
Dickens and Flynn (2001) argued that the "heritability" figure includes both a direct effect of the genotype on IQ and also indirect effects where the genotype changes the environment, in turn affecting IQ. That is, those with a higher IQ tend to seek out stimulating environments that further increase IQ. The direct effect can initially have been very small but feedback loops can create large differences in IQ. In their model an environmental stimulus can have a very large effect on IQ, even in adults, but this effect also decays over time unless the stimulus continues (the model could be adapted to include possible factors, like nutrition in early childhood, that may cause permanent effects). The Flynn effect can be explained by a generally more stimulating environment for all people. The authors suggest that programs aiming to increase IQ would be most likely to produce long-term IQ gains if they taught children how to replicate outside the program the kinds of cognitively demanding experiences that produce IQ gains while they are in the program and motivate them to persist in that replication long after they have left the program.

Interventions
In general, educational interventions, as those described below, have shown short-term effects on IQ, but long-term follow-up is often missing. In the US for example some interventive programs such as the Head Start Program have not produced lasting gains in IQ scores, although the more intensive Abecedarian Project have.

A placebo controlled double-blind experiment found that vegetarians who took 5 grams of creatine per day for six weeks showed a significant improvement on two separate tests of fluid intelligence, Raven's Progressive Matrices, and the backward digit span test from the WAIS. The treatment group was able to repeat longer sequences of numbers from memory and had higher overall IQ scores than the control group. The researchers concluded that "supplementation with creatine significantly increased intelligence compared with placebo." A subsequent study found that creatine supplements improved cognitive ability in the elderly. A study on young adults (0.03 g/kg/day for six weeks, e.g., 2 g/day for 150-pound individual) failed, however, to find any improvements.

Musical training in childhood has also been found to correlate with higher than average IQ.

Recent studies have shown that training in using one's working memory may increase IQ. A study on young adults published in April 2008 by a team from the Universities of Michigan and Bern supports the possibility of the transfer of fluid intelligence from specifically designed working memory training. Further research will be needed to determine nature, extent and duration of the proposed transfer. Among other questions, it remains to be seen whether the results extend to other kinds of fluid intelligence tests than the matrix test used in the study, and if so, whether, after training, fluid intelligence measures retain their correlation with educational and occupational achievement or if the value of fluid intelligence for predicting performance on other tasks changes. It is also unclear whether the training is durable of extended periods of time.

IQ and brain anatomy
Several neurophysiological factors have been correlated with intelligence in humans, including the ratio of brain weight to body weight and the size, shape and activity level of different parts of the brain. Specific features that may affect Intelligence Quotient (IQ) include the size and shape of the frontal lobes, the amount of blood and chemical activity in the frontal lobes, the total amount of gray matter in the brain, the overall thickness of the cortex and the glucose metabolic rate.

Health and IQ
Health is important in understanding differences in IQ test scores and other measures of cognitive ability. Several factors can lead to significant cognitive impairment, particularly if they occur during pregnancy and childhood when the brain is growing and the blood-brain barrier is less effective. Such impairment may sometimes be permanent, sometimes be partially or wholly compensated for by later growth.

Developed nations have implemented several health policies regarding nutrients and toxins known to influence cognitive function. These include laws requiring fortification of certain food products and laws establishing safe levels of pollutants (e.g. lead, mercury, and organochlorides). Improvements in nutrition, and in public policy in general, have been implicated in worldwide IQ increases.

Cognitive epidemiology is a field of research that examines the associations between intelligence test scores and health. Researchers in the field argue that intelligence measured at an early age is an important predictor of later health and mortality differences.

Social outcomes
Outside of academic research and medicine, IQ testing is often done due to its ability to predict future job performance, social pathologies, or academic achievement. Academic research has also examined these associations, as well as the effect of IQ on other social outcomes, such as income and wealth.

Many of the arguments and criticisms assume that explained variance can be calculated as the square of the correlation coefficient. This way of calculating explained variance has been criticized as inappropriate for most social scientific work. Also, as for the heritability figure, the explained variance only refers to the proportion of variation in an outcome that is explained by a factor, and not the proportion of an outcome that is explained by a factor.

Other tests
One study found a correlation of 0.82 between g (general intelligence factor) and SAT scores; another has found correlation of 0.81 between g and GCSE scores.

Correlations between IQ scores (general cognitive ability) and achievement test scores are reported to be 0.81 by Deary and colleagues, with the explained variance ranging "from 58.6% in Mathematics and 48% in English to 18.1% in Art and Design".

School performance
The American Psychological Association's report "Intelligence: Knowns and Unknowns" states that wherever it has been studied, children with high scores on tests of intelligence tend to learn more of what is taught in school than their lower-scoring peers. The correlation between IQ scores and grades is about .50. This means that the explained variance is 25%. Achieving good grades depends on many factors other than IQ, such as "persistence, interest in school, and willingness to study" (p. 81).

It has been found that the IQ correlation with school performance depends on the IQ measurement used. For undergraduate students, the Verbal IQ as measured by WAIS-R has been found to correlate significantly (0.53) with the GPA of the last 60 hours. In contrast, Performance IQ correlation with the same GPA was only 0.22 in the same study.

Job performance
According to Frank Schmidt and John Hunter, "for hiring employees without previous experience in the job the most valid predictor of future performance is general mental ability." The validity of IQ as a predictor of job performance is above zero for all work studied to date, but varies with the type of job and across different studies, ranging from 0.2 to 0.6. The correlations were higher when the unreliability of measurement methods were controlled for. While IQ is more strongly correlated with reasoning and less so with motor function, IQ-test scores predict performance ratings in all occupations. That said, for highly qualified activities (research, management) low IQ scores are more likely to be a barrier to adequate performance, whereas for minimally-skilled activities, athletic strength (manual strength, speed, stamina, and coordination) are more likely to influence performance. It is largely mediated through the quicker acquisition of job-relevant knowledge that IQ predicts job performance.

In establishing a causal direction to the link between IQ and work performance, longitudinal studies by Watkins and others suggest that IQ exerts a causal influence on future academic achievement, whereas academic achievement does not substantially influence future IQ scores. Treena Eileen Rohde and Lee Anne Thompson write that general cognitive ability but not specific ability scores predict academic achievement, with the exception that processing speed and spatial ability predict performance on the SAT math beyond the effect of general cognitive ability.

The US military has minimum enlistment standards at about the IQ 85 level. There have been two experiments with lowering this to 80 but in both cases these men could not master soldiering well enough to justify their costs

The American Psychological Association's report "Intelligence: Knowns and Unknowns" states that since the explained variance is 29%, other individual characteristics such as interpersonal skills, aspects of personality etc. are probably of equal or greater importance, but at this point there are no equally reliable instruments to measure them.

Income
Some researchers claim that "in economic terms it appears that the IQ score measures something with decreasing marginal value. It is important to have enough of it, but having lots and lots does not buy you that much."

Other studies show that ability and performance for jobs are linearly related, such that at all IQ levels, an increase in IQ translates into a concomitant increase in performance. Charles Murray, coauthor of The Bell Curve, found that IQ has a substantial effect on income independently of family background.

Taking the above two principles together, very high IQ produces very high job performance, but no greater income than slightly high IQ. Studies also show that high IQ is related to higher net worth.

The American Psychological Association's 1995 report Intelligence: Knowns and Unknowns stated that IQ scores accounted for (explained variance) about quarter of the social status variance and one-sixth of the income variance. Statistical controls for parental SES eliminate about a quarter of this predictive power. Psychometric intelligence appears as only one of a great many factors that influence social outcomes.

Some studies claim that IQ only accounts for (explained variance) a sixth of the variation in income because many studies are based on young adults (many of whom have not yet completed their education). On pg 568 of The g Factor, Arthur Jensen claims that although the correlation between IQ and income averages a moderate 0.4 (one sixth or 16% of the variance), the relationship increases with age, and peaks at middle age when people have reached their maximum career potential. In the book, A Question of Intelligence, Daniel Seligman cites an IQ income correlation of 0.5 (25% of the variance).

A 2002 study further examined the impact of non-IQ factors on income and concluded that an individual's location, inherited wealth, race, and schooling are more important as factors in determining income than IQ.

IQ and crime
The American Psychological Association's 1995 report Intelligence: Knowns and Unknowns stated that the correlation between IQ and crime was -0.2. It was -0.19 between IQ scores and number of juvenile offenses in a large Danish sample; with social class controlled, the correlation dropped to -0.17. A correlation of 0.20 means that the explained variance is less than 4%. It is important to realize that the causal links between psychometric ability and social outcomes may be indirect. Children with poor scholastic performance may feel alienated. Consequently, they may be more likely to engage in delinquent behavior, compared to other children who do well.

In his book The g Factor (1998), Arthur Jensen cited data which showed that, regardless of race, people with IQs between 70 and 90 have higher crime rates than people with IQs below or above this range, with the peak range being between 80 and 90.

The 2009 Handbook of Crime Correlates stated that reviews have found that around eight IQ points, or 0.5 SD, separate criminals from the general population, especially for persistent serious offenders. It has been suggested that this simply reflects that "only dumb ones get caught" but there is similarly a negative relation between IQ and self-reported offending. That children with conduct disorder have lower IQ than their peers "strongly argue" against the theory.

A study of the relationship between US county-level IQ and US county-level crime rates found that higher average IQs were associated with lower levels of property crime, burglary, larceny rate, motor vehicle theft, violent crime, robbery, and aggravated assault. These results were not "confounded by a measure of concentrated disadvantage that captures the effects of race, poverty, and other social disadvantages of the county."

Other correlations with IQ
In addition, IQ and its correlation to health, violent crime, gross state product, and government effectiveness are the subject of a 2006 paper in the publication Intelligence. The paper breaks down IQ averages by U.S. states using the federal government's National Assessment of Educational Progress math and reading test scores as a source.

The American Psychological Association's 1995 report Intelligence: Knowns and Unknowns stated that the correlations for most "negative outcome" variables are typically smaller than 0.20, which means that the explained variance is less than 4%.

Tambs et al. found that occupational status, educational attainment, and IQ are individually heritable; and further found that "genetic variance influencing educational attainment ... contributed approximately one-fourth of the genetic variance for occupational status and nearly half the genetic variance for IQ." In a sample of U.S. siblings, Rowe et al. report that the inequality in education and income was predominantly due to genes, with shared environmental factors playing a subordinate role.

There are also other correlations such as those between religiosity and intelligence and fertility and intelligence.

Real-life accomplishments
Average adult combined IQs associated with real-life accomplishments by various tests:
 * Neurosurgeons, research scientists, university professors 135+
 * MDs or PhDs 125 (WAIS-R, 1987)
 * College graduates 112 (KAIT, 2000; K-BIT, 1992), 115 (WAIS-R)
 * 1–3 years of college 104 (KAIT, K-BIT), 105-110 (WAIS-R)
 * Clerical and sales workers 100-105
 * High school graduates, skilled workers (e.g., electricians, cabinetmakers) 100 (KAIT, WAIS-R), 97 (K-BIT)
 * 1–3 years of high school (completed 9–11 years of school) 94 (KAIT), 90 (K-BIT), 95 (WAIS-R)
 * Semi-skilled workers (e.g., truck drivers, factory workers) 90-95
 * Elementary school graduates (completed eighth grade) 90
 * Elementary school dropouts (completed 0–7 years of school) 80-85
 * Have 50/50 chance of reaching high school 75

Average IQ of various occupational groups:
 * Professional and technical 112
 * Managers and administrators 104
 * Clerical workers; sales workers; skilled workers, craftsmen, and foremen 101
 * Semi-skilled workers (operatives, service workers, including private household) 92
 * Unskilled workers 87

Type of work that can be accomplished:
 * Adults can harvest vegetables, repair furniture 60
 * Adults can do domestic work, simple carpentry 50
 * Adults can mow lawns, do simple laundry 40

There is considerable variation within and overlap between these categories. People with high IQs are found at all levels of education and occupational categories. The biggest difference occurs for low IQs with only an occasional college graduate or professional scoring below 90.

Group differences
Among the most controversial issues related to the study of intelligence is the observation that intelligence measures such as IQ scores vary between ethnic and racial groups and sexes. While there is little scholarly debate about the existence of some of these differences, their causes remain highly controversial both within academia and in the public sphere.

Sex
Most IQ tests are constructed so that there are no overall score differences between females and males. Because environmental factors affect brain activity and behavior, where differences are found, it can be difficult for researchers to assess whether or not the differences are innate. Areas where differences have been found include verbal and mathematical ability.

Race
The 1996 Task Force investigation on Intelligence sponsored by the American Psychological Association concluded that there are significant variations in IQ across races. The problem of determining the causes underlying this variation relates to the question of the contributions of "nature and nurture" to IQ. Psychologists such as Alan S. Kaufman and Nathan Brody and statisticians such as Bernie Devlin argue that there are insufficient data to conclude that this is because of genetic influences. One of the most notable researchers arguing for a strong genetic influence on these average score differences is Arthur Jensen. In contrast, other researchers such as Richard Nisbett argue that environmental factors can explain all of the average group differences.

Public policy
In the United States, certain public policies and laws regarding military service, education, public benefits, capital punishment, and employment incorporate an individual's IQ into their decisions. However, in the case of Griggs v. Duke Power Co. in 1971, for the purpose of minimizing employment practices that disparately impacted racial minorities, the U.S. Supreme Court banned the use of IQ tests in employment, except in very rare cases. Internationally, certain public policies, such as improving nutrition and prohibiting neurotoxins, have as one of their goals raising, or preventing a decline in, intelligence.

A diagnosis of mental retardation is in part based on the results of IQ testing. Borderline intellectual functioning is a categorization where a person has below average cognitive ability (an IQ of 71–85), but the deficit is not as severe as mental retardation (70 or below).

In the United Kingdom, the eleven plus exam which incorporated an intelligence test has been used from 1945 to decide, at eleven years old, which type of school a child should go to. They have been much less used since the widespread introduction of comprehensive schools.

Relation between IQ and intelligence
IQ is the most researched approach to intelligence and by far the most widely used in practical setting. However, although IQ attempts to measure some notion of intelligence, it may fail to act as an accurate measure of "intelligence" in its broadest sense. IQ tests only examine particular areas embodied by the broadest notion of "intelligence", failing to account for certain areas which are also associated with "intelligence" such as creativity or emotional intelligence.

There are critics who do not dispute the stability of IQ test scores or the fact that they predict certain forms of achievement rather effectively. They do argue, however, that to base a concept of intelligence on IQ test scores alone is to ignore many important aspects of mental ability.

Criticism of g
Some scientists dispute IQ entirely. In The Mismeasure of Man (1996), paleontologist Stephen Jay Gould criticized IQ tests and argued that that they were used for scientific racism. He argued that g was a mathematical artifact and criticized:

"...the abstraction of intelligence as a single entity, its location within the brain, its quantification as one number for each individual, and the use of these numbers to rank people in a single series of worthiness, invariably to find that oppressed and disadvantaged groups—races, classes, or sexes—are innately inferior and deserve their status.(pp. 24–25)"

Psychologist Peter Schönemann was also a persistent critic of IQ, calling it "the IQ myth". He argued that g is a flawed theory and that the high heritability estimates of IQ are based on false assumptions.

Psychologist Arthur Jensen has rejected the criticism by Gould and also argued that even if g was replaced by a model with several intelligences this would change the situation less than expected. All tests of cognitive ability would continue to be highly correlated with one another and there would still be a black-white gap on cognitive tests.

Test bias
The American Psychological Association's report Intelligence: Knowns and Unknowns stated that in the United States IQ tests as predictors of social achievement are not biased against African Americans since they predict future performance, such as school achievement, similarly to the way they predict future performance for Whites.

However, IQ tests may well be biased when used in other situations. A 2005 study stated that "differential validity in prediction suggests that the WAIS-R test may contain cultural influences that reduce the validity of the WAIS-R as a measure of cognitive ability for Mexican American students," indicating a weaker positive correlation relative to sampled white students. Other recent studies have questioned the culture-fairness of IQ tests when used in South Africa. Standard intelligence tests, such as the Stanford-Binet, are often inappropriate for children with autism; the alternative of using developmental or adaptive skills measures are relatively poor measures of intelligence in autistic children, and may have resulted in incorrect claims that a majority of children with autism are mentally retarded.

Outdated methodology
A 2006 article stated that contemporary psychologic research often did not reflect substantial recent developments in psychometrics and "bears an uncanny resemblance to the psychometric state of the art as it existed in the 1950s." However, it also states that an "increasing number of psychometrically informed research papers that have been appearing in the past decade."

"Intelligence: Knowns and Unknowns"
In response to the controversy surrounding The Bell Curve, the American Psychological Association's Board of Scientific Affairs established a task force in 1995 to write a report on the state of intelligence research which could be used by all sides as a basis for discussion, "Intelligence: Knowns and Unknowns". The full text of the report is available through several websites.

In this paper the representatives of the association regret that IQ-related works are frequently written with a view to their political consequences: "research findings were often assessed not so much on their merits or their scientific standing as on their supposed political implications".

The task force concluded that IQ scores do have high predictive validity for individual differences in school achievement. They confirm the predictive validity of IQ for adult occupational status, even when variables such as education and family background have been statistically controlled. They stated that individual differences in intelligence are substantially influenced by both genetics and environment.

The report stated that a number of biological factors, including malnutrition, exposure to toxic substances, and various prenatal and perinatal stressors, result in lowered psychometric intelligence under at least some conditions. The task force agrees that large differences do exist between the average IQ scores of blacks and whites. "The cause of that differential is not known; it is apparently not due to any simple form of bias in the content or administration of the tests themselves. The Flynn effect shows that environmental factors can produce differences of at least this magnitude, but that effect is mysterious in its own right. Several culturally based explanations of the Black/ White IQ differential have been proposed; some are plausible, but so far none has been conclusively supported. There is even less empirical support for a genetic interpretation. In short, no adequate explanation of the differential between the IQ means of Blacks and Whites is presently available."

The APA journal that published the statement, American Psychologist, subsequently published eleven critical responses in January 1997, several of them arguing that the report failed to examine adequately the evidence for partly genetic explanations.

High IQ societies
There are social organizations, some international, which limit membership to people who have scores as high as or higher than the 98th percentile on some IQ test or equivalent. Mensa International is perhaps the most well known of these. There are other groups requiring a score above the 98th percentile.

Reference charts
IQ reference charts are tables suggested by test publishers to divide intelligence ranges in various categories.