Intelligence quotients and mathematics

Summary: Intelligence tests are created and analyzed using mathematics.

The term “intelligence” is broadly synonymous with the term “cognitive ability.” Intelligence tests are tests designed to measure cognitive abilities. According to Ian Deary and David Batty, cognitive abilities are mental abilities “that are not principally sensory, emotional or conative (related to the will).” Standardized intelligence tests produce a score called the “Intelligence Quotient” (IQ). IQ tests are usually copyrighted, and to prevent people from practicing for them, they must be administered in supervised conditions. Many tests that claim to measure IQ have appeared on the Internet but may not have been validated by professional psychologists. Intelligence, or cognitive ability, has been defined in different ways but broadly refers to people’s ability to process complexity “on the spot.”

Since psychologists such as Alfred Binet (originator of the test that later evolved into the Stanford–Binet) and David Wechsler (creator of the Wechsler Adult Intelligence Scale and Wechsler Intelligence Scale for Children) began measuring cognitive abilities over 100 years ago, nearly all measures of cognition have been shown to correlate. This fact is interpreted as evidence for a general factor, called g, representing general intelligence. At the beginning of the twenty-first century, no test of cognitive ability has been created that does not correlate with other cognitive ability tests. In practice, this means that people who are good at processing complexity in one area tend to be good at processing complexity in another. A person’s IQ score is a numerical representation of their level of g.

Most IQ tests are designed to have a mean of 100 and scores are normally distributed. However, the standard deviation varies across different tests. The interpretation of the standard deviation is that it represented the average distance from the mean, in either direction. To understand and interpret a person’s IQ score, it is necessary to know the standard deviation of the test they took. Common standard deviations are 15 or 16, and the range of IQ scores is generally between about 55 and 145 for a test with a standard deviation of 15. Further, about two-thirds of individuals will have scores within one standard deviation of the mean and about 95 percent will have scores within two standard deviations of the mean. For this reason, IQ scores are sometimes evaluated using percentile scores, which divide the normal distribution into 100 parts so that 1% of the scores are in each part. For example, admission to the high-IQ society Mensa requires a person to score in the 98th percentile or higher on several different validated IQ tests. This requirement means about one in 50 people would be eligible to join.

Percentile IQ scores can be useful, but they can be misinterpreted since the distance between each percentile is not equal. In contrast, standard deviations are the same distance apart, sometimes making it more sensible to compare individuals in terms of average distance from the mean. Also, IQ tests are imperfect measures of intelligence because they generally do not produce the exact same score for the same person, even if the test is taken more than once. This inaccuracy is quantified by the standard error of measurement and represents how much variability an individual person’s scores would have if they took the test many times. For example, if a person scored 100 on an IQ test that had a standard error of 2, the person’s true IQ score would often be interpreted as being somewhere between 96 and 104. Some researchers and others have suggested that the average of three IQ tests provides a better indication of a person’s true IQ score than a single test.

There are three features of general intelligence that are important because they negate arguments that IQ scores have no meaning: their stability, their heritability, and their correlation with external phenomena. First, IQ scores are remarkably stable across the life course from childhood to old age. Data to demonstrate this are exceptionally rare, but one exception can be found in Scotland. During one day in 1932, every 11-year-old in the country took an IQ test. They were retested 66 years later, and the scores were found to correlate highly with childhood IQ score (0.76), providing evidence of stability of IQ scores over time. Second, IQ scores are highly heritable. The heritability of individual differences has been estimated as between 30% and 80%, illustrating that genetics contributes strongly to IQ scores. However, no single gene or set of genes has been identified. This suggests that the genetic contribution to intelligence is multifactorial, as with other observable characteristics (phenotypes), such as height. There are no sex differences in IQ, although the distribution of males’ scores is slightly wider at both ends of the distribution. Third, IQ scores correlate with variables that can be considered external, or outside the IQ test itself. IQ correlates with indicators of socioeconomic status (SES)—a indication of factors like educational attainment, income, and occupational social class—and with many biological variables, including brain size, height, sperm quality, and mortality. The causes of these correlations are disputed.

Content of IQ Tests

The content of IQ tests differs, depending on the specific cognitive abilities they are intended to measure. Some tests have been criticized as being culturally biased because they ask questions that require culturally specific knowledge. Tests that do not evaluate “general knowledge” are considered more “culture fair.” For example, Raven’s Matrices is a test that contains no written information, requiring abstract reasoning skills. This test contains no culturally specific information, so that it is not possible to learn how to take the test. Similarly, tests of reaction time are considered indicators of g, because they reflect speed of information processing. These do not assess culturally specific information or knowledge. Clifford Pickover imagined how aliens might test human intelligence and designed related mathematics and logic puzzles. Other intelligence researchers argue that knowledge is a reliable indicator of g and should therefore be included in IQ tests. IQ tests also differ in the extent to which it is necessary to complete every question. Traditional IQ tests are designed using classical test theory. In these tests, the IQ score is more reliable for people with an average level of IQ. Since people with high IQs find many questions easy and people with low IQs find many questions difficult, fewer relevant questions are answered by people at either end of the IQ distribution. More recently, computerized adaptive tests have been developed and informed by item response theory, which addresses these problems. These tests can alter the difficulty of test items, so that people with high IQs receive a larger number of difficult items. Reliability is improved and testing length can be reduced because respondents do not have to answer every question.

Age and Intelligence

Although IQ scores are relatively stable, cognitive decline typically occurs with increasing age. This fact is important because cognitive decline may indicate mild cognitive impairment and risk of dementia. When considered over time, specific kinds of cognitive abilities appear to deteriorate at different rates. Fluid intelligence, referring to processing speed (particularly of new information), declines from age 26 onward. In contrast, crystallized intelligence, referring to speed of recall of existing knowledge (for example, vocabulary and general knowledge) is relatively stable.

For this reason, standardized tests of word recognition, such as the National Adult Reading Test (NART), are useful at estimating premorbid IQ in patients suspected of having dementia. A discrepancy between IQ as estimated by the NART and IQ estimated from another test could indicate that cognitive decline has occurred. Cognitive decline can result in mild cognitive impairment and dementia or Alzheimer’s disease, which have high mortality, morbidity, and treatment and care costs.

Research into the prevention of cognitive decline is ongoing, but several risk factors have emerged consistently, such as cigarette smoking and physical inactivity. Consumption of fish oils, either from oily fish or fish oil supplements, may help prevent cognitive decline. Prior IQ is a strong protective factor, such that a higher initial IQ appears to protect against cognitive decline in later life. Claims that IQ can be changed are controversial. Although brain plasticity is known to be greater than once thought—and there is evidence that children exposed to cognitive stimulation enjoy increases in IQ—it is not clear how stable these gains are. Furthermore, attempts to increase IQ in adults have not been successful.

Lower IQ scores are associated with earlier mortality and higher morbidity. This association provides further evidence for the validity of IQ tests. It is noteworthy that the relationship between IQ and mortality often remains after adjusting for indicators of socioeconomic status (SES), such as income, educational attainment, and occupational social class. Given that IQ is largely stable after childhood, this relationship is unlikely to be explained by societal factors. Evidence suggests that IQ contributes strongly to health literacy, which, according to the World Health Organization, refers to “the cognitive and social skills which determine the motivation and ability of individuals to gain access to, understand, and use information in ways which promote and maintain good health.” People with inadequate health literacy skills tend to have unhealthier lifestyles, adhere less well to medical regimens, and do not understand written health information or the need for regular screening for diseases.

Access to healthcare does not solely explain the IQ-health relationship because it can also be found in countries that have free healthcare, such as the United Kingdom, which has the National Health Service (NHS). Managing chronic diseases, such as diabetes, involves repeating many complex tasks, such as monitoring blood sugar and planning activities around meals. Without supervision and support, the risk of making dangerous mistakes could accumulate over time. Many areas of life involve repeating a set of unpredictable, complex tasks, which can damage health in the long term. The field of cognitive epidemiology studies why IQ is linked to worse health outcomes and the role that literacy plays in this relationship.

Bibliography

Deary, Ian. Intelligence: A Very Short Introduction. Oxford, England: Oxford University Press, 2001.

Deary, Ian, Lars Penke, and Wendy Johnson. “The Neuroscience of Human Intelligence Differences.” Nature Reviews Neuroscience 11, no. 3 (2010).

Gottfredson, Linda. “Intelligence: Is It the Epidemiologists’ Elusive ‘Fundamental Cause’ of Social Class Inequalities in Health?” Journal of Personality and Social Psychology 86, no. 1 (2004).

Gottfredson, Linda, and Ian Deary. “Intelligence Predicts Health and Longevity, But Why?” Current Directions in Psychological Science 13, no. 1 (2004).