# Intelligence quotient IQ tests are constructed in such a way that the results are approximately normally distributed for a sufficiently large sample of the population . Areas with different colors each correspond to a standard deviation .

The intelligence quotient ( IQ ) is a parameter determined by an intelligence test to assess intellectual performance in general (general intelligence ) or within a certain range (e.g. intelligence factors) in comparison to a reference group. It always refers to the respective test, because there is no scientifically recognized, unambiguous definition of intelligence.

The “population representative” reference group can be age or school class specific (especially for children and adolescents) or specific for educational levels (for example high school students or occupational groups) (see standardization ). In today's tests that use an IQ norm, based on the distribution of the test results of a sufficiently large sample, the norm value is usually determined by normal rank transformation assuming a normal distribution of intelligence and converted into a scale with the mean value 100 and the standard deviation 15. According to a normal distribution, around 68% of the people in this reference group have an IQ in the so-called middle range (where the greatest probability measure of the density function is) between 85 and 115.

Differences result from the representativeness of the standardization sample for this reference group (size of the sample, representativeness when recruiting people). When interpreting the IQ, the type of measurement method (e.g. type of intelligence test ) and the underlying intelligence concept as well as the reference group used for normalization must be taken into account, which influence the stability and generalizability of the estimation of a person's intelligence. The standards must also be checked with regard to temporal stability and redetermined if they are out of date.

In addition to other specialist areas, cognitive science also deals with the measurement of intelligence.

## Calculations

### Historical

Alfred Binet , who developed the first useful intelligence test with the Binet-Simon test in 1905, stated mental performance as the age of intelligence . The test consisted of tasks with increasing difficulty, which should be able to be solved as clearly as possible for the respective age groups. Example: An average eight-year-old should be able to solve all tasks in his age group (and below), but not the tasks of the nine-year-olds. If a child did not manage all of the tasks in its age group, it had a lower one, and if it also managed tasks in the older age group, it had a higher “intelligence age”.

William Stern put this intelligence age in relation to age and thus invented the intelligence quotient in 1912 at the University of Breslau .

Lewis M. Terman from Stanford University developed the Simon-and-Binet quotient , which Goddard translated from French into English. To remove the decimal places, he multiplied the intelligence age-age quotient by 100.

${\ displaystyle {IQ} = {\ frac {\ text {Intelligent Age}} {\ text {Age}}} \ times 100}$ ### Modern

Since the age of intelligence increases more slowly than age, the IQ according to Stern's formula decreases steadily. Terman also recognized this problem as it continued to develop. To counter this problem, he standardized the test for different age groups. He adjusted the distribution to a normal distribution for each age . In the Stanford-Binet test developed in 1937, the standard deviation varies between 15 and 16 IQ points depending on age ( cf. Valencia and Suzuki, 2000, p. 5 ff.).

The IQ calculation, originally developed only for children, specifically for school readiness tests, was later extended to adults by David Wechsler by applying population- related scaling with a mean value of 100. For today's deviation IQ scale, a mean of 100 and a standard deviation (SD) of 15 apply. B. Application in the Hamburg-Wechsler intelligence test series. Since the IQ is overestimated in public as a “label” by people, for example with regard to stability and universality, some tests deliberately use different standard scales.

### Conversions

You can also include other standard scales set, such as the percentile rank (percentile). Using the reference to the normal distribution, values ​​from other scalings can be converted into an IQ scale with a mean value of 100 without any loss of information:

${\ displaystyle {IQ} = 100 + 15 \ times {\ frac {(x- \ mu)} {\ sigma}}}$ • ${\ displaystyle x}$ determined scale value in the test used
• ${\ displaystyle \ mu}$ Average of the scale used
• ${\ displaystyle \ sigma}$ Standard deviation of the scale used

example

The IST-2000 uses what is known as the Standard Value Scale (SW), which has a mean of 100 and a standard deviation of 10. If a person has achieved a standard value of 110, this can be converted into an IQ standard value as follows:
Inserted:
${\ displaystyle {IQ} = 100 + 15 \ times {\ frac {(110-100)} {10}} = 115}$ Since 110 on the standard value scale is exactly one standard deviation above the mean, the same must also apply to the AW-IQ value. And, as calculated, this is also true with a value of 115. An AW-IQ value of 85, which is exactly one standard deviation below the mean, corresponds to an actual value of 90 ( see also linear transformation ).

## Reliability and measurement errors

When interpreting results, the measurement error and the probability of error to be accepted must be taken into account (cf. type 1 error ). The probability of error determines the length of the confidence interval . The latter is influenced by the necessary certainty of the diagnostic decision to be made.

In 2014, the US Supreme Court had to decide up to which IQ a perpetrator was to be considered insane and therefore not to be executed in the event of a death sentence. In that process, the American Psychological Association and the American Association on Intellectual and Developmental Disabilities argued that IQ tests have a margin of error of 10 points up and down.

The intelligence tests have to be regularly re-standardized (or the validity of the standards checked) in order to keep the average value at 100. Until the 1990s, the IQ tests in the industrialized countries had shown a steadily increasing average. There is no consensus on the cause of this “ Flynn effect ”, such as a more evenly developed schooling or the informative influence of the mass media. The numerical values ​​cannot be compared without knowledge of the underlying test and its standardization. Eight years, which is suggested in DIN 33430 for the field of suitability diagnostics, apply as a guideline for the inspection .

## literature

• Jürgen Guthke : Can intelligence be measured? Introduction to problems of psychological intelligence research and intelligence diagnostics . 2nd Edition. German Science Publishing House, Berlin 1980.
• Walter Gutjahr: The measurement of psychological properties . Kiepenheuer and Witsch, Cologne 1977, ISBN 3-462-01116-2 .
• Siegfried Lehrl : RAM instead of IQ . Vless, Ebersberg 1997, ISBN 3-88562-079-0 .
• Nicholas John MacKintosh: IQ and Human Intelligence . Oxford University Press, Oxford 1998, ISBN 0-19-852368-8 .