The topic intelligence has inspired any different beliefs, myths and theories, yet still to date, there is no universal definition of intelligence. Here, you will read about how the abstract topic of intelligence can be made concrete and measurable, about which models of intelligence were developed and which tests are used by medical practitioners.

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Intelligence: What is it?

To this day, there is still no standardized scientific definition for the term intelligence. W. Stern (1911), a pioneer in the field of intelligence, defines intelligence as the “general capacity of an individual consciously to adjust his thinking to new requirements”. Intelligence is a hypothetical construct which can only be observed in behavior. Read here about methodological basics.

The term intelligence comprises verbal and mathematical abilities as well as logical reasoning.

Note: Creativity and emotional intelligence are not included in the term intelligence.

Cognitive flexibility is comprised of two pillars:

  • Acquiring knowledge
  • Adaptation to changing circumstances

Intelligence Quotient

The classical IQ by Binet and Stern

Alfred Binet

Image: “Alfredo Benet Junior (July 11, 1857 – October 18, 1911)”. License: Public Domain

Binet was one of the first trying to make intelligence measurable. At the beginning of the 20th century he was commissioned to develop an intelligence test, in order to measure the intellectual capacity of school children. Goal of the test was to identify children with learning disabilities in order to provide them with special individualized help.

The level of difficulty of the test was scaled in ascending order and supposed to assess the intellectual age of a child with tasks usually passed by six-year-olds, seven-year-olds, and so on.

Based on Binet’s work, Stern developed the classic intelligence quotient (IQ), which is, however, no applicable to adults.

IQ = (mental age / chronological age) x 100

Example: John is 9 years old and solves all the tasks for 11-year-old children → (11/9) x 100 = 122.2

The deviation IQ by Wechsler

David Wechsler later developed as an alternative the deviation intelligence quotient, which is the most common type of intelligence measurement still today. The subject’s score on the intelligence test is compared to the average IQ of people of the same age (the average is standardized to 100 points).

The quotient reflects the subject’s relative position within the selected reference group (e.g. high school students, children in special schools of the same age). Scores obtained from different reference groups are not directly comparable. A similarity between the deviation IQ and the classic IQ  is that both compare the test performance with the respective age group.

The 4 Most Important Models of Intelligence

Important terms on models of intelligence

  • Factor analysis: In factor analysis, the correlation of the individual tasks of an intelligence test is calculated. Tasks with closely related topics represent their content on a higher level. Example: Tasks that demand spatial sense correlate among each other to such a degree that they can be summarized as the spatial factor.
  • Extraction: Possiblities of generating factors

Two-factor theory by Spearman (1904): the g factor

Spearman observed that subjects who were able to easily solve intelligence tasks (calculating) also scored high on other tasks (picture arrangements). From this, he concluded that there must be an inherent cognitive ability.

This intelligence is active in any performance of a task, independent of the type of task. Spearman called this basic ability the general factor of intelligence, the g factor. In hierarchical terms, this g factor is placed above the s factors.

For specific intelligence performances, s factors are necessary. Spearman argued that these s factors do not correlate among each other, meaning that an individual does not necessarily have to perform well or badly in multiple specific areas.

  • g factor determines: processing speed, mental capacity or intellectual performance (“genius” or “simple character”?)
  • s factors determine: spatial, numerical, verbal, mechanical abilities for specific areas



Multiple-factor theory of intelligence by Thurstone (1938)

Thurstone opposed Spearman’s idea of a superordinate general intelligence factor. Instead, he developed a multiple-factor theory of intelligence which established seven primary factors. These primary factors are all on the same level.

Thurstone’s 7 Primary Mental Abilities (PMA):

  • Number Facility
  • Verbal Comprehension
  • Word Fluency
  • Spatial Visualization
  • Associative Memory
  • Reasoning
  • Perceptual Speed

Berlin model of intelligence structure (BIS) by Jäger (1984)

In German-speaking countries, intelligence research was strongly influenced by Jäger’s descriptive model which can be divided into two modalities: operational abilities and content-related abilities. Like Spearman, he assumes a superior general factor g. The Berlin Model of Intelligence Structure (BIS) is derived directly from Jäger’s model.

g factor
4 Operational abilities 3 Content-related abilities
Memory: actively memorizing and short-term or medium-term recall or reproduction Verbal Thinking: degree of acquirement and availability of verbal material
Creativity: fluid, flexible, inventive production of ideas Figural Thinking: figural, pictographic
Processing Capacity: easiness of processing complex information and concentration Numerical Thinking: degree of acquirement and availability of numerical material
Processing Speed: speed of operation, speed at which information is processed

Model of fluid and crystallized intelligence by Cattell (1971)

Fluid intelligence is the native ability to handle new situations and to solve problems without utilizing previously acquired knowledge. Fluid intelligence is independent of culture and develops during childhood.

Crystallized intelligence describes the acquired knowledge. This knowledge is culture-specific with respect to knowledge contents and possible experiences. Crystallized intelligence has its peak during adolescence and usually remains constant even in old age.

Note: Crystallized intelligence is retained in old age; fluid intelligence continuously decreases from adolescence onwards.

Changes in Intelligence

The proportion of older people in the population continually increases and understanding the development of intelligence in old age is becoming a focus of medicine and research. Old people astonishingly differ in their degree of cognitive abilities. For the most part, not age is crucial but rather training.

Average values of the development of intelligence:

  • Until the age of 75: minor changes
  • Afterwards: Accelerated degradation of cognitive functions

Measuring Intelligence: Intelligence Tests

Intelligence tests are psychological methods for the assessment of cognitive performances or of intelligence, characterized as intelligence quotient. They are always standardized to a group, meaning that the results of the tests have a normal distribution in a certain population and the result of an individual is always a comparison with other individuals within this group.

Wechsler intelligence scale: WIS

To date, the Wechsler Intelligence Scale for Children (WISC) and adults (WAIS), developed by the psychologist David Wechsler, is the most commonly used intelligence test. It is based on the general factor by Spearman and is broadly divided into a verbal subtest and a performance subtest. Accordingly, a verbal IQ and a performance IQ is calculated; their mean make the full scale IQ.

The different subtests test for:

table of verbal vs action part


The test is suitable for the assessment of the general cognitive state of development and for the examination of age-, environment-, or disease-related performance impairments in specific areas.

The WIS represents an individual test: a subject acts with an examiner. The test takes about 60-90 minutes. In order to ensure the objectivity of the administration, the examiner follows highly standardized instructions. Furthermore, the WIS expresses a culture-independent assessment of intelligence.

Note: General knowledge (i.e. „information“) and vocabulary of the WIS are standardized on specific groups who live and grew up in specific countries and received a specific education (e.g. the WISC-IV US standardization sample consisted of 2,200 children between the ages of 6 and 16 years). Hence, the test must consistently be revised again in order to renew obsolete questions and wordings.

Analysis of the WIS

The mean of the WIS is at 100 points, the standard deviation is at 15 points and its design precludes gender differences. Furthermore, there are versions for adults, school children and preschool children. The IQ is taken from the averaged verbal and performance subtests.

Examples of tasks included in the WIS

Verbal subtest:

  • Information: What is the capital of France?
  • Comprehension: What is the thing you do if you find an injured person laying on the sidewalk?
  • Arithmetic: John bought three books for five dollars each, and paid ten percent sales tax. How much did he pay all together?
  • Similarities: How are a snake and an alligator alike?
  • Digit Span: The subject hears a number string once (e. g. 7 4 9 7 2) and has to verbally repeat it forward or backwards.
  • Vocabulary: What is the meaning of the word ‚articulate’?

Performance subtest:

  • Digit-Symbol Coding: The subject receives a code which should help to assign specific symbols to specific numbers (e. g. 1, 2, 3, 4).
  • Picture Completion: In a displayed picture, the subject has to name what is missing in the depiction (e.g. ox without horns)
  • Block Design: Specific displayed patterns must be reconstructed with cubes.
  • Picture Arrangement: A quantity of jumbled up pictures (e.g. comics) have to be arranged in chronological order so that they make an intelligible story.
  • Object Assembly: The subject has to assemble a known object from a certain quantity of pieces of a puzzle.

Intelligence structure test (IST)

The Intelligence Structure Test is based on the multiple-factor theory by Thurstone and is designed to be a group test which can be taken individually. It comprises a verbal, figural and numerical subtest; a newer version of the IST 2000 also tests for memory. From the verbal, figural and numerical factors, a secondary factor reasoning is calculated. The administration of the IST lasts around 90 minutes and can be taken by pen and paper or on the computer.

The objectivity of the IST is very high, because the subjects work individually without any interference of an examiner.

The mean is at 100 points, the standard deviation is 10 points. An overall IQ cannot be determined from the IST; it only yields values for the separate subtests.

Culture fair test CFT

The Culture Fair Test is based on Cattell’s model of crystallized and fluid intelligence. The test assesses culture-independent fluid intelligence. It consists of the four nonverbal subtests Series, Classifications, Matrices and Conditions.

Progressive matrices test by Raven (1936)

Raven Matrix

Image: “Raven’s Progressive Matrices Example” by Lifeof Riley. License: CC BY-SA 3.0

The Progressive Matrices Test by Raven is a nonverbal multiple-choice intelligence test. During World War II, every draftee was tested with the Progressive Matrices Test, independent of literacy. The tasks of the test are based on understanding a present pattern and selecting the missing piece from a series of several provided pieces.  There are three different types of matrices:  Standard, Colored and Advanced Matrices.

In 2007, two studies concluded that people with Asperger Syndrome or classic Autism achieve averagely higher scores on the Progressive Matrices Test than on the WIS.

Intelligence and Achievement

The question why intelligence should be assessed at all is associated with the prediction of achievement variables: achievement in school,  at work, in academics.  Students are divided into two groups, according to their achievements and their intelligence:

  • Underachiever: Achievement is not as high as expected (frequent cause: motivational deficits).
  • Overachiever: Achievement is higher than expected (frequent cause: high conformity, ambition and efforts).

Excursus: The Dunning-Kruger Effect

If you’re incompetent, you can’t know you’re incompetent… [T]he skills you need to produce a right answer are exactly the skills you need to recognize what a right answer is”. (David Dunning)

In their studies, Dunning and Kruger were able to identify certain characteristics that can typically be found in individuals who are unconsciously incompetent. Incompetent people:

  • Overestimate their own abilities and skills
  • Fail to recognize their own lack of competence

Popular Exam Questions on Intelligence

The answers are below the references.

1. Mr. E., 79 years old, complains to his family doctor: “I used to be far more mentally fit than I am now. I can still solve my crossword puzzles, but when I am confronted with an unfamiliar problem, I’m having a hard time solving it.“ Which term from the factor analysis model of intelligence by Cattell best describes the area of intelligenceMister E. complains about?

  1. Cognitive intelligence
  2. Fluid intelligence
  3. Crystallized intelligence
  4. Semantic memory
  5. Verbal intelligence

2. Which theory of intelligence is the Wechsler Adult Intelligence Scale built on?

  1. General factor theory
  2. Model of Intelligence by Jäger
  3. Model of crystallized and fluid intelligence
  4. Multiple-factor theory of intelligence
  5. Phase model of the development of intelligence

3. Jane is 8 years old and already solves tasks that are averagely solved by 10-year-old children. What is her IQ (classic intelligence quotient by W. Stern)?

  1. 80
  2. 110
  3. 125
  4. 135
  5. 150
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