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IQ Octopus

Guide

What does an IQ test measure?

An IQ test measures how well you reason, solve problems and learn new patterns, compared with other people your age. It does not measure your worth, your knowledge of the world or what you will do with your life. Here is what sits between those two statements.

Want your own number? The test is 25 visual puzzles, about 12 minutes, no sign-up.

An IQ score is a position, not a quantity

The most useful thing to know about an IQ score is that it is a ranking. Modern tests such as the Wechsler scales and the Stanford-Binet report a deviation IQ: raw results are converted so that the average for each age group is 100 and the standard deviation is 15 (Wikipedia: Intelligence quotient). A score of 115 does not mean you have 15% more of something. It means you scored one standard deviation above the average for people your age, which places you higher than about 84% of them.

That design choice explains a lot. It is why the average is always 100, why scores from different tests can be compared at all, and why the same person can see different numbers on tests that use different scales. Our guide to the IQ bell curve walks through the math.

Where the idea came from

Alfred Binet and Theodore Simon published the first practical intelligence test in 1905. William Stern proposed the term “intelligence quotient” in 1912, and Lewis Terman published the Stanford revision of Binet's test in 1916 (Wikipedia: Intelligence quotient).

In 1939 David Wechsler introduced the deviation IQ with the Wechsler-Bellevue scale: a score based on how far you sit from the average of people your own age, measured in standard deviations (Wikipedia: WAIS). Modern tests such as the Wechsler scales and the Stanford-Binet still report scores this way (Wikipedia: Intelligence quotient).

From mental age to the deviation IQ

Binet and Simon's goal was practical: to identify schoolchildren who could not keep up with the regular curriculum (Simonton 2020). The first IQ was a ratio, mental age divided by chronological age, times 100, so a 10-year-old performing like an average 12-year-old scored 120 (Britannica, IQ). Modern tests replaced it with the deviation IQ, which compares you with people your own age. See what the original IQ formula was.

General ability: the g factor

In 1904 Charles Spearman noticed that people who do well on one kind of mental test tend to do well on others, even when the tests look nothing alike. He proposed a general intelligence factor, “g”, to explain that overlap (Wikipedia: g factor).

This is the key idea behind a single IQ number. A test samples a range of tasks, such as solving puzzles, spotting patterns, holding information in mind and working quickly, and the overall score estimates the common ability that runs through all of them. No single task is the point. Each one is a window onto the general factor, with some noise of its own.

Try one · Quantitative Reasoning

Which number comes next?

10, 32, 13, 30, 16, ?

Tap the option you think is right, or show the answer.

Show the answer

The next number is 28 (option 6).

How to solve it

  1. The gaps jump around, so look at every other number.
  2. The 1st, 3rd, 5th numbers (10, 13, 16) go up by 3 each time.
  3. The 2nd, 4th, 6th numbers (32, 30) go down by 2 each time.
  4. The missing number continues the second series: 30 - 2 = 28.

That was 1 puzzle. The full test has 25.

Fluid and crystallized intelligence

In 1963 Raymond Cattell drew a distinction that is still central to how tests are built (Wikipedia: Fluid and crystallized intelligence):

  • Fluid intelligence is reasoning with new material: seeing the rule in an unfamiliar pattern, solving a problem you have not met before.
  • Crystallized intelligence is what you have learned and can use: vocabulary, facts, methods.

Clinical batteries usually measure both, through a mix of verbal and nonverbal tasks. Nonverbal tests, such as matrix puzzles, lean heavily toward fluid reasoning because they give you material nobody has studied. That is the approach IQ Octopus takes, and it is explained further in our guides to culture-fair tests and matrix reasoning.

What IQ scores are linked to

IQ is one of the most studied measurements in psychology, and across large groups it is linked to real outcomes:

  • School. In a sample of about 70,000 English children, general intelligence at age 11 correlated 0.81 with total exam points at age 16 (Deary, Strand, Smith & Fernandes, 2007).
  • Work. A review of 85 years of personnel research estimated the correlation between general mental ability and job performance at 0.51 (Schmidt & Hunter, 1998).
  • Life outcomes. A 2007 meta-analysis reported correlations with education of about 0.56, with occupational level of about 0.45, and with income of about 0.23 (Strenze, 2007).

A correlation describes how two things move together across many people. A correlation of 0.81 is strong, and one of 0.23 is modest, but neither tells you what will happen to a particular person. Many people do much better or worse than their score would suggest, because so much else matters: effort, health, opportunity, interests, luck and the people around them.

What an IQ test does not measure

An IQ test samples reasoning on short, well-defined problems with one right answer. It does not ask about:

  • creativity, or how many good ideas you produce when there is no single right answer;
  • motivation, persistence or how you handle setbacks;
  • social and emotional judgment;
  • expertise in a particular field, from plumbing to cardiology;
  • character, values or kindness.

These things matter for most of what people care about, and an IQ score is silent on all of them. That is not a flaw in the test. It is the limit of what any short measurement can do.

Is IQ fixed?

Not entirely. Twin and family studies find that the heritability of intelligence rises with age, from about 20% in infancy to perhaps 80% in later adulthood (Plomin & Deary, 2015). Heritability is a statement about what explains differences across a population, not a measure of how much of any one person's ability is “genetic”, and it does not mean a score cannot change.

Scores do move. Average measured IQ rose through much of the 20th century, by about 2.8 points per decade across 31 countries (Pietschnig & Voracek, 2015), which is called the Flynn effect. Individual scores shift with practice and test conditions. And because IQ is age-normed, a person whose raw speed slows with age does not lose IQ points for that reason alone. Our guide to IQ and age covers what does change.

Where IQ Octopus fits

IQ Octopus is a short online test of fluid reasoning: 25 generated visual and number puzzles in five sections, scored with a Rasch model and reported as an estimated IQ with a confidence range. It is designed to give you an honest estimate of the general reasoning ability described above. It is not a clinical test and cannot replace one. The how it works page explains the method in full, and online vs clinical tests explains when you need which.

Sources

  1. Intelligence quotient. Wikipedia. en.wikipedia.org/wiki/Intelligence_quotient
  2. g factor (psychometrics). Wikipedia. en.wikipedia.org/wiki/G_factor_(psychometrics)
  3. Fluid and crystallized intelligence. Wikipedia. en.wikipedia.org/wiki/Fluid_and_crystallized_intelligence
  4. Wechsler Adult Intelligence Scale. Wikipedia. en.wikipedia.org/wiki/Wechsler_Adult_Intelligence_Scale
  5. Deary, I. J., Strand, S., Smith, P., & Fernandes, C. (2007). Intelligence, 35(1), 13-21. doi.org/10.1016/j.intell.2006.02.001
  6. Schmidt, F. L., & Hunter, J. E. (1998). Psychological Bulletin, 124(2), 262-274. doi.org/10.1037/0033-2909.124.2.262
  7. Strenze, T. (2007). Intelligence, 35(5), 401-426. doi.org/10.1016/j.intell.2006.09.004
  8. Plomin, R., & Deary, I. J. (2015). Molecular Psychiatry, 20, 98-108. doi.org/10.1038/mp.2014.105
  9. Pietschnig, J., & Voracek, M. (2015). One century of global IQ gains. Perspectives on Psychological Science, 10(3), 282-306. doi.org/10.1177/1745691615577701
  10. Simonton, D. K. (2020). Galton, Terman, Cox: The Distinctive Volume II in Genetic Studies of Genius. Gifted Child Quarterly. doi:10.1177/0016986220921360 doi.org/10.1177/0016986220921360
  11. Encyclopaedia Britannica. IQ, revised by Jeannette L. Nolen (read via Wayback Machine, December 2024) www.britannica.com/science/IQ

3 questions

Questions

Does an IQ test measure intelligence?

It measures a central part of what people usually mean by intelligence: reasoning, problem solving and learning new patterns. It leaves out much else, such as creativity, practical skill and social judgment, so it is best read as a measure of general reasoning ability rather than of intelligence in every sense.

Is IQ the same as knowledge?

No. Many clinical tests include knowledge tasks such as vocabulary, but psychologists separate crystallized intelligence (what you have learned) from fluid intelligence (reasoning with new material). Nonverbal tests like matrix puzzles lean toward the fluid side.

Can IQ change?

Scores can move. Retaking tests raises scores a little through practice, and average scores across whole populations rose through the 20th century, which is known as the Flynn effect. Because IQ is age-normed, getting older does not by itself lower your score.

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