What Is IQ? Intelligence, Cognitive Tests and Scores | FermatMind
Evidence and judgmentEvidence evaluation
What Is IQ? Intelligence, Cognitive Tests and Scores
Understand cognitive abilities, raw scores, age norms, standard scores, percentiles and measurement uncertainty through a worked fictional example. Learn how to compare tools and choose formal assessment.
IQ is a score from a particular cognitive assessment and reference system. It usually expresses performance relative to a defined group. It is not the percentage of questions answered correctly, and it does not directly reveal everything about a person’s intelligence.
Three layers need to stay distinct: the cognitive abilities being investigated, the tasks used to observe them, and the scores derived from performance. Solving a visual pattern is a task observation. Interpreting that result as an IQ for a particular purpose requires evidence about the instrument, its coverage, administration, reference group and uncertainty.
General intelligence and different cognitive abilities
General intelligence, often represented by g, is a statistical construct used to describe shared variation across cognitive tasks. Tasks also make different demands. Understanding words, analysing spatial relationships, reasoning through unfamiliar rules, holding and manipulating information, and efficiently completing simple operations are not interchangeable activities.
A shared factor and distinct task demands can both matter. A total score does not establish that every domain is identical; evidence of multiple components does not by itself show that g does not exist. Conclusions depend on the tasks, participants and statistical models used.
Hampshire and colleagues’ 2012 study examined performance across 12 cognitive tasks in a large internet volunteer sample and discussed short-term memory, reasoning and verbal components alongside network interpretations. It illustrates why task coverage matters. It was not population probability sampling, did not validate FermatMind, and should not be reduced to a claim that intelligence consists of exactly three independent abilities. Original study
What different tasks can contribute
Domain
A question tasks may address
What one task does not establish
Verbal comprehension
How someone understands particular words, concepts and relationships
All reasoning ability or performance in every language setting
Visual spatial ability
How someone analyses spatial positions and part–whole relationships
Creativity or competence in every design activity
Fluid reasoning
How someone handles unfamiliar relationships and rules
All knowledge, memory or practical decision-making
Working memory
How someone holds and manipulates information within a task
All long-term memory or a diagnosis of attention difficulties
Processing speed
How efficiently someone performs specified simple operations
Depth of thought, learning potential or personal worth
This is a conceptual guide, not a diagnostic checklist. A particular composite score may cover a different set of tasks. The official WAIS-5 overview describes five cognitive domains: verbal comprehension, visual spatial ability, fluid reasoning, working memory and processing speed. Its stated age range of 16 years through 90 years 11 months belongs to that version; it cannot establish eligibility for another language version or an unrelated exercise. WAIS-5 overview
Matrix reasoning asks a person to identify relationships and changes in visual material and infer a missing element. It is one kind of cognitive task, not a substitute for every domain above. Raven’s 2 is a particular professional instrument with its own version, administration, scoring and reference system. Another set of original visual questions does not become Raven’s 2 because the format looks similar. Raven’s 2 product scope
From task performance to a reference score
A raw score is the direct result of an instrument’s scoring rules, such as the number correct. The same raw number can have different meanings on forms with different difficulty, coverage or scoring.
Norms describe scores obtained for a specified instrument and reference population. Age-referenced norms compare performance with an appropriate age group rather than placing everyone on an unadjusted raw-score leaderboard. Useful documentation identifies the population, sampling and participation, collection dates and version. A large number of website users does not automatically form a representative sample.
A standard score places performance on an agreed scale. Some IQ scales use a mean of 100 and a standard deviation of 15, but adopting those numbers does not create valid norms. Actual assessments may use age-specific tables, transformed subtest scores and composite procedures; a simple formula cannot replace their methods.
A percentile describes position relative to a distribution or sample. Percentile 84 does not mean 84% of questions were correct or that someone has 84% more ability. A model-derived percentile also needs to be distinguished from a directly calculated rank in a specified sample. Testing standards on norms and comparable scores
A fictional example you can recalculate
Every task, parameter and error estimate in this example is invented for teaching. None is a FermatMind algorithm, an actual norm table or an individual’s report.
Suppose a 20-question exercise awards one point per correct answer. Alex and Morgan both answer 16 correctly. Each has a raw score of 16 and 16÷20 = 80% correct.
For their fictional age group, assume the raw-score mean is 12 and the standard deviation is 4. For teaching, place this result on a linear scale with mean 100 and standard deviation 15:
If we additionally assume a normal reference distribution, z = 1 corresponds to a model percentile of about 84.1. Four quantities now have separate meanings: raw score 16, percentage correct 80%, transformed score 115, and model percentile 84.1. No step converts 80% correct directly into percentile 80.
Now imagine a different age reference group with a mean of 16 and the same standard deviation of 4. A raw score of 16 gives z = 0 and a transformed score of 100. Changing the reference changes the interpretation. These numbers are not real age conversions or proof of an actual ability difference.
Add two more fictional observations. Both people still score 16/20 on visual patterns, but Alex scores 8/10 and Morgan 5/10 on an information-holding task. On a word-meaning task, Alex scores 5/10 and Morgan 8/10. Equal visual-task scores coexist with different observations elsewhere. These results do not establish diagnoses, and averaging them does not produce a valid full-scale IQ: task difficulty, reliability, relationships and composite rules have not been established. The example simply shows why one task cannot cover everything.
Why a score needs uncertainty
Measurement error concerns the precision of a score as an estimate. It does not mean someone necessarily marked an answer incorrectly. Item sampling, scoring and administration contribute to measurement quality. Some influences may be systematic bias rather than random error, and an interval cannot resolve them all.
Continuing the invented example, suppose the standard error of measurement on this teaching scale is 3 and a normal-error approximation is appropriate. Then 115±1.96×3 is approximately 109–121. This hypothetical interval illustrates uncertainty around a point score. It is not a confidence interval for FermatMind or for any professional assessment.
An actual report’s interval must come from the relevant instrument’s methods and evidence. Nearby point scores should not immediately be treated as enduring differences. Comparisons across attempts also require attention to versions, exposure, conditions and appropriate methods for interpreting change.
Accurate for which interpretation and use?
Reliability concerns consistency or precision. Validity concerns whether evidence supports the proposed interpretation and use. Stable scores do not prove complete construct coverage; broad task coverage does not automatically justify an educational or clinical decision.
The testing standards connect validity with particular score interpretations and uses. Ask what conclusions the evidence supports rather than seeking a universal accuracy percentage. A professional assessment may combine test results with interviews, developmental and educational history, observations and other relevant information. One number cannot automatically replace that process. Standards for Educational and Psychological Testing
Online and offline describe delivery methods. They are not a validity verdict. An online instrument may have rigorous evidence, and an in-person puzzle may lack it. Evaluate the particular instrument, version, administration controls, reference population and intended interpretation.
Age, language and culture are part of the measurement
Professional instruments specify age applicability and reference information. Raven’s 2 lists an age range of 4–90 years; the WAIS-5 overview lists 16 years through 90 years 11 months. These ranges belong to those products and do not transfer to another test.
Visual material may reduce reading and vocabulary demands without eliminating cultural, educational, visual or format-familiarity influences. Raven’s 2’s publisher describes reduced language and cultural effects; that is not evidence that all visual tasks are culture-free.
A fluent translation does not establish interchangeable scores. Instructions, methods, item meanings, group responses and reference systems may differ. Cross-language and cross-group interpretations require corresponding evidence. ITC guidelines for translating and adapting tests
Even when two versions both report 115, they may cover different tasks or use different references. Without appropriate equating or linking evidence, do not invent a conversion or combine scores from several websites into a precise ability-growth curve.
A result cannot determine inheritance or a developmental ceiling
A single assessment observes performance in particular tasks and conditions. It cannot calculate an individual’s genetic percentage, separate genetic and environmental causes of a difficulty, or establish an unchangeable ceiling. Those questions require other research designs; the examples and instrument descriptions here do not provide that evidence.
More useful personal questions are where difficulties occur, whether they persist across settings, how they affect daily functioning, and what support helps. Treating one result as destiny is unwarranted; treating a practice gain as proven growth in general intelligence is also unwarranted.
Choosing formal assessment or exploratory practice
For educational placement, clinical interpretation or formal documentation, identify the purpose and the receiving institution’s requirements first. Ask a qualified practitioner which instrument and version is appropriate for your age and language, who the norms represent, how conditions and uncertainty will be handled, and which decisions the evidence supports. Childhood assessment and persistent difficulties affecting daily life require suitable professional evaluation rather than self-diagnosis through multiple online quizzes.
Intelligence is the construct being investigated; IQ is a score from a particular assessment and reference system. Coverage, methods, norms and intended uses constrain its interpretation.
Can matrix reasoning measure all intelligence?
It contributes visual relationship and rule-inference information. Other domains require other observations; the coverage and validity of any composite must be established for the specific instrument.
Is 80% correct the 80th percentile?
No. Percentage correct refers to questions, while a percentile refers to a reference distribution or sample. The fictional example separately produces 80% correct, a transformed score of 115 and a model percentile near 84.1.
Why can the same raw score produce different standard scores?
Forms, scoring and reference groups may differ. In the invented example, changing the reference mean changes the transformed score; those teaching values are not actual conversion tables.
How precise is an IQ score?
Precision needs instrument-specific measurement-error evidence. The hypothetical 109–121 interval in the article illustrates a calculation under stated assumptions and must not be applied to an actual report.
Are nonverbal tests culture-free?
Reduced language demands do not remove all cultural, educational, visual or familiarity influences. Fairness and adaptation need evidence for the instrument, groups and proposed uses.
Can scores from different versions, languages or websites be converted?
Only where relevant comparability or linking evidence supports the conversion. Shared names, visual formats or a 100-based scale are insufficient.
Are all online IQ tests invalid?
No. Delivery medium alone does not settle validity. Evaluate coverage, administration, population, norms, reliability and evidence for the intended interpretation.
Does a score reveal genetic potential?
A single task score cannot separate individual genetic and environmental causes, calculate a personal genetic percentage or establish a fixed developmental ceiling.
