Intelligence: What Tests Measure, Predict, and Cannot Explain Alone

Two people can receive the same test score yet differ greatly in knowledge, persistence, opportunities, and everyday judgment. Intelligence testing summarizes some cognitive performances under specified conditions. Understanding the summary means asking how it was measured, whom it was compared with, and what conclusions the evidence supports.

Learning goals and Feynman practice

Explain standardized scores and their uncertainty, compare major intelligence models, interpret correlations and heritability, and distinguish evidence of environmental effects from claims about individuals or groups.

Read a section, close it, and explain it to a beginner using a new example. State the measurement, the inference, and one limitation. Attempt the questions before opening their answers; revisit and simplify the step you cannot explain.

1. What do we mean by intelligence?

Psychologists study capacities including reasoning, learning, solving unfamiliar problems, and adapting to demands. Definitions differ in scope. Processing speed is one relevant ability, not a requirement that every intelligent response be fast.

A test score is an observed performance; a construct such as general cognitive ability is inferred from patterns across observations. Fatigue, language familiarity, sensory access, education, motivation, and measurement error can affect performance. A score is neither a person’s worth nor an exhaustive inventory of their abilities.

Achievement tests emphasize acquired knowledge or skill. Aptitude tests aim to predict later performance or learning. These purposes overlap: admission tests also draw on learned knowledge, and achievement can predict future learning. SAT, GRE, MCAT, and LSAT should not be treated as pure, culture-free measures of innate potential.

Teach it back: Why can a test predict future performance while still depending on past educational experience?

2. Prediction: association is not a percentage of someone’s destiny

Cognitive scores predict aspects of educational and occupational performance, with effect sizes varying by test, outcome, sample, and statistical correction. Associations with income, health, and longevity also require considering education, resources, social conditions, and other influences. One correlation range cannot summarize every outcome.

For a simple linear model with one predictor, a correlation of r = 0.50 corresponds to r² = 0.25, or 25% of outcome variance statistically accounted for in that sample and model.

That does not mean that IQ causes 25% of a person’s success or that the remaining 75% has been cleanly assigned to personality and environment. Unexplained variance includes other predictors, measurement error, nonlinear relations, and factors not measured. Predictors can overlap rather than contribute independent slices.

Think of predicting journey time from distance. Distance can be informative without fixing every trip’s duration. Traffic, route, transport, and measurement still matter. The analogy explains statistical prediction, not the causes of intelligence.

Teach-back check: does r = 0.40 mean 40% of variation is explained?

No. In the simple one-predictor linear case, square the correlation: 0.40 × 0.40 = 0.16, or 16%. Even then, statistical explanation is not a causal partition or an individual probability of success.

Much intelligence research is correlational, but the field also uses experiments and quasi-experiments on education, training, and other influences. Researchers cannot randomly assign an intrinsic trait directly, yet they can investigate causes of measured cognitive change. Educational research provides one example. [1]

3. From mental age to modern standardized scores

Binet and Simon developed early tests in France to identify children who might benefit from educational assistance. Comparing age-related performance helped motivate mental-age approaches. Stern proposed the intelligence quotient, later expressed in the familiar historical form:

$\text{Ratio IQ} = \frac{\text{Mental age}}{\text{Chronological age}} \times 100$

A fictional child performing at a mental-age level of 12 at age 10 would receive a ratio score of 120. Mental age is not a literal age of the brain, and the ratio becomes unsuitable when adult development does not increase proportionately with chronological age.

Modern deviation IQ compares performance with an age-appropriate norm group. Many scales use mean 100 and standard deviation 15. This convention is a scoring choice applied to a reference distribution, not proof that every raw ability is naturally perfectly bell-shaped.

Score band	Distance from mean on that scale	Approximate proportion under a normal distribution
85–115	Within one standard deviation.	68%.
70–130	Within two standard deviations.	95%.
Above 130	Above two standard deviations.	About 2.3%.
Below 70	Below two standard deviations.	About 2.3%.

These are population approximations under the model, not diagnostic instructions. Scores have uncertainty intervals and must be interpreted using suitable norms and testing conditions.

A score around 130 is sometimes used in gifted-program criteria, but definitions and eligibility vary. Intellectual disability is not diagnosed by a score below 70 alone: limitations in adaptive functioning and developmental onset are also required, with context and measurement uncertainty considered. [2]

Teach it back: Why can two people with similar test scores have different practical support needs?

4. The Flynn effect: the reference group matters

The Flynn effect refers to historical increases in performance on many cognitive tests across successive cohorts. Around three points per decade is a commonly cited broad historical approximation, not a universal rate for all countries, subtests, and periods.

Renorming updates the reference sample, so a score of 100 remains near the new norm group’s mean. It does not mean no underlying performance change occurred. Conversely, applying old norms to a later cohort can produce a higher score without changing the person’s answers.

Some populations and periods show slowing, stabilization, or reversal. A Norwegian within-family study found evidence that both gains and reversal reflected environmental influences within its study context. [3] It did not identify one universal environmental cause.

A fixed claim that someone scoring 100 today would score 120 two generations ago requires specific tests, dates, populations, and linking assumptions. It cannot be inferred from the label “Flynn effect” alone. Also, three points per decade yields 15 points over fifty years, not automatically one standard deviation in every generation.

5. Models: shared variance and distinct abilities can coexist

Positive manifold means that scores on diverse cognitive tests tend to correlate positively. Factor analysis models their shared variation. Spearman proposed a general factor, g, alongside task-specific contributions. A statistical factor summarizes covariance; it is not automatically a single neural substance or a complete causal mechanism.

Account	Main proposal	How to interpret it
Spearman	A general factor plus specific abilities.	Explains shared test performance without requiring identical profiles.
Thurstone	Primary mental abilities, such as verbal, spatial, numerical, and perceptual skills.	Broad abilities can be distinguished while still correlating.
Cattell and Horn	Fluid reasoning and crystallized knowledge, alongside other broad abilities.	New-problem solving and acquired knowledge differ but interact.
Carroll	Three strata: general, broad, and narrow abilities.	A hierarchical synthesis rather than a denial of specialized skills.
Cattell–Horn–Carroll approaches	Related hierarchical frameworks integrating broad and narrow abilities.	Details vary; do not treat every historical model as the same tree.
Gardner	Multiple intelligences, including linguistic, spatial, musical, interpersonal, and other domains.	Influential for recognizing diverse talents; evidence for fully independent intelligences is contested.
Emotional intelligence	Abilities or self-reported traits concerning emotion.	Ability tests and broad trait questionnaires measure different things.

Fluid and crystallized intelligence

Fluid intelligence concerns reasoning in relatively novel situations. It is not wholly independent of experience: strategies, familiarity with tests, and education still matter. Crystallized intelligence concerns acquired knowledge and its use.

Some speed and novel-reasoning abilities tend to decline earlier in adulthood, while vocabulary and knowledge may remain stable or improve longer. Components peak at different times, and health, experience, cohort, and individual differences matter. “Fluid peaks once; crystallized always rises” is too rigid.

Diverse talents and emotional abilities

Gardner’s eight commonly discussed domains are linguistic, logical-mathematical, spatial, musical, bodily-kinesthetic, interpersonal, intrapersonal, and naturalist. Appreciating diverse expertise does not establish that these are psychometrically independent or that instruction should be matched to a supposed learning-style label.

Salovey and Mayer developed an ability-based account of emotional intelligence, including perceiving, using, understanding, and managing emotion. “EQ” is not a single universally standardized quotient comparable across every instrument. Some broader measures overlap substantially with personality, motivation, or self-beliefs.

Teach-back check: why does finding g not imply everyone has the same strengths and weaknesses?

A shared factor captures some common variation across people and tasks. Broad and narrow abilities, knowledge, practice, and measurement differences can still produce distinct individual profiles.

6. Cognitive and neural mechanisms

Processing speed and working-memory measures correlate with cognitive test performance. They are possible explanatory contributors, not interchangeable definitions of intelligence. Reaction time includes perceptual and motor demands, while an n-back task includes updating, interference control, and strategy; neither is a pure readout of a single mental capacity.

Improvement on a practiced working-memory task does not automatically establish broad improvement in fluid reasoning. Distinguish task learning from transfer to different abilities using appropriate controls and untrained outcomes.

Frontoparietal networks contribute to reasoning and control, interacting with other systems according to task demands. Dorsolateral prefrontal and parietal activity does not constitute one isolated intelligence circuit.

The neural efficiency hypothesis proposes that some higher-performing people use fewer measured resources for a task under certain conditions. Reduced activation can reflect efficiency, but also lower engagement, different strategies, or measurement features. With greater difficulty, higher-performing people may show more recruitment rather than less. BOLD activity and glucose metabolism are different measurements, not a universal mental energy meter.

Teach it back: What additional information would you need before interpreting lower brain activation as better efficiency?

7. Heritability: variation in a population, not ingredients in a person

Heritability estimates the proportion of observed differences associated with genetic differences under a specified model, in a particular population and environment. Estimates can be substantial in adult samples, but vary with age, population, methods, and environmental range.

A heritability estimate of 60% does not mean that 60% of one person’s intelligence is genetic, that the trait cannot change, or that an intervention can improve only the remaining 40%. It also does not explain the causes of average differences between populations.

Twin studies compare similarity across degrees of genetic relatedness. Their estimates depend on assumptions about environments, mating patterns, measurement, and sampling. Correlations such as 0.86 for identical twins and 0.60 for fraternal twins should not be treated as biological constants applying to every study.

Think of plant height in a garden. Genetic differences can explain much variation when conditions are similar, while a change in water or soil can still alter average height. This illustrates the statistical distinction; human development is more complex than the analogy.

Teach-back check: can a highly heritable trait respond to an environmental intervention?

Yes. Heritability describes variation under existing conditions. An intervention can change those conditions and shift outcomes without contradicting the original estimate. It does not partition a person’s fixed potential into independent genetic and environmental pieces.

8. Socioeconomic context: a hypothesis with population limits

Turkheimer and colleagues’ 2003 study reported that genetic and shared-environmental variance estimates differed by socioeconomic status in a sample of young US twins. [4] These were model-based estimates of variation, not measurements of how much genetic potential an individual child expressed.

Later cross-national work found that the gene-by-SES pattern differed across countries and samples. [5] Fixed figures such as 70% heritability in affluence and 10% in poverty are not universal laws. Social institutions, age, environmental range, sampling, and model assumptions can change estimates.

Also distinguish gene–environment interaction, in which associations vary with environment, from gene–environment correlation, in which genetically influenced characteristics relate to the environments people experience or select. Neither reduces development to one-way genetic determination.

9. Environmental determinants: separate plausible causes from correlations

Factor	What to investigate	Causal caution
Education	Whether additional schooling changes measured cognitive performance.	Quasi-experiments strengthen inference, but effects vary by design and outcome.
Early health and nutrition	Prenatal development, illness, toxic exposure, and access to care.	Correlated family and social conditions can influence both exposure and outcomes.
Breastfeeding	Feeding history and later performance.	Maternal characteristics and resources can confound observational associations; a fixed 5–7-point causal benefit is not established by correlation.
Birth weight	Associations with later development.	Gestation, health, and social conditions complicate interpretation; heavier is not universally better.
Birth order	Small average within-family differences in some studies.	Family size, cohort, age, and resources require control; an average is not an individual prediction.

A meta-analysis of quasi-experimental schooling studies supports education as an influence on cognitive test performance. [1] It does not imply identical effects for every student or every educational programme.

Historical studies of children from different parental backgrounds, including postwar settings, can challenge simplistic genetic accounts but cannot alone prove that every observed group difference is entirely environmental. Social racial categories do not identify a single biological mechanism. Average score differences require evaluation of testing comparability, schooling, health, discrimination, language, opportunity, and sampling; neither within-group heritability nor one historical sample settles their causes.

10. Worked interpretation: a fictional test report

Suppose a report gives a standardized score of 115, mean 100 and standard deviation 15, and says the test correlates 0.50 with a particular educational outcome.

1. The score is one standard deviation above the reference mean under that scale.
2. It is an estimate with uncertainty, not an exact permanent quantity.
3. The correlation describes a sample-level relationship with a specified outcome, not a guarantee about this person’s future.
4. In a simple one-predictor linear model, the associated r² is 0.25; it is not a causal percentage of success.
5. Nothing in those numbers alone identifies genetic causes, adaptive functioning, motivation, or the person’s full ability profile.

Teach it back: Explain the report without using “potential,” “destiny,” or “born smart.” Which additional information would make the interpretation more useful?

Retrieval workshop and spaced review

Reconstruct the model-comparison table from memory. Explain deviation IQ, r², the Flynn effect, heritability, and gene-by-environment interaction using different examples. For each, separate the statistic from a causal claim.

Repair: “A low IQ score alone diagnoses intellectual disability”

Diagnosis also requires limitations in adaptive functioning and developmental onset, interpreted with appropriate norms, context, and measurement uncertainty. A score does not replace a comprehensive assessment.

Repair: “If 25% is explained, the other 75% must be personality”

The unexplained portion includes all omitted influences and measurement limitations in that model. Personality may predict some outcomes, but its unique contribution must be measured and can overlap with other predictors.

Apply: why does high within-group heritability not explain a difference between group averages?

Within-group variation and between-group means answer different statistical questions. Two groups can each show substantial genetic variance while differing in relevant environments. The causes of the mean difference need separate evidence.

Review tomorrow and in a week. Score each explanation: 0 for a label, 1 for a definition, 2 for a mechanism plus example and limitation. Repair the weakest one first.

One-minute explanation: Intelligence tests summarize some cognitive performances against a reference group and can predict specified outcomes imperfectly. General and specialized abilities can coexist in hierarchical models. Scores, brain measurements, and heritability estimates answer different questions and do not independently establish causes or determine an individual’s future. Development reflects biological and environmental processes, while education and context can influence measured performance.

Sources and further reading

The supplied outline’s citation fragments did not include a bibliography. These references support the educational, diagnostic, cohort, and socioeconomic qualifications; the test report and plant analogy are teaching aids.

1. Ritchie, S. J., and Tucker-Drob, E. M. (2018). How much does education improve intelligence? A meta-analysis.
2. American Association on Intellectual and Developmental Disabilities. Defining criteria for intellectual disability.
3. Bratsberg, B., and Rogeberg, O. (2018). Flynn effect and its reversal are both environmentally caused.
4. Turkheimer, E., et al. (2003). Socioeconomic status modifies heritability of IQ in young children.
5. Tucker-Drob, E. M., and Bates, T. C. (2016). Large cross-national differences in gene × socioeconomic status interaction on intelligence.