Is math ability the same as IQ? What the meta-analyses actually found

0 The short answer

Math ability is closely related to IQ but is not the same thing: general intelligence accounts for roughly a sixth to more than half of the differences in math performance, depending on the design and the measure, and the remainder is taught skill, working memory, motivation and a math-specific ability. The 2019 meta-analysis of 680 studies found a correlation of .41 between fluid reasoning and mathematics, and the English cohort of more than 70,000 children found that general intelligence at age 11 accounted for 58.6 percent of the variance in math exam results at 16. Both figures leave a large share unshared, and the direction of the link runs both ways. This page sorts the studies by design, age and measure.

1 What Do People Mean by Math Ability, and What Does an IQ Score Measure?

"Math ability" is at least four different things, and whether it equals IQ depends on which of them is set against which part of an intelligence test. The first is learned mathematical knowledge and procedure: number facts, operations, formulas, the method for a quadratic. In the Cattell-Horn-Carroll framework described on the page on the CHC model of cognitive abilities, this is quantitative knowledge, Gq, an acquired ability that instruction builds. The second is reasoning with quantities and relations in a problem the person has not seen before, which the CHC literature files with fluid reasoning, Gf, and which the page on quantitative reasoning tests treats in detail. The third is the working memory and attention that mental calculation uses to hold a number while transforming it. The fourth is a school mark or an exam result, which bundles all of the above with effort, attendance, teaching quality and the judgment of a marker.

An IQ score is a different kind of object. A Full Scale IQ summarizes performance across several cognitive domains, and the shared variance that runs through all of them is what researchers call g, the subject of the page on the general factor of intelligence. The page on what IQ measures covers the domains. For the question here, the important point is that IQ batteries usually contain a mix of items that resemble mathematics (number series, mental arithmetic) and items that do not (vocabulary, matrices, symbol coding). A correlation between "IQ" and "math" therefore depends on which IQ components are used, and some of the overlap is built into the tests by design, a point the section on the ACIS profile returns to.

The table sets the four things side by side. It also gives the quantity that most studies report, the correlation coefficient r. A correlation runs from minus 1 to plus 1, and its square is the proportion of variance in one measure that a straight line through the other accounts for. A correlation of .41, for example, corresponds to 16.8 percent of variance by our arithmetic. The studies below use the word "accounted for" in this statistical sense, which does not mean "caused by".

Two terms recur below. Fluid intelligence is reasoning in unfamiliar problems, and the page on fluid and crystallized intelligence explains how it differs from acquired knowledge. Mathematics in these studies is almost never one test. It is a grade, an exam, a teacher rating or an achievement composite, and the choice moves the correlation, as the section on why the numbers differ shows.

2 What Did the Largest Meta-Analysis Find About Fluid Reasoning and Math?

The largest meta-analysis found that fluid reasoning correlates .41 with mathematics and .38 with reading, a difference that is real but small. Peng, Wang, Wang and Lin published it in 2019 in Psychological Bulletin, pooling 680 studies that contributed 793 independent samples and more than 370,000 participants. The measure of intelligence was fluid reasoning, Gf, and the outcomes were reading and mathematics skills, so this is a study of one broad ability and two academic skills, not of a Full Scale IQ and a grade. The authors called both relations moderate.

The most useful comparison inside the paper is between mathematics and reading. If mathematics were the subject that most directly drew on reasoning, its correlation with Gf would be far above that of reading. It is above it, but only by three hundredths, which is why the question "is math just IQ?" has a harder answer than "does IQ help with math?". Reasoning helps with both subjects, and it helps with mathematics a little more.

The paper also reports four moderator findings that matter for the rest of this page. Gf related more strongly to mathematics than to reading. Within each subject, Gf related more strongly to complex skills than to foundational skills, which fits the idea that reasoning matters more when a problem has to be worked out than when a fact or a procedure can be retrieved. The relations increased with age. And family socioeconomic status mostly affected the relations in early development, which the authors read as evidence that children may rely on Gf to learn reading and mathematics early on and that a favorable family environment can boost that effect.

Three cautions apply. First, a correlation of .41 means that about 17 percent of the variance in math performance is statistically shared with fluid reasoning in a simple linear reading, by our arithmetic, which leaves most of the variance elsewhere. Second, the figure is an average across very different samples, tasks and ages, so it describes the literature and not any child. Third, the longitudinal result says that the two predicted each other, which is the mutualism the section on direction takes up and is not a one-way arrow from reasoning to math. The authors themselves describe their findings as partly in line with investment theory and more in line with intrinsic cognitive load theory, mutualism theory and a gene and socioeconomic status interaction hypothesis, of which mutualism is the idea that learning and reasoning feed each other.

3 How Much of Math Performance Did General Intelligence Account for in 70,000 English Children?

In the largest single cohort, general intelligence at age 11 accounted for 58.6 percent of the variance in math exam results at age 16, more than for any of the other 24 subjects. Deary, Strand, Smith and Fernandes followed more than 70,000 English children for five years in a prospective design and published the results in 2007 in Intelligence. Intelligence was measured at age 11, and achievement was the national examination results in 25 academic subjects at age 16. The latent correlation between general intelligence and the achievement trait was .81, and general intelligence contributed to success in every one of the 25 subjects.

The abstract reports how much variance general intelligence accounted for in individual subjects. It ranged from 58.6 percent in mathematics, through 48 percent in English, to 18.1 percent in art and design. Mathematics therefore sits at the top of a gradient that runs from subjects with a strong logical and cumulative structure to subjects in which expression, taste and judgment carry the grade. The same abstract reports that girls did not differ from boys in general intelligence yet outperformed boys in every subject except physics, a reminder that exam results carry more than ability.

The summary on the University of Edinburgh research portal, which was opened on October 20, 2026, adds a concrete illustration. Among students of average intelligence, 58 percent earned five or more GCSE passes at grades A* to C, and a one standard deviation change in intelligence moved that figure to 91 percent for students above average and 16 percent for students below. The page on how a standard deviation of 15 works shows what a one standard deviation step is on the IQ scale. For the question of this page, the sentence to hold on to is that a very strong relation between intelligence and exam results at the population level still leaves a spread. By our arithmetic, 9 percent of students one standard deviation above average missed the five-pass mark, and 16 percent of students one standard deviation below average reached it.

The figure of 58.6 percent circulates widely, so it helps to state what it is not. It is not a constant. It is a latent-variable estimate for one cohort of English children, one national examination system, one intelligence test at age 11 and one outcome at age 16. It is also not a statement that 41.4 percent of math ability is "something else" in the sense of a separate talent, because the remainder includes teaching, effort, measurement error in both the test and the exam, and everything else that varies between students. The sections that follow try to name the parts of that remainder that research has actually identified.

4 Why Do Different Studies Report .41, .49, .54 and 58.6 Percent?

The figures differ because they answer different questions: which intelligence measure, which math measure, whether the number is corrected for error, and whether it is a correlation or a share of variance. The table puts five of the studies side by side. The numbers cannot be ranked as "the real one" and "the wrong ones", and putting them on one line without the design columns is the most common way the topic is misreported.

The school grades meta-analysis explains one of the main reasons the figures differ. Roth and colleagues, writing in Intelligence in 2015, analyzed 240 independent samples with 105,185 participants. The sample-size weighted observed correlation between intelligence tests and school grades was .44. After correcting for measurement error and range restriction in the intelligence measure, the population correlation was .54. Only 31.7 percent of the variance of the observed correlations was attributable to those artifacts, so the authors did not generalize the single figure and looked for moderators instead.

The moderator for subject is the part that bears on mathematics. The mathematics and science subgroup, which the authors defined to include mathematics, biology and physics, had 100 samples and 60,533 participants, an observed correlation of .42 and a corrected correlation of .49, with a 95 percent confidence interval of .47 to .52. Languages had 96 samples and 61,865 participants, an observed .36 and a corrected .44, with an interval of .41 to .47. Social sciences came out at .43, fine art and music at .31 and sports at .09. The authors judged the difference between mathematics and science and the languages to be rather small, because the confidence intervals overlap, and suggested that a moderating effect can be assumed only carefully. Their two proposed reasons were that mathematics and science content relies heavily on logic and that grades in these subjects can be marked right or wrong with less room for a teacher's judgment, which raises the reliability of the grade.

The type of intelligence test mattered too. Mixed tests, which combine several kinds of items, gave the highest corrected correlation, .60, followed by verbal tests at .53, and by grade level the high school subgroup gave .58. Reading the table with this in mind, three rules follow. A correction for measurement error raises a number, so a corrected .54 and an observed .44 describe the same data. A latent-variable estimate, such as the .81 in the English cohort, is higher than a correlation between two observed scores because it removes error from both. And a share of variance is the square of a correlation, which makes it look smaller or larger than the correlation depending on the reader's expectations. A reader who sees "58.6 percent" next to "r = .41" is not looking at a contradiction. They are looking at different quantities.

5 Is There a Math-Specific Ability Beyond g?

Two quite different kinds of evidence, large-scale school assessments and twin studies, both point to a substantial overlap between mathematics and general intelligence and to a smaller math-specific part that general intelligence does not absorb. The first comes from Saß, Kampa and Köller, who published in Intelligence in 2017 a study of German large-scale assessments across three school levels. They drew on six assessments of three cohorts, Grade 5, Grade 9 and Grade 13, with sample sizes from 730 students in Grade 5 to 3,893 in Grade 9, and two kinds of framework, one built around literacy and one around the curriculum. They compared three measurement models: one in which a single g factor accounts for the common variance, one with two correlated factors, and a nested-factor model with a g factor, a domain-specific mathematical factor and cognitive ability. Their conclusion was that the assessments measure mathematical ability beyond g. The g factor and the math-specific factor also related differently to math self-concept, gender, socioeconomic status and the math grade, which is consistent with two constructs and not one construct measured twice.

The second kind of evidence is genetic. Kovas, Harlaar, Petrill and Plomin analyzed almost 3,000 pairs of same-sex twins at age 7 in a study published in Intelligence in 2005, with mathematics rated by teachers against national curriculum criteria. The genetic correlation between mathematics and general intelligence was .67, and between mathematics and reading it was .74. The authors report that about a third of the genetic variance in mathematics is independent of reading and general intelligence, which they read as evidence for some genes with effects specific to mathematics, alongside the generalist genes that affect several abilities at once. The page on what heritability means for IQ explains why a genetic correlation describes a population and does not fix any child's ability.

The two studies agree on the shape of the answer even though their methods share almost nothing. Mathematics is neither a separate trait nor a mere label for g. It is a domain in which general ability, learned knowledge and some specific aptitude all contribute, and the proportions shift with age, curriculum and the way mathematics is measured. That is the practical reason an intelligence battery can report a quantitative reasoning index as its own score and not only as part of a total, a point the section on how a profile can show the pieces returns to.

6 What Do Working Memory, Complex Skills and Early Math Knowledge Add?

Working memory, the difficulty of the skill and the amount of math already learned each account for part of the variation that general intelligence leaves over. Start with working memory. Peng, Namkung, Barnes and Sun reported a meta-analysis of 110 studies with 829 effect sizes in the Journal of Educational Psychology in 2016 and found a significant medium correlation between mathematics and working memory, with the relation examined by working memory domain, type of mathematics skill and sample characteristics. That fits what mental arithmetic demands: the person must hold a number, apply an operation and keep the next step in mind at once. It is also why the Wechsler scales place their arithmetic task under working memory and not under a quantitative index, a point the ACIS page on the Arithmetic subtest makes explicit. The page on working memory tests for adults and the page on the Digit Span subtest describe the ability itself.

The second contribution is the difficulty of the skill. The 2019 meta-analysis described above found that fluid reasoning related more strongly to complex skills than to foundational ones within both reading and mathematics. In plain terms, retrieving a multiplication fact leans on learned memory and practice, while working out how to set up an unfamiliar word problem leans on reasoning. A person can therefore be fast and accurate at routine calculation and still find novel problems hard, or the reverse, and a math test that mostly samples routine procedures will correlate less with fluid reasoning than one that mostly samples new problems. The ACIS page on the Mathematical Achievement subtest describes a format that leans on learned knowledge and familiar procedures.

The third contribution is how much mathematics a child already knows. Duncan and colleagues used six longitudinal data sets in a study published in Developmental Psychology in 2007 to estimate links between skills at school entry and reading and math achievement later on. Most of their regression models controlled for cognitive, attention and socioemotional skills measured before school entry, and for a range of family background measures. Across all six studies, the strongest predictors of later achievement were school-entry math, reading and attention skills, and a meta-analysis of the results showed that early math skills had the greatest predictive power, followed by reading and then attention. The word "cognitive" there refers to whatever cognitive measures each study had before school entry, which are not the same thing as a full intelligence test, so the study cannot say that early math adds to a measured IQ. What it can say is that early math knowledge predicts later math achievement even when the earlier skills available are held constant, which is what a cumulative, taught subject would produce.

Put together, the three contributions explain why a child with a strong reasoning score can still struggle with a unit that builds on earlier units that were missed, and why a child with an ordinary reasoning score can excel after years of practice. The page on intelligence versus knowledge makes the general distinction, and the sibling page on deliberate practice versus IQ covers how practice and ability trade off in skilled performance.

7 Which Way Does the Arrow Run Between Math and IQ?

The best designs suggest that the link runs in both directions: reasoning helps learning, and schooling raises test scores, so asking which one causes the other has no single answer. The 2019 meta-analysis found that fluid reasoning and reading or mathematics predicted each other in longitudinal samples, even after controlling for initial performance. The authors read this alongside theories in which children rely on reasoning early on and in which learning and schooling later raise reasoning in turn.

A cross-lagged panel study tests the direction directly. Watkins and Styck analyzed Wechsler Intelligence Scale for Children, Fourth Edition scores and reading and math achievement composites for 337 students who were assessed twice for special education eligibility, about 2.85 years apart, in the Journal of Intelligence in 2017. General intelligence was built from the four index scores, and measurement invariance was confirmed. The path from general intelligence at the first testing to math at the second was 0.39, and the path from math at the first testing to general intelligence at the second was 0.23. The first was significantly greater than zero and the second was not. For reading the corresponding paths were 0.26 and 0.03. The authors tentatively inferred that general intelligence was the temporal precursor of reading and math achievement.

The caveats are part of the finding. The sample was children referred for special education evaluation, with a mean age of 8.7 years at the first testing and 11.6 at the second, so it does not represent all students. A path of 0.23 from math to later intelligence is not small even though it did not reach significance in a sample of 337, and the authors described their inference as tentative. A cross-lagged design improves on a single correlation by using time order, but it does not randomize anything, and it leaves room for third variables such as home environment.

Quasi-experimental studies of schooling itself come closer to isolating a cause. Ritchie and Tucker-Drob meta-analyzed three kinds of such studies in Psychological Science in 2018: studies that controlled for earlier intelligence, studies that used compulsory schooling policy changes as instrumental variables, and studies that used regression discontinuity at school-entry age cutoffs. Across 142 effect sizes from 42 data sets and over 600,000 participants, they found consistent evidence for beneficial effects of education on cognitive abilities of approximately 1 to 5 IQ points for an additional year of education. The effects persisted across the life span and were present on all broad categories of cognitive ability studied. The study is about education in general and not about mathematics teaching specifically, so it supports a general conclusion: part of what the correlation between IQ and math reflects is what school does to the tests, not only what ability does to school. The page on whether you can improve your IQ takes up what that does and does not mean.

The honest summary on direction has three parts. Reasoning ability predicts later math achievement. In the pooled longitudinal samples, math and reading also predicted later reasoning, although the one cross-lagged study here found that reverse path not significant, and schooling raises test scores by a modest and durable amount. And the designs that would isolate a one-way cause, such as randomizing math instruction and measuring later IQ, are rare. Anyone who states a one-way arrow in either direction is going beyond the designs.

8 What Do Studies of Adults and of Mathematically Talented Youth Add?

Almost all of the large studies of this question follow children, so what is known about adults rests on fewer and narrower samples, but those samples point the same way. The 2019 meta-analysis found that the relation between fluid reasoning and mathematics increased with age, and the German study included a Grade 13 cohort, the oldest school group in that study. Beyond schooling, three adult-relevant findings stand out.

First, mathematically talented youth followed into adulthood. In the late 1970s, 563 intellectually talented 13-year-olds, identified by the SAT as in the top 0.5 percent of ability, were assessed on spatial ability, and Kell, Lubinski, Benbow and Steiger followed them for more than 30 years, reporting in Psychological Science in 2013. The SAT mathematical and verbal reasoning subtests jointly accounted for 10.8 percent of the variance among adult outcomes, which were having patents and three classes of refereed publications. Adding spatial ability accounted for an additional 7.6 percent, a statistically significant increase. The authors concluded that spatial ability has a unique role in creativity beyond the abilities traditionally measured in educational selection. For this page, the finding means that even among people selected for very high math reasoning at age 13, a distinct ability, not captured by a math or verbal score, added to the prediction of adult accomplishment. The page on spatial intelligence covers that ability.

Second, numeracy in the general adult population. Best, Carman, Parker and Peters tracked 524 adults, aged 20 to 78 in 2008, from the RAND American Life Panel, testing numeracy in 2008 and again in 2019 and publishing the result in Psychology and Aging in 2022. Numeracy there means the ability to understand and use basic probability and numerical concepts. Using a linear mixed-effects model, they found a decline in numeracy scores beginning in later middle age, a trend that falls in between those previously found for crystallized and fluid cognitive abilities. The abstract adds that earlier cross-sectional work found positive correlations of numeracy with education attainment and with measures of fluid and crystallized intelligence. That is consistent with numeracy as a blend of both kinds of ability, and with the page on how IQ changes with age, where crystallized and fluid abilities follow different paths.

Third, the limits. The talent study is a highly selected sample, and its outcomes are patents and publications, not everyday competence with numbers. The numeracy study measures basic probability and number concepts, not the kind of mathematics taught at university. Neither compares a measured Full Scale IQ with a measured math score in the same adults. There are simply fewer adult studies than child studies, and a reader who is an adult should treat the child-based correlations as an approximation that probably carries over in direction and less certainly in size.

9 Can Someone Have a High IQ and Struggle With Math, or the Reverse?

Yes, and a correlation of this size says how often: a person far above average in reasoning will usually, but far from always, be above average in math. The table is our arithmetic, not a finding of any study, and it assumes that both scores follow a normal distribution and relate in a straight line. Under that assumption, a person two standard deviations above the mean on one measure is expected to be r times two standard deviations above the mean on the other, with a remaining spread of the square root of one minus r squared. On the IQ scale, two standard deviations above the mean is a score of 130, about the 98th percentile, which the IQ percentile calculator converts.

Read the table with three cautions. The corrected correlations (.49 and .54) remove measurement error, which a single real test score always carries, so the row with .41 and the observed values in the studies are the closer guide to what one person's two scores will do. The numbers are symmetrical, so a person two standard deviations below average in reasoning has the same 18 percent chance of above-average math under the first row. And the table concerns two measured scores, not ability, so a gap between them can come from measurement error, from a day that went badly, or from a difference in what was taught.

When a gap is real, the evidence reviewed above suggests where to look. A high reasoning score with weaker math can reflect missed instruction in a cumulative subject, limited practice, or working memory load in mental calculation. A modest reasoning score with strong math can reflect years of practice and good teaching, which raise test performance by a durable amount in the quasi-experimental studies. Neither pattern is a diagnosis, and either calls for looking at the separate scores and not at one total. The page on index score differences discusses how often gaps between indices occur and when they are worth interpreting.

10 How Can a Profile Show Reasoning, Working Memory and Learned Math Apart?

A single IQ total cannot answer whether a person reasons well, calculates well or has learned a lot of mathematics, but a profile with separate indices can show the three apart. ACIS reports scores for 20 subtests grouped into six cognitive domains, as a Full Scale IQ and six primary indices on the standard scale with a mean of 100 and a standard deviation of 15, with scaled subtest scores from 1 to 19 and a mean of 10. Each report gives percentiles and a 95 percent confidence interval. The page on how IQ scores are normed explains the scale, and the page on reliability and validity explains what a confidence interval means.

For the question of this page, three of the six indices matter. The Quantitative Reasoning Index has two subtests, Mathematical Achievement, which samples learned quantitative knowledge and familiar procedures, and Arithmetic, which asks for mental calculation and so carries a working memory load. The Fluid Reasoning Index has five subtests: Matrix Reasoning, Figure Weights, Visual Number Series, Logic Grid and Complex Relations. Visual Number Series is the one that looks most like mathematics, and it sits in the fluid reasoning index, which is consistent with the CHC placement of quantitative reasoning under Gf. The Working Memory Index has three subtests: Digit Span, Alphanumeric Sequencing and Visual Sequence. A report that shows a quantitative index well below the fluid reasoning index, for example, would be pointing at the pattern in this page's evidence: reasoning is available, but learned mathematics or the working memory that mental calculation uses is lagging. The reverse would point to learned mathematics running ahead of unfamiliar reasoning. The page on the Visual Number Series subtest and the page on the Matrix Reasoning subtest describe formats without reproducing items.

Prices and forms were read on October 20, 2026, and can change. ACIS is a one time payment with no subscription. The Quick form costs 15 dollars, has 6 subtests across 3 domains and takes about 45 minutes. The Optimized form costs 30 dollars, has 13 subtests across 5 domains and takes about 110 minutes. The Full Scale form costs 50 dollars, covers all 20 subtests across six domains and takes about 175 minutes. Breaks are allowed, there is a free trial with no card, a 5 day quality guarantee and 30 days to complete a test. The limits matter for how a score is read. ACIS is online and unsupervised, it is not a clinical or diagnostic instrument, it is not for hiring, school accommodations or admission to high IQ societies, and it is available in English only. Norms cover ages 16 to 90, and the page on the technical manual holds the documentation.

11 What Does This Not Say About You, Your Child or an Admissions Score?

These studies describe groups, and none of them tells you what a particular person can do in mathematics, why a particular child finds it hard, or what a particular admissions score means. A correlation of .41 describes how two measures move together across hundreds of thousands of people. It does not say that a child with an average reasoning score will be average in math, and the table above shows that it leaves a wide spread around any prediction.

It does not say that struggling with mathematics means a low IQ, or that excelling in it means a high one. The evidence on taught skills and direction points the other way: much of math performance is built by instruction and practice, and a gap between a reasoning score and a math score is more often a clue about learning history than about intelligence. Nothing here speaks to a learning disability in mathematics. That is a clinical question for a qualified professional who can assess the person in full, and a group correlation, or an online profile, does not answer it.

It does not turn a math test score into an IQ. Admissions tests such as the SAT, ACT and GRE mix quantitative knowledge, verbal skill, test preparation and speed, and the pages on IQ versus the SAT, IQ versus the ACT and IQ versus the GRE explain why a conversion table between them and IQ is not a measurement. For the same reason, the distinction between aptitude and intelligence matters when a school or an employer asks for a quantitative score: they are asking about a mixed construct that overlaps with IQ and does not equal it.

Finally, it does not say that math talent is just high IQ under another name. The study of talented youth found that a distinct ability, spatial ability in that case, added to the prediction of adult accomplishment. The correct reading is that mathematics and IQ overlap heavily at the population level and diverge enough at the individual level that neither stands in for the other.

12 What the Evidence Supports, Stated Narrowly

The evidence supports a strong but incomplete overlap between math performance and general intelligence, a smaller math-specific part, a contribution from working memory and taught skill, and a link that runs in both directions. Stated narrowly, the findings reviewed on this page are these.

1. In 680 studies, fluid reasoning correlated .41 with mathematics and .38 with reading, and the relation grew with age and was stronger for complex than for foundational skills.
2. In more than 70,000 English children, general intelligence at age 11 accounted for 58.6 percent of the variance in math exam results at 16, against 48 percent for English and 18.1 percent for art and design.
3. Across 240 samples, the corrected correlation of intelligence tests with school grades was .54, and .49 for mathematics and science grades, with overlapping intervals for languages.
4. German school assessments and a twin study both indicate a mathematical component beyond g, with a genetic correlation of .67 between mathematics and general intelligence in 7-year-olds.
5. Working memory relates to mathematics at a medium level, and early math knowledge predicts later achievement beyond other early skills.
6. Reasoning predicts later math more clearly than math predicts later reasoning in one cross-lagged study of referred students, while schooling raises cognitive test scores by about 1 to 5 IQ points per year in quasi-experimental studies.
7. Evidence on adults is thinner, and it comes from selected or narrow samples.

The study designs limit each of these. Most are observational, most follow children, and several use samples that are special in some way, so none supports a claim about one person's score. A score is also an interpretation, and the Standards for Educational and Psychological Testing (AERA, APA and NCME, 2014) define validity as the degree to which evidence and theory support the interpretations of test scores for proposed uses. By that definition, reading an IQ score as a prediction of one person's math grade, or a math score as a measure of IQ, is an interpretation that these studies support only in part and only for groups. The American Psychological Association's Ethical Principles of Psychologists and Code of Conduct, in the version effective January 1, 2017, asks in Standard 9.02(a) that assessment instruments be used for purposes appropriate in light of the evidence on their usefulness. Standard 9.06 asks psychologists who interpret results to consider the purpose of the assessment, test factors and the characteristics of the person assessed that might reduce the accuracy of the interpretation, and to indicate significant limitations of their interpretations. Both documents were opened on October 20, 2026. The practical reading for anyone looking at a quantitative score is to look at the separate scores, to ask which ability each one samples, and to treat a gap as a question and not as an answer.

13 Sources Behind This Page

Every figure on this page is traceable to one of the following, and each is linked at the point where it is used. Where the page does arithmetic on published numbers, for example squaring a correlation or computing the chance of a gap, it says so and attributes the result to no author.

• Peng P and colleagues. A meta-analysis on the relation between fluid intelligence and reading/mathematics: Effects of tasks, age, and social economics status. Psychological Bulletin, 2019, volume 145, issue 2, pages 189 to 236.
• Deary I and colleagues. Intelligence and educational achievement. Intelligence, 2007, volume 35, issue 1, pages 13 to 21. Summary read on the University of Edinburgh research portal on October 20, 2026.
• Roth B and colleagues. Intelligence and school grades: A meta-analysis. Intelligence, 2015, volume 53, pages 118 to 137.
• Saß S, Kampa N and Köller O. The interplay of g and mathematical abilities in large-scale assessments across grades. Intelligence, 2017, volume 63, pages 33 to 44.
• Kovas Y and colleagues. "Generalist genes" and mathematics in 7-year-old twins. Intelligence, 2005, volume 33, issue 5, pages 473 to 489.
• Peng P and colleagues. A meta-analysis of mathematics and working memory: Moderating effects of working memory domain, type of mathematics skill, and sample characteristics. Journal of Educational Psychology, 2016, volume 108, issue 4, pages 455 to 473.
• Duncan G and colleagues. School readiness and later achievement. Developmental Psychology, 2007, volume 43, issue 6, pages 1428 to 1446.
• Watkins M and Styck K. A cross-lagged panel analysis of psychometric intelligence and achievement in reading and math. Journal of Intelligence, 2017, volume 5, issue 3, article 31.
• Ritchie S and Tucker-Drob E. How much does education improve intelligence? A meta-analysis. Psychological Science, 2018, volume 29, issue 8, pages 1358 to 1369.
• Kell H and colleagues. Creativity and technical innovation: Spatial ability's unique role. Psychological Science, 2013, volume 24, issue 9, pages 1831 to 1836.
• Best R and colleagues. Age declines in numeracy: An analysis of longitudinal data. Psychology and Aging, 2022, volume 37, issue 3, pages 298 to 306.
• American Educational Research Association, American Psychological Association and National Council on Measurement in Education. Standards for Educational and Psychological Testing, 2014.
• American Psychological Association. Ethical Principles of Psychologists and Code of Conduct, Standards 9.02 and 9.06, version effective January 1, 2017.

14 Frequently Asked Questions