Quantitative reasoning test: what the name covers, what a battery scores, and how to read the index

0 The short answer

A quantitative reasoning test samples how well a person reasons with quantities and relations, and in the Cattell-Horn-Carroll (CHC) model that is a narrow ability, quantitative reasoning (RQ), inside fluid reasoning (Gf), not the same thing as knowing mathematics. What a math exam scores is mostly quantitative knowledge (Gq), a separate broad ability built through instruction. A Quantitative Reasoning Index in an intelligence battery reports the first ability, usually with some contribution from the second, which is why one index can be read two ways. The sections below show the tasks, the composites and the evidence, and a fair reading of the number.

1 What Is Quantitative Reasoning in the CHC Model?

Quantitative reasoning (RQ) is the ability to reason with quantities, mathematical relations and operators, and the CHC model files it as a narrow ability under fluid reasoning (Gf), beside induction and general sequential (deductive) reasoning. That placement comes from the factor analytic work of John B. Carroll, whose 1993 survey Human Cognitive Abilities reanalyzed the factor analytic literature and described quantitative reasoning as part of fluid or novel reasoning. The Cattell-Horn Gf-Gc tradition had treated quantitative skill differently, as an acquired, achievement-like ability, and McGrew's 2009 paper on CHC theory and the human cognitive abilities project is the paper that sets CHC theory beside Carroll's human cognitive abilities project. The result is that CHC carries two quantitative abilities at once, and which one a test samples depends on what the test asks.

The definition that matters for test design is in Schneider and McGrew's chapter on the CHC theory in Contemporary Intellectual Assessment (4th edition, 2018). They describe quantitative reasoning as reasoning with quantities, mathematical relations and operators. They add that tests of it do not require advanced knowledge of mathematics, that the computation in them is typically quite simple, and that what makes the problems hard is the complexity of the reasoning required. That sentence is the whole argument of this page in miniature. A task can be arithmetic in costume and still be a reasoning task, because the difficulty lies in seeing the relation, not in carrying out the operation.

Schneider and McGrew also say plainly that the placement is untidy. Induction and deductive reasoning are process factors, while quantitative reasoning is defined by its content, numbers and relations among them, so it mixes a process with a content. They point to confirmatory factor analyses showing that fluid reasoning tests separate into verbal, spatial or figural, and numerical or quantitative content factors. In their assessment recommendations they rank induction as the core of Gf, put general sequential reasoning second, and treat a quantitative reasoning test as a lower priority unless there is a specific concern about mathematics difficulties or another clinical reason to look at it. A battery that gives quantitative reasoning its own reported index is therefore making a design choice, not following a CHC requirement.

Timothy Keith and Matthew Reynolds illustrate the placement in their chapter on confirmatory factor analysis in the same volume. They used the Woodcock-Johnson III standardization data, more than 5,000 participants, which include two clear quantitative reasoning tests, number series and number matrices. A model in which the narrow Gf and RQ factors loaded on a broader Gf factor fit considerably better than the initial model that kept them apart. Keith and Reynolds describe this as a preliminary investigation that supports the view that quantitative reasoning is part of fluid, novel reasoning. Because the authors call it preliminary, this page treats the placement as supported in the handbook but not closed.

Fluid reasoning itself is the ability to solve novel problems that cannot be solved by retrieving something already learned. If that distinction is new, the page on fluid versus crystallized intelligence and the page on what a fluid intelligence test measures cover the broad ability, and the page on the g factor covers why the broad abilities correlate.

2 What Is Quantitative Knowledge (Gq), and Why Is It a Different Ability?

Quantitative knowledge (Gq) is the depth and breadth of declarative and procedural knowledge about mathematics, which makes it an acquired body of knowledge and a different ability from the reasoning that RQ describes. Schneider and McGrew define Gq as acquired knowledge about mathematical symbols, operations and computational procedures, along with math related skills such as using a calculator. Their examples are the vocabulary and routines a person learns in school: the meaning of a symbol, the steps of long division, the quadratic formula.

They draw three consequences from that definition. First, Gq is not strictly separate from crystallized knowledge (Gc), and they suggest it is best seen as a construct that straddles general and domain specific knowledge. Second, because the content of Gq is largely set by curriculum guides, Gq scores can be described in absolute terms (this person can multiply two digit numbers) as well as relative terms (this person's index score). Third, measures of Gq are usually selected as academic achievement tests, so they must be aligned with the student's curriculum to say anything about math difficulties, a condition that does not hold when the same kind of content is used as an aptitude test on admissions exams such as the SAT, GRE or ACT.

The two narrow abilities the chapter places under Gq are mathematical knowledge (KM) and mathematical achievement (A3). Mathematical knowledge is knowing what a symbol or theorem means, not performing operations. Mathematical achievement is measured two ways, and the difference between them is where the confusion about the whole topic starts. One method gives decontextualized calculation problems, which the authors say gets at the heart of the factor with the demands of quantitative reasoning minimized. The other method gives a scenario and a problem, so the examinee must reason to translate the word problem into something computable and then calculate. The authors state that such tests clearly draw on quantitative reasoning, a facet of Gf. A word problem is therefore a Gq task and an RQ task at once, and the two contributions are hard to separate within a single score.

The table is built from the Schneider and McGrew chapter, and the last row follows their definitions rather than a separate measurement study. A later section returns to what schooling does to scores, with the studies that exist. For the broader question of what intelligence tests do and do not cover, see the page on what IQ measures and the page on intelligence versus knowledge.

3 Which Tasks Measure Quantitative Reasoning?

Publishers measure quantitative reasoning with a small family of formats, number series, number matrices, number analogies and balance scale problems, and in the reasoning tasks the relation is the problem while the arithmetic stays simple. This section describes formats from the publishers' and handbook authors' own descriptions and reproduces no items.

The Woodcock-Johnson IV, described in the handbook chapter by Fredrick Schrank and Barbara Wendling, classifies its Number Series test as a measure of fluid reasoning (Gf) that assesses quantitative reasoning (RQ) and induction. Number Series sits in the cognitive battery. The achievement battery, which is where a reader might expect only learned mathematics, carries a quantitative reasoning test of its own: Number Matrices requires the examinee to supply the missing number from a matrix and is described as measuring quantitative reasoning. The achievement battery also includes Math Facts Fluency, which the chapter describes as requiring rapid calculation of single digit facts under a three minute limit and measuring aspects of number facility and math achievement. Applied Problems is described as a measure of quantitative reasoning, math achievement and math knowledge at once, which is the blend the previous section predicted, and the chapter pairs Applied Problems with Number Matrices in a Math Problem Solving cluster that it describes as a measure of mathematical knowledge and quantitative reasoning.

The Wechsler scales add the balance scale format. The chapter by Dustin Wahlstrom and colleagues on the WISC-V describes Figure Weights as a task in which the examinee must work out the relationship between shapes that balanced one scale and apply it to an incomplete scale within a time limit, and says it measures quantitative and inductive reasoning along with mental flexibility and set shifting. The WISC-V chapter describes Arithmetic as a subtest that appears alongside Figure Weights in the quantitative reasoning composite. In the adult WAIS-IV chapter, Lisa Whipple Drozdick and colleagues note that Arithmetic draws on quantitative reasoning even though it sits in the working memory index, and that Figure Weights was added to the WAIS-IV to expand coverage of quantitative fluid reasoning.

The Cognitive Abilities Test (CogAT) has a Quantitative Battery of three tests. Riverside Insights' test description page, read on October 6, 2026, lists Number Analogies, Number Puzzles and Number Series. It says Number Analogies uses a two by two matrix and requires the same processes as the picture analogies test with quantitative concepts in place of verbal ones. Number Puzzles at higher levels uses an equation with a missing number, and Number Series asks for the pattern in a sequence of numbers.

Sources: Schrank and Wendling and Wahlstrom and colleagues in Flanagan and McDonough (2018); Drozdick and colleagues in the same volume for the WAIS-IV; Riverside Insights for the CogAT, read October 6, 2026.

Two things follow from the formats. The reasoning tasks are described in terms of patterns, missing values and relations, in line with the Schneider and McGrew point that the computation in such tests is typically simple. And the tasks that blend calculation with reasoning, Applied Problems and Arithmetic, are described by their own authors as drawing on several abilities. The page on subtest types shows how these formats sit among the other kinds of subtest, and the page on nonverbal IQ tests covers the figural side of the same logic.

4 How Do Wechsler Batteries Report a Quantitative Reasoning Index?

On the WISC-V and the WAIS-5 the Quantitative Reasoning Index is an ancillary score built from two subtests, Figure Weights and Arithmetic, and it sits beside the five primary indices instead of replacing any of them. The Wahlstrom and colleagues chapter on the WISC-V describes the QRI as an ancillary index derived from Figure Weights and Arithmetic and intended to measure quantitative reasoning skills. They report that quantitative reasoning is closely related to g and predictive of reading and math achievement, creativity and success in giftedness programs, citing Lakin and Lohman and Robertson and colleagues. They also say the index may be of special interest when a specific learning disability in mathematics is suspected, and that a low score may reflect difficulties with mental math manipulation, a poor understanding of quantitative relationships, or low working memory. Those are interpretive hypotheses for a clinician examining a child, not findings about any one reader.

For adults, Pearson's WAIS-5 ancillary index scores flyer, read on October 6, 2026, lists a Quantitative Reasoning ancillary index made of Figure Weights and Arithmetic. The same flyer lists an Expanded Fluid index of Matrix Reasoning, Figure Weights, Arithmetic and Set Relations, so Arithmetic and Figure Weights count toward a fluid composite as well as the quantitative one. Pearson's text says the expanded indices can be useful when a closer evaluation of a domain is needed, for example when two subtests of a primary index differ unusually, or when an application such as learning disability determination in some U.S. states or admission to programs for intellectually gifted individuals requires one. The earlier WAIS-IV is described differently. According to the Drozdick chapter, its working memory index drew on quantitative reasoning through Arithmetic, which is one reason the page on WAIS-4 versus WAIS-5 is worth reading before comparing scores across editions, and the page on what the WAIS-5 is describes the current structure.

Two readings of the table matter. A Wechsler QRI and an ACIS QRI share a name and the Arithmetic subtest, but they are not the same composite, because the Wechsler version includes Figure Weights and the ACIS version lists Figure Weights under its fluid reasoning index instead. A score on one is not a prediction of a score on the other. And the Wechsler batteries treat quantitative reasoning as an ancillary score that a clinician can choose to compute, in line with the CHC handbook's view that it is a lower priority in Gf assessment. ACIS reports it as one of six primary indices. The page on the general ability index explains a related idea, a composite built from a deliberately chosen subset of subtests.

5 How Does ACIS Report Quantitative Reasoning?

ACIS reports quantitative reasoning as the Quantitative Reasoning Index (QRI), one of six primary indices, built from two subtests, Mathematical Achievement and Arithmetic. The other five are the Verbal Comprehension Index (Antonyms, Vocabulary, Information, Synonyms, Similarities), the Fluid Reasoning Index (Matrix Reasoning, Figure Weights, Visual Number Series, Logic Grid, Complex Relations), the Visual Spatial Index (Visual Puzzles, Layer Rotation, Spatial Comprehension), the Working Memory Index (Digit Span, Alphanumeric Sequencing, Visual Sequence) and the Processing Speed Index (Symbol Search, Coding). Each subtest has its own page, including Mathematical Achievement and Arithmetic, which describe the task each one sets. Figure Weights and Visual Number Series are fluid reasoning subtests in ACIS, so two numeric formats are scored in the FRI and not in the QRI. The page on Figure Weights and the page on Visual Number Series cover those tasks.

The reporting follows the same conventions as the rest of the ACIS report. Indices and the Full Scale IQ are on the standard scale with a mean of 100 and a standard deviation of 15, and subtests are scaled scores from 1 to 19 with a mean of 10 and a standard deviation of 3. The report gives percentiles and a 95 percent confidence interval. Adult norms cover ages 16 to 90. The Full Scale form includes all 20 subtests in six domains, takes about 175 minutes with breaks allowed, and cost 50 dollars as read on October 6, 2026. Prices can change. The page on how IQ scores are normed explains norm referenced scoring in general, and the page on the standard deviation of 15 explains the scale.

The ACIS QRI sits across the boundary this page has been describing. CHC places quantitative reasoning in Gf and quantitative knowledge in Gq, so an index named for quantitative performance is likely to draw on both to some degree, and a reader should not treat it as a pure measure of either. The technical manual is where ACIS documents its instrument, and this page leaves those details to it instead of paraphrasing them. What the reader can do here is read the index with the right question: not "how good is my math" but "how does my performance on quantitative tasks compare with adults of my age, and how does it compare with my own other indices".

State the limits plainly. ACIS is online and unsupervised, which differs from a clinician administering a battery in person. It is not a clinical or diagnostic instrument, it is not for hiring, for school accommodations or for admission to high IQ societies, and it is offered in English only. A quantitative index from ACIS therefore informs a reader's own understanding of their profile. It does not substitute for an evaluation by a qualified professional if a learning difficulty is the question.

6 How Does a Quantitative Reasoning Index Differ From a Math Exam?

A math exam asks whether you learned a defined body of material, and a quantitative reasoning index asks how well you reason with quantitative relations, which is why the two can disagree in either direction. The first is an achievement measure, anchored to a curriculum, so a score can be described against absolute standards such as being able to solve a type of equation. The second is a norm referenced ability measure, so a score says where performance falls relative to other adults of the same age and nothing about which topics were mastered. Schneider and McGrew state the first half directly: Gq metrics can be given both in relative terms and in absolute standards, and the absolute description is what a curriculum aligned test supplies.

The boundary is not clean, and the handbook authors say so about word problems: mathematical achievement tests that use them draw on quantitative reasoning. Tests of quantitative reasoning that use numbers require at least basic arithmetic knowledge to be attempted at all. The Woodcock-Johnson IV places Number Series in its cognitive battery and Applied Problems in its achievement battery, yet describes Applied Problems as a measure of quantitative reasoning, math achievement and math knowledge. In practice the dividing line is the purpose of the score, not the content of the item. The same cluster of problems can be labeled aptitude or achievement depending on whether the interpretation is about learning potential or about what has been taught.

Jack Naglieri and Tulio Otero press this point further in their chapter on the PASS theory in the same handbook. They argue that ability tests and achievement tests contain strikingly similar items, including simple counting and addition items that appear on both kinds of test, and that this is a problem because knowledge of math should be used to understand achievement and not to determine level of intelligence. They also argue that the correlation between ability and achievement scores, often cited as validity evidence for IQ tests, is an overestimate when content overlaps. That is one theory's critique of the field. It is useful here for one reason: it shows that the line between a quantitative reasoning index and a math exam is a live design question among test authors, not a settled one.

For the reader, three practical differences follow.

• Scale of the question. A math exam is usually about one course or one level. A quantitative index is one of several indices that together describe a cognitive profile.
• Reference group. A grade or a raw score depends on the course and the grader. An index score depends on the norm group, which is why the page on how IQ scores are normed matters.
• Interpretation. A low grade in algebra can reflect what was taught as well as how the student reasons. An index cannot separate these by itself. It can show whether the quantitative reasoning result sits with or apart from the reader's other indices.

The page on intelligence versus knowledge and the page on aptitude versus intelligence follow the same distinction outside mathematics, and the page on IQ and academic achievement reports how cognitive scores and school results relate.

7 Is a Quantitative Reasoning Index the Same as the GRE or GMAT Quantitative Section?

No: admissions tests report a quantitative score for a specific decision and a specific content list, while an index in an intelligence battery reports a norm referenced ability for a general population of adults. The ETS page on the GRE General Test Quantitative Reasoning measure, read on October 6, 2026, says the measure assesses basic mathematical skills, understanding of elementary mathematical concepts and the ability to reason quantitatively and to model and solve problems. It lists four content areas, arithmetic, algebra, geometry and data analysis, four question types, quantitative comparison, multiple choice with one answer, multiple choice with one or more answers and numeric entry, and it says a basic on-screen calculator is provided.

That content list is mathematics that a person learns. Schneider and McGrew note that the need to align a Gq measure with a student's curriculum does not apply in the same way when the measure is used as an aptitude test, as on the SAT, GRE or ACT. The ETS page describes the measure by its content and by what it assesses, not by a comparison with the general adult population, so the inference it supports is a different one from a norm referenced index. Both uses can be defensible, and they are not interchangeable.

Two consequences matter for a reader. A GRE quantitative score does not convert to an index score, and an index score does not convert to a GRE score. This page offers no conversion, and the pages on IQ versus the GRE and IQ versus the GMAT take up those two exams. The sibling pages on IQ versus the MCAT and IQ versus the bar exam make the same point for two professional exams. Preparation for any of them is a different project from reading an index. The page on how to prepare for an IQ test covers preparation for ability batteries.

Employer "numerical reasoning" tests are a third category. They are designed for selection decisions. This page does not review them, and an ACIS index is not for hiring. The page on pre-employment cognitive tests covers that setting.

8 How Strongly Are Fluid Reasoning and Mathematics Related?

Fluid reasoning and mathematics are moderately correlated, about .41 on average across a very large literature, which is strong enough to make the two related and weak enough to make them separable. A large synthesis is the meta-analysis by Peng, Wang, Wang and Lin in Psychological Bulletin (2019). It combined 680 studies with 793 independent samples and more than 370,000 participants. Fluid reasoning was moderately related to reading, with a correlation of .38, and to mathematics, with a correlation of .41. The 95 percent confidence interval for the mathematics figure runs from about .39 to .44.

A correlation of .41 has a plain translation. Squared, it is about .17, so by our arithmetic roughly 17 percent of the variation in one measure is shared with the other and about 83 percent is not. That is the quantitative footing for the separation this page has drawn. Reasoning explains part of mathematics performance, and other influences account for the rest.

The moderator results are more informative than the average. According to the authors, fluid reasoning showed stronger relations to mathematics than to reading, and within each domain it showed stronger relations to complex skills than to foundational ones. The relations increased with age, and family socioeconomic status mostly affected the relations in early development. The longitudinal syntheses found that fluid reasoning and reading or mathematics predicted each other over time even after controlling for initial performance. The authors read the pattern as consistent with children relying on fluid reasoning to learn early on, and with mathematics improvement later promoting the development of fluid reasoning as formal schooling accumulates.

Three cautions apply. The design is correlational, so the meta-analysis supports a relation and a two way developmental pattern, not a claim that raising one score raises the other by a stated amount. The abstract describes fluid reasoning generally and does not isolate quantitative reasoning tasks from other fluid tasks, so .41 is a figure for Gf and mathematics, not for RQ alone. And an average over 793 samples says nothing about any one person. A reader whose quantitative index differs from the fluid reasoning index is within the range this literature expects, a point a later section turns into numbers.

For the wider evidence on how cognitive scores relate to school results, the page on IQ and academic achievement goes beyond mathematics, and the page on what IQ measures sets out the abilities behind the correlations.

9 How Much Do Schooling and Practice Change a Quantitative Score?

Schooling raises cognitive test scores by a small but consistent amount, retesting produces an adjusted practice effect of .26, and neither result says how much of a quantitative index is knowledge and how much is reasoning. Two meta-analyses give the sizes.

Ritchie and Tucker-Drob (2018) meta-analyzed three kinds of quasiexperimental studies of education and intelligence: studies controlling for earlier intelligence, studies using compulsory schooling policy changes as instrumental variables, and regression-discontinuity studies on school-entry age cutoffs. Across 142 effect sizes from 42 data sets with over 600,000 participants, they found consistent evidence of beneficial effects of education on cognitive abilities of approximately 1 to 5 IQ points for an additional year. The effects persisted across the life span and were present on all broad categories of cognitive ability the authors studied. The designs are the reason the causal verb is defensible here: these studies were chosen to get at education as a cause, not only as a correlate.

Hausknecht and colleagues (2007) summarized practice and coaching effects when people retake cognitive ability tests, a common situation in selection and admissions. Across 50 studies, 107 samples and 134,436 participants, they reported an adjusted overall effect size of .26. Effects were larger when practice was accompanied by coaching and when identical forms were used. The setting was applicant retesting for organizational and educational purposes, so the figure describes that context and not an unproctored online battery taken once.

What the three studies do not do is split a quantitative score into its Gq and RQ parts. The CHC definitions imply a prediction, that a measure of acquired mathematical knowledge should respond more to instruction than a measure built on novel relations, but that is a consequence of the definitions and not a result these studies report. The practical reading is cautious. A quantitative index taken after a period of heavy mathematics study may sit higher than it would otherwise, and an index taken by someone who has not used mathematics in years may sit lower, in both cases possibly without any change in how well they reason with novel relations. The page on whether you can improve your IQ takes up the wider question, and the page on whether the Flynn effect matters for scores covers population level changes over decades.

10 How Should a Quantitative Reasoning Index Be Read Within a Profile?

Read a quantitative reasoning index against the reader's other indices first, then against the population, because the gap between two indices is a smaller signal than it looks. An index on the standard scale has a mean of 100 and a standard deviation of 15. By normal curve arithmetic, an index of 115 falls at about the 84th percentile, 85 at about the 16th, and 130 at about the 98th. The page on IQ score versus percentile and the sibling page on converting a percentile to an IQ explain the conversion, and the percentile calculator does it for any score.

Gaps are noisier than single scores. Two indices that are positively correlated differ by less than two unrelated scores would, but the difference still varies from person to person. If both indices have a standard deviation of 15 and correlate at r, the standard deviation of the difference between them is 15 times the square root of 2 times (1 minus r). The table applies that formula at three illustrative correlations. These are our arithmetic and are not values published by ACIS or by any test publisher.

The reading is that a 15 point gap in one stated direction, one full standard deviation of the scale, is a gap that between about 6 and 13 percent of people would show in a general population under these assumptions. It is not rare, and it is not by itself a sign of a weakness or a talent. The page on how a Full Scale IQ is composed explains why a composite can hide differences between indices, and the page on reliability and validity explains why each index carries error that makes small gaps hard to interpret.

Possible explanations for a gap belong in the category of hypotheses to check. If the quantitative index is below the fluid reasoning index, the Wahlstrom and colleagues chapter lists mental math manipulation, understanding of quantitative relationships and working memory among the factors a clinician considers in children, and the Gq definition adds the amount of mathematics learned. If it is above, the same logic runs the other way: more exposure to mathematics can raise a measure that includes acquired knowledge. Which explanation fits depends on facts a score cannot supply, such as schooling, occupation, language and health. The reader can look at the working memory and processing speed indices, at the subtest pages for Arithmetic and Mathematical Achievement, and at the page on working memory tests, and then ask a professional if the question matters for a decision.

11 What Does a Quantitative Reasoning Score Not Tell You?

A quantitative reasoning score does not diagnose a math learning disability, does not measure how much mathematics you know, does not rank you for a job or an admission, and does not describe a person beyond the day and conditions of testing. Each limit comes from a source.

First, it does not diagnose. The handbook chapter on the WISC-V mentions specific learning disability in mathematics as a situation where the index may be of special interest to a clinician. That is a clinical use by a qualified examiner, who under the APA guidance discussed below draws on multiple sources of information. Group statistics and index scores are not individual diagnoses, and ACIS is not a clinical or diagnostic instrument. A reader worried about a persistent math difficulty should ask a licensed professional for an evaluation, and the page on neuropsychological testing for adults describes what such an evaluation involves.

Second, it does not measure how much mathematics a person knows. That is the Gq question, and curriculum aligned achievement tests answer it with absolute standards, which an index does not give.

Third, it is not a selection tool. ACIS is not for hiring, for school accommodations or for admission to high IQ societies, and who administers a test and under what conditions matters for those purposes.

Fourth, it reflects conditions. ACIS is online and unsupervised, English only, and a quantitative word problem places reading and language demands on the examinee that a number series does not.

Fifth, it does not say what a person can learn. The Peng meta-analysis finds that mathematics learning and fluid reasoning predict each other over development, and the Ritchie meta-analysis finds that education is associated with higher cognitive scores. Neither supports treating an index as a ceiling on what instruction can build.

12 What Do the Standards and APA Guidance Say About Reading a Score Like This?

The Standards for Educational and Psychological Testing (AERA, APA and NCME, 2014) and the American Psychological Association's assessment guidelines both treat a score as evidence to be interpreted for a stated purpose, not as a fact about a person. The Standards are the joint publication of the American Educational Research Association, the American Psychological Association and the National Council on Measurement in Education, and the three organizations provide them in an open access files page, read on October 6, 2026. In their chapter on the validity evidence for intelligence tests, Alyssa Montgomery, Erica Torres and Jamie Eiseman organize the Standards' validity evidence under test content, response processes, internal structure, relations to other variables, and fairness, bias and consequences. They also quote the Standards' remark that the validation process never ends, because there is always more information to gather about a test and the inferences drawn from it. Applied to this page, that means a Quantitative Reasoning Index needs evidence for what its tasks sample, how people respond to them, how the subtests combine, and how the index relates to outside criteria, and a reader should ask where that evidence is documented. For ACIS it is the technical manual.

The American Psychological Association's Guidelines for Psychological Assessment and Evaluation, approved by the APA Council of Representatives in March 2020, add two points that bear directly on a quantitative score. Guideline 7 says psychologists strive to use multiple sources of relevant and reliable clinical information, and its rationale says individual performance on a psychological test is only one piece of an assessment. Guideline 8 says test selection, scoring and administration should reflect the appropriate normative comparison, situational influences, effort and standardized administration. A self administered online index meets the first condition only in part, because it is one source, and it differs on the last, because administration is unsupervised. Neither guideline forbids reading such a score for self understanding. Both argue against using it alone for a consequential decision.

The practical reading of the standards and guidelines for this topic is short.

• Ask what the index is meant to support, understanding a profile or deciding something about a person, and use it only for the first unless a qualified examiner is involved.
• Read the percentile and the confidence interval together, and treat a single point as the middle of a range that reflects measurement error.
• Compare the index with the other indices and with life context before drawing a conclusion, and leave a diagnostic question to a clinician.

The page on what intelligence is and how researchers define it is a good next read for the wider frame.

13 Sources Behind This Page

Every figure and claim above is traceable to one of the following, and each is linked or named where it is used. Page counts and chapter titles are given as printed. The handbook chapters were read in a local copy of Contemporary Intellectual Assessment (4th edition), and the squared correlation and the table of index gaps are our own calculations on published figures or on the stated assumptions. McGrew (2009) is cited for the integration of the two traditions named in its title, and its text was not available to us beyond the publisher record.

• Carroll JB. Human Cognitive Abilities: A Survey of Factor Analytic Studies. Cambridge University Press, 1993.
• McGrew KS. CHC theory and the human cognitive abilities project: Standing on the shoulders of the giants of psychometric intelligence research. Intelligence, 2009, volume 37, issue 1, pages 1 to 10.
• Schneider WJ, McGrew KS. The Cattell-Horn-Carroll theory of cognitive abilities (chapter 3, pages 73 to 163). In Flanagan DP, McDonough EM, editors, Contemporary Intellectual Assessment: Theories, Tests, and Issues, 4th edition. Guilford Press, 2018.
• Other chapters of the same volume (Guilford Press, 2018): Naglieri JA, Otero TM, Redefining intelligence with the Planning, Attention, Simultaneous, and Successive theory of neurocognitive processes (chapter 6, pages 195 to 218); Wahlstrom D, Raiford SE, Breaux KC, Zhu J, Weiss LG, the Wechsler Preschool and Primary Scale of Intelligence, Fourth Edition, Wechsler Intelligence Scale for Children, Fifth Edition, and Wechsler Individual Achievement Test, Third Edition (chapter 9, pages 245 to 282); Schrank FA, Wendling BJ, The Woodcock-Johnson IV: Tests of Cognitive Abilities, Tests of Oral Language, Tests of Achievement (chapter 14, pages 383 to 451); Drozdick LW, Raiford SE, Wahlstrom D, Weiss LG, The Wechsler Adult Intelligence Scale, Fourth Edition and the Wechsler Memory Scale, Fourth Edition (chapter 16, pages 486 to 511); Montgomery A, Torres E, Eiseman J, Using the Joint Test Standards to evaluate the validity evidence for intelligence tests (chapter 30, pages 841 to 852); Keith TZ, Reynolds MR, Using confirmatory factor analysis to aid in understanding the constructs measured by intelligence tests (chapter 31, pages 853 to 900).
• Peng P, Wang T, Wang C, Lin X. 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.
• Ritchie SJ, Tucker-Drob EM. How much does education improve intelligence? A meta-analysis. Psychological Science, 2018, volume 29, issue 8, pages 1358 to 1369.
• Hausknecht JP, Halpert JA, Di Paolo NT, Moriarty Gerrard MO. Retesting in selection: A meta-analysis of coaching and practice effects for tests of cognitive ability. Journal of Applied Psychology, 2007, volume 92, issue 2, pages 373 to 385.
• Pearson. WAIS-5 ancillary index scores flyer. Pearson Education, 2024, read October 6, 2026.
• Educational Testing Service. GRE General Test Quantitative Reasoning overview. Read October 6, 2026.
• Riverside Insights. CogAT test descriptions. Read October 6, 2026.
• American Educational Research Association, American Psychological Association, National Council on Measurement in Education. Standards for Educational and Psychological Testing. AERA, 2014, read October 6, 2026.
• American Psychological Association. Guidelines for Psychological Assessment and Evaluation. APA Task Force on Psychological Assessment and Evaluation Guidelines, approved by the APA Council of Representatives, March 2020.

14 Frequently Asked Questions