How big a gap between index scores is actually unusual

0 The short answer

A gap between two index scores has to pass two separate tests before it deserves attention: it must be larger than measurement error (a critical value), and it must be rare among people with the same overall level (a base rate), and the second test fails far more often than readers expect once every pair in a profile is compared. Simulation work on the WAIS-IV found that 49 percent of normal individuals have at least one 15 point gap among its four indices, and 16 percent have at least one gap of 25 points. A six index profile has 15 pairs, so large gaps are even easier to find. Decide which comparison matters before looking, and treat the rest as the expected texture of a normal profile.

1 What Does a Gap Between Two Index Scores Tell You?

A gap between two index scores answers three separate questions, and most confusion comes from treating them as one. The first question is whether the gap is real, meaning larger than the noise that any score carries. The second is whether it is unusual, meaning rare among people in the reference group. The third is whether it means anything, meaning whether the pattern predicts something that matters outside the test. A gap can pass the first test and fail the second, and it can pass both and still fail the third.

The first two questions have names in the Wechsler manuals. A critical value is the smallest difference that is statistically reliable at a stated confidence level. A base rate is the percentage of the normative sample that shows a difference of at least that size. The excerpt of the WAIS-IV Technical and Interpretive Manual hosted by Pearson Clinical Australia states the distinction in one sentence: a statistically significant difference between index scores may not indicate a clinically significant difference, and the frequency of occurrence in the normative sample, not just the critical value, should be considered. The same excerpt reports that Sattler suggested treating differences that occur in less than 15 percent of the normative sample as unusual. That 15 percent line is a convention from one author, quoted by the publisher, and not a law of measurement.

The third question, whether a gap means anything, belongs to validity, and it is the one least often answered in consumer pages. The page on reliability and validity explains why a score can be precise and still be silent about a particular conclusion. This page takes the three questions in order. The next section covers the critical value, then the base rate for one pair, then the arithmetic of many pairs, then the research on whether uneven profiles carry any information beyond the overall score.

Two scope notes keep the page honest. First, the studies cited here are mostly about Wechsler batteries, the instruments with the largest published literature on index scatter, and the reasoning transfers to any test that reports several indices on the same scale, but the exact percentages do not. Second, nothing here is diagnostic. Group statistics describe how often a pattern occurs in normal samples, and a pattern that is common in the general population says nothing about whether a particular person has any condition. The page on the General Ability Index and the Full Scale gap covers one specific pair, and this page deliberately leaves that pair to it.

2 How Big Does a Gap Have to Be Before It Is Real?

A gap is statistically reliable when it exceeds 1.96 times the standard error of the difference, which is the square root of the two scores' squared standard errors of measurement added together. Each index score is an estimate with error around it. When two estimates are compared, the errors of both enter the difference, so the difference is less precise than either score alone. The Standards for Educational and Psychological Testing (AERA, APA and NCME, 2014) say this in Standard 2.4: when a score interpretation emphasizes differences between two observed scores of an individual, reliability and precision data, including standard errors, should be provided for such differences. Its comment adds that when interpretation centers on the peaks and valleys of a profile, the reliability of score differences is critical.

A published report lets us check the formula. Pearson's sample WAIS-5 score report, dated September 16, 2024, prints a standard error of measurement (SEM) beside each primary index and a critical value, "reported at the .05 level", beside each pairwise comparison. The SEMs are 4.50 for the Verbal Comprehension Index, 4.74 for the Visual Spatial Index, 3.00 for the Fluid Reasoning Index, 4.50 for the Working Memory Index and 5.61 for the Processing Speed Index. For the Verbal Comprehension and Visual Spatial pair, the square root of 4.50 squared plus 4.74 squared is 6.54, and 1.96 times 6.54 is 12.8, which is the printed critical value of 12.81. We repeated the calculation for all ten pairs on the page and each matches the printed value to the second decimal place (our arithmetic). Table 1 shows four of them.

Two lessons follow. The critical value is not one number for every pair: here it runs from 10.60 to 14.39 depending on which two indices are compared, because indices with larger SEMs, such as Processing Speed, make noisier differences. And a critical value near 11 to 14 points means that a gap of 10 points between two indices on a sample like this one is within measurement error. The page on the standard deviation of 15 explains why 15 points is the size of one standard deviation on this scale, which gives a feel for the scale: a gap of 10 to 14 points can arise from error alone.

A rough check works for a reader without the printed critical values. If a report prints a 95 percent confidence interval around each index, as the ACIS report does, the half width of each interval approximates 1.96 times that score's standard error. The half width of a difference is then about the square root of the two half widths squared and added. Two intervals that each extend about 8 points either side of the score give a reliable gap of about 11 points. This is our approximation, and it assumes symmetric intervals. Intervals around estimated true scores are often not symmetric, so it is a guide and not a substitute for the critical values of a full report.

A reliable gap is also not a rare one. The report uses the .05 level, which means that for any one pair, a gap beyond the critical value would appear by chance in about 5 of 100 comparisons if the person's true abilities were identical. That is a statement about reliability. It says nothing about how many people have gaps of that size, which is the next question.

3 How Rare Is a Gap of a Given Size for One Pair of Indices?

For one pair chosen in advance, the share of people with a gap of at least a stated size is the base rate, and it depends on the pair, on the size of the gap and on the reference group. Base rates are tabulated from the standardization sample, not computed from the critical value. The sample WAIS-5 report prints a base rate beside every comparison and states that "base rates are reported by ability level", and a note on a later page says the Full Scale IQ level is used when ability level is selected as the reference group, so the comparison group is defined by overall level and not by age alone. Table 2 reproduces the ten primary pairs.

Read the table the way the Sattler convention suggests. The Verbal Comprehension and Working Memory gap of 27 points has a printed base rate of 5 percent or less, so it passes both tests for that one pair. The Verbal Comprehension and Processing Speed gap of 16 points is significant but has a printed base rate of 25 percent or less, so it is reliable and not unusual. The 21 point and 19 point gaps both sit at 10 percent or less. The report prints these as bands, not exact percentages, so the table cannot say more than the bands do.

Why do base rates vary by pair? Because the indices are correlated, and the strength of the correlation controls how far apart two scores wander. If two indices correlate at 0.7, the difference between them has a standard deviation of about 11.6 points on the standard scale, which is 15 times the square root of 0.6 (our arithmetic). If they correlate at 0.5, it is 15 points. Mainly, a pair that moves together closely produces small gaps, and a pair that shares less produces larger ones. That is also why a Verbal Comprehension and Working Memory gap and a Verbal Comprehension and Fluid Reasoning gap of the same size need not have the same base rate.

Our simulation, described in the section on six indices below, puts a number on it under a simplifying assumption. If one pair of indices correlates at 0.7, about 21 percent of people show a gap of 15 points or more between them, about 9 percent a gap of 20 or more and about 4 percent a gap of 25 or more. Those are illustrations, not ACIS statistics and not any test's published base rates. The takeaway is the shape: for a single pair chosen in advance, 15 points is uncommon but far from rare, and 25 points is rare.

One caution about reading the printed band. A base rate such as "10 percent or less" is conditional on the reference group the report uses. The sample report compares the examinee with a reference group defined by overall ability level. A different report could compare with everyone of the same age, and the same gap would then have a different base rate. When a score report prints a base rate, check which group it refers to before comparing it with any figure from a study.

4 Why Does Almost Everyone Have Some Large Gap Somewhere in a Profile?

Almost everyone has some large gap because a profile is a set of many comparisons, and the chance that at least one of them is large grows quickly with the number of comparisons. Four indices make 6 pairs, five make 10, six make 15, and twenty subtests make 190 (our arithmetic). Suppose each pair had a 5 percent chance of crossing its critical value and the pairs were independent. The chance that at least one of 15 crosses would be 1 minus 0.95 to the 15th power, which is 54 percent (our arithmetic). The pairs are not independent, because they share indices, so that figure only illustrates the principle. The real rates have to be simulated.

The sample WAIS-5 report shows the sharing. Four of its ten primary pairs are flagged as significant, and all four include the Verbal Comprehension Index, the highest of the five indices. One high index produces several flagged pairs at once, which is not four separate findings. The same page compares each index with the mean of the five and flags two of them (Verbal Comprehension as a strength and Working Memory as a weakness). The report prints each comparison at the .05 level, and the page states no adjustment for the number of comparisons made. The reader therefore has to supply the judgment about how many comparisons were looked at.

One quantification comes from an abstract by Carroll for the 31st annual meeting of the National Academy of Neuropsychology, Rates of Apparently Abnormal WAIS-4 Patterns in the Normal Population (2011). It reports that 49 percent of normal individuals had one or more 15 point index differences, 35 percent had a 20 point difference between some two indices, and 16 percent had at least one 25 point difference. For subtests, the same abstract reports that 78 percent had at least one subtest 3 points below their subtest mean, 61 percent at least one 4 points below and 25 percent at least one 5 points below. This is a conference abstract and not a peer reviewed article, and we cite only the figures it prints. A peer reviewed paper applies the same Monte Carlo approach to memory indices: Carrasco and colleagues (Applied Neuropsychology: Adult, 2015) used Monte Carlo simulation, validated against standardization data, and found that 15 point differences between any two memory indices occurred in 60 percent of the normative sample, and between memory and ability indices in 48 percent. They concluded that Wechsler index discrepancies are normally common and therefore not clinically meaningful when numerous such comparisons are made, and that explicit prior interpretive hypotheses are needed to reduce the number of comparisons and the false-positive conclusions that follow.

Why simulate instead of using a formula? Crawford, Garthwaite and Gault described the general method in Neuropsychology (2007): a Monte Carlo procedure that needs only the matrix of correlations between tests and estimates the share of the healthy population expected to show a given number of abnormally low scores or abnormally large pairwise differences, contrasted with the use of binomial probabilities. A binomial calculation treats each comparison as an independent coin flip, which shared indices make false. Schretlen and colleagues tested the two approaches against real people in the Journal of the International Neuropsychological Society (2008): among 327 neurologically normal adults aged 18 to 92, observed rates of abnormal scores were generally closer to Monte Carlo predictions than to binomial ones, and they rose with the number of tests administered.

The practical consequence is a change of question. "Is my largest gap large?" has an almost automatic yes for a six index profile. "Is this specific gap, which I had a reason to examine before seeing the scores, unusual?" is the question a base rate answers. The page on what each IQ subtest measures describes the 20 tasks that sit under the indices, which is where the subtest side of the same issue begins, and the next section turns the index side into numbers.

5 How Common Are Large Gaps Among Six Indices? A Simulation With Stated Assumptions

Under a simple assumption that every pair of indices correlates equally, at least one gap of 15 points among six indices occurs in about 81 percent of profiles when the correlation is 0.7, and the share falls only slowly as the correlation rises. The published Monte Carlo studies use the real correlation matrix of each battery. We do not publish the ACIS correlation matrix on this page, and we do not need it to show the principle. We simulated 3 million profiles of equally correlated indices on the standard scale (mean 100, standard deviation 15), rounded each score to a whole number as a report does, and counted profiles whose highest and lowest indices differ by at least 15, 20 and 25 points. Every number in Table 3 is our own arithmetic under the equal correlation assumption. It is not an ACIS statistic, not a published base rate and not a claim about any person.

Three readings of Table 3 matter. First, the one pair rows and the six index rows are very different: at a correlation of 0.7, a 20 point gap is 9 percent for one pair and 55 percent when any of six indices is allowed to supply it. Second, the four index rows land near the published figures from Carroll's abstract (49, 35 and 16 percent for 15, 20 and 25 points): between our 0.7 and 0.8 columns for the 15 point gap, and close to the 0.7 column for the other two. Real indices correlate unequally, so that agreement is a plausibility check on the method and not a validation of any figure. Third, correlation is the dial that moves everything. Indices that share more variance produce smaller gaps, and indices that share less produce larger ones.

What would the correlation be for a given battery? It differs by battery and by sample, and it is the quantity that the technical documentation of a test reports. ACIS documents its own instrument on the technical manual page, and this page does not quote from it. The honest summary for a six index profile is that a gap of 15 points somewhere is the usual case, a gap of 20 is common, and a gap of 25 occurs in anything from roughly a tenth to well over half of profiles depending on how related the indices are.

6 What Do Studies of Healthy Adults Show About Uneven Profiles?

Studies of healthy adults consistently find that low scores and wide scatter are normal features of a profile, and that the amount of scatter depends on how many scores are compared. Binder, Iverson and Brooks reviewed the normative literature in Archives of Clinical Neuropsychology (2009). They found that normative participants often have large discrepancies between their best and worst scores, and that when abnormality was defined as a score more than one standard deviation below the mean, the great majority of participants in batteries with at least 20 measures had one or more abnormalities. Restricting samples to above average IQ or education, or using a stricter definition such as two standard deviations below the mean, did not eliminate abnormal scores. They concluded that abnormal performance on some proportion of tests in a battery is psychometrically normal, and recommended that test developers publish base rate tables.

The WAIS-IV literature applies the same reasoning at the index level. Grégoire, Coalson and Zhu analyzed the four WAIS-IV index scores in Assessment (2011), using each person's mean of the four indices as the baseline, so that each index is compared with the person's own average and not with one other index. They found that more than 70 percent of the normative sample had at least one index that differed significantly from that personal mean, that this variability appeared to have little relationship to age or gender, and that it was strongly related to the Full Scale IQ. That last finding leads into the next section.

Crawford, Garthwaite, Longman and Batty extended the toolkit in the Journal of Neuropsychology (2012), providing methods to estimate the percentage of the normative population expected to show at least as many abnormal deviations or abnormal pairwise differences as a given case, and a Mahalanobis distance index as a multivariate estimate of how abnormal a whole index profile is. The idea behind both is the one this page makes: judge a profile against how often profiles like it occur, and do not pick out its most extreme gap.

Brooks, Holdnack and Iverson built base rates from 900 healthy adults in Assessment (2011) and validated them on 28 patients with moderate or severe traumatic brain injury. Healthy people obtained some low scores on the WAIS-IV and WMS-IV, with prevalence rates increasing with fewer years of education and lower predicted intelligence, and the patients were 13 times more likely than the controls to be identified as having a low cognitive profile. That second result illustrates why base rates are used in clinical work: they let a clinician set an informed threshold. It is not a statement that a large gap in a healthy reader indicates anything.

What these studies share is a design. Each starts from healthy normative samples, measures how often a pattern occurs, and then asks how much weight the pattern can bear. They are descriptive base rate studies. None of them shows that a person with a larger gap differs in any life outcome, and none is a basis for reading a gap as a trait. The page on the CHC model describes the abilities that each index is built to represent, which is the starting point for deciding whether a particular comparison has any reason to be made.

7 Does Overall Ability Level Change How Uneven a Profile Should Look?

Index scatter depends on overall level, and the meta-analytic evidence that correlations among ability tests fall as ability rises implies that wider gaps are expected in high scoring profiles. Three lines support the dependence. First, the Grégoire study above found index scatter strongly related to Full Scale IQ, and the Brooks study found that the prevalence of low scores depended on predicted intelligence. Second, Pearson's sample report prints base rates "by ability level", which is the publisher treating the same gap as having a different frequency at different levels of the Full Scale IQ. Third, Blum and Holling's meta-analysis in Intelligence (2017) analyzed 106 articles containing 408 studies and found that the mean correlation and the g loadings of cognitive ability tests decrease with increasing ability, the pattern called Spearman's law of diminishing returns.

The link between the last finding and index gaps is our inference, and it is mechanical. Table 3 shows that when indices correlate less, gaps between them are larger. If indices correlate less in higher ability groups, larger gaps are expected there. A reader whose Full Scale IQ is well above average should therefore expect wider scatter than a base rate for the whole population suggests, and a published base rate that is conditional on ability level is the right comparison. The page on gifted adults discusses uneven profiles in that group, and the page on twice exceptional people covers the narrower situation where a strong ability and a disability coexist, a clinical topic that this page does not address.

The same reasoning needs a caution. The studies show an association between level and scatter in normative samples. They do not show that every high scorer has an uneven profile, and they do not say what causes a particular person's gap. A reader should not conclude from a wide gap that they are gifted, and should not conclude from a flat profile that they are not. The page on what IQ measures explains why an overall score and a profile answer different questions.

Describe gaps in IQ points, not in percentile points. Equal steps in percentile are unequal steps in IQ: on the standard scale, going from the 50th to the 60th percentile adds about 3.8 IQ points, while the same ten percentile points near the top add several times that (our arithmetic). A gap quoted as "20 percentile points" can therefore hide a trivial IQ difference near the middle and a large one near the top. The page on why IQ scores and percentiles cannot be averaged explains the shape problem, and the IQ percentile calculator converts any score.

8 Do Uneven Profiles Predict Anything Beyond the Overall Score?

The best available evidence says the Full Scale IQ keeps most of the predictive weight, the index scores add small increments, and reviews of profile analysis have challenged the idea that gaps between scores carry independent meaning. Canivez examined this directly for the WAIS-IV in Psychological Assessment (2013). The Full Scale IQ accounted for statistically significant and generally large portions of the variance in scores on the Wechsler Individual Achievement Test, second and third editions. The four index scores combined added statistically significant increments in most achievement scores over and above the Full Scale IQ, but the effect sizes ranged from trivial to medium, and individually each index provided trivial to small unique contributions. Canivez concluded that the Full Scale IQ should retain primacy and the greatest interpretive weight.

Notice what that study did and did not test. It asked whether index scores predict academic achievement beyond the overall score, which is a test of the indices as separate predictors. It did not ask whether a gap between two indices predicts anything, which is the narrower claim that underlies most profile reading. For that, the useful reference is a review: McGill, Dombrowski and Canivez, Cognitive profile analysis in school psychology: History, issues, and continued concerns (Journal of School Psychology, 2018). It traces the history of cognitive profile analysis, the class of methods that encourage diagnostic decisions or treatment recommendations from strengths and weaknesses in ability score profiles, notes that numerous empirical studies and reviews have challenged long standing assumptions about their utility, and describes new and continued concerns with those methods. That review concerns school psychology, and this page is about adult self assessment, so we cite it for the state of the debate and not for any adult finding.

The Standards state the principle behind the caution. Standard 1.14 says that when interpretation of subscores, score differences or profiles is suggested, the rationale and relevant evidence in support of such interpretation should be provided. Its comment adds that evidence for the validity of interpretations of two or more separate scores would not necessarily justify a statistical or substantive interpretation of the difference between them. Put plainly, a test can have valid indices and still lack evidence that a particular gap between two of them means something. The burden of proof sits with the person who wants to read the gap.

None of this says that profile differences are meaningless or that indices should be ignored. The indices measure different broad abilities, which the page on the CHC model lays out, and a person may reasonably care which one is relatively strong. The evidence says something narrower: do not expect a gap to carry independent predictive information that the overall score and the indices separately do not, and do not treat a gap as a finding without evidence specific to that gap. The page on the General Ability Index covers the one comparison, the general ability composite against the Full Scale, where publishers have offered a specific rationale, and it gives that pair its own treatment.

9 How Should You Read Your Own Index Profile?

Read a profile in a fixed order: overall level first, then a short list of comparisons chosen before looking at the gaps, then reliability, then base rate, then context. The order protects against the main failure, which is to scan every pair, find the largest gap and build a story around it. The steps below apply to any report that prints several indices on the standard scale.

1. Start with the overall score and the intervals. Note the Full Scale IQ and the width of the 95 percent confidence interval around each index. Wide intervals mean that large gaps are easier to produce by error alone.
2. Choose a small number of comparisons in advance. Pick the comparisons for which you had a reason before seeing the numbers, such as "does my Working Memory Index trail my Verbal Comprehension Index?". The page on verbal and performance IQ explains why the old two part split gave way to indices, and the page on subtest types shows what sits under each. The fewer the comparisons, the more a base rate means.
3. Check reliability. Use the half width approximation from earlier: take the square root of the two half widths squared and added. A gap smaller than that is within error.
4. Check the base rate for the pair, not for the profile. Compare the gap with a published base rate for that pair and that reference group. Where only illustrations are available, such as Table 3 here, use the one pair rows if the comparison was chosen in advance and the six index rows if it was not.
5. Look underneath the index. An index is built from subtests, and a gap can come from a single task. Processing speed, for instance, is built from two subtests in the ACIS profile (Symbol Search and Coding), so one unusual performance moves the index a lot. A gap driven by one subtest is a statement about that task and not about a broad ability.
6. Consider the conditions. Online, unsupervised testing does not control the room, the noise, the sleep before the session or the device, which adds a source of variation that a supervised battery tries to remove. The page on how accurate online IQ tests are discusses that limit.

Here is a worked example with an invented profile, not a real person and not an ACIS result. Suppose the six indices are Verbal Comprehension 118, Quantitative Reasoning 111, Visual Spatial 109, Fluid Reasoning 104, Processing Speed 102 and Working Memory 96. The largest gap is 22 points between Verbal Comprehension and Working Memory, and the pairs at or above 15 points are that one, Verbal Comprehension against Processing Speed (16) and Quantitative Reasoning against Working Memory (15). In Table 3, the share of six index profiles with some gap of 20 or more is 78 percent at a correlation of 0.5, 55 percent at 0.7 and 31 percent at 0.8. So a 22 point gap somewhere is typical, and it should not prompt a story. If the reader had asked before seeing the scores whether Working Memory trails Verbal Comprehension, the one pair rows apply instead: 20 points is 19 percent at 0.5, 9 percent at 0.7 and 4 percent at 0.8. With confidence intervals about 8 points either side, the critical value is about 11 points, so the gap is reliable. The fair conclusion is that this pair shows a reliable, moderately unusual gap that is worth a note and a second look at the subtests beneath it, and that it supports no conclusion about the person.

10 What Are the Most Common Misreadings of an Uneven Profile?

The most common misreadings treat a gap as a diagnosis, a verdict on which score is real, or a flaw in the test. Five come up repeatedly.

The first is "a 15 point gap means one ability is impaired". A 15 point gap is one standard deviation on the scale, and 49 percent of normal individuals had one somewhere among four indices in the abstract above. Group base rates describe how common a pattern is. They do not describe what a person has. The pages on ADHD and IQ and autism and IQ cover those topics separately, and nothing on this page is a screen for either.

The second is "my highest index is my real intelligence". Every index carries error, and the highest of several noisy scores is more likely than the others to have been pushed up by error. That is a property of selecting a maximum from several imprecise numbers, and it is the reason the overall score and the intervals come first. The Full Scale IQ, in the Canivez findings above, carries the largest share of prediction.

The third is "a large gap means the Full Scale IQ is meaningless". The evidence does not say that. Where a publisher offers a specific alternative composite for a specific pair, as with the General Ability Index, the alternative is a supplement and not a replacement, as the page on the General Ability Index explains. The evidence reviewed above points the other way: Canivez concluded that the Full Scale IQ should retain primacy.

The fourth is "two tests gave me different profiles, so one of them is wrong". Different batteries use different tasks, different norms and different index definitions, so profiles differ without either being wrong. The page on WAIS-IV and WAIS-5 differences covers the case of two editions of one family of tests.

The fifth is "the gap is the interesting part". A gap can be the least informative part of a report. The overall level, the width of the intervals and the pattern across subtests carry more information, and the base rate research says that a gap found by scanning many pairs is expected to appear whether or not anything is behind it.

11 What Does an ACIS Profile Show, and What Should You Not Conclude From It?

An ACIS report gives a Full Scale IQ and six primary indices on the standard scale, each with a percentile and a 95 percent confidence interval, and it is a measurement to read with the cautions above, not a clinical finding. The six indices are Verbal Comprehension (Antonyms, Vocabulary, Information, Synonyms, Similarities), Fluid Reasoning (Matrix Reasoning, Figure Weights, Visual Number Series, Logic Grid, Complex Relations), Quantitative Reasoning (Mathematical Achievement, Arithmetic), Visual Spatial (Visual Puzzles, Layer Rotation, Spatial Comprehension), Working Memory (Digit Span, Alphanumeric Sequencing, Visual Sequence) and Processing Speed (Symbol Search, Coding). Scores use the standard scale with a mean of 100 and a standard deviation of 15, and scaled subtest scores run from 1 to 19 with a mean of 10 and a standard deviation of 3. Adult norms cover ages 16 to 90.

The number of comparisons you can make depends on the form. Prices read on October 13, 2026: the Quick form costs 15 dollars and covers 6 subtests in 3 domains, the Optimized form costs 30 dollars and covers 13 subtests in 5 domains, and the Full Scale form costs 50 dollars and covers all 20 subtests in six domains. All are one time payments with no subscription. Three domains give 3 pairs of indices to compare, five give 10 and six give 15 (our arithmetic), so a longer form gives richer information and also more chances for a large gap that means nothing. A free trial is available with no card, and a 5 day quality guarantee applies. The time estimates are about 45 minutes, 110 minutes and 175 minutes, with breaks allowed.

The limits matter as much as the strengths. The test 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 in English only. An ACIS profile can show where your relative strengths lie among six broad abilities, and the method above tells you how much weight a gap can bear. It cannot tell you why a gap exists. The documentation of the instrument is on the technical manual page, and the page on how IQ tests are made explains how a test of this kind is built from item writing to norms.

12 What Do the Standards and the APA Guidelines Say About Reading a Score Profile?

The Standards for Educational and Psychological Testing (AERA, APA and NCME, 2014) and the American Psychological Association guidelines both treat profile reading as something that needs stated evidence, stated precision and more than one source of information. The Standards make three demands that bear on index gaps. Standard 2.3 says that for each total score, subscore or combination of scores that is to be interpreted, estimates of reliability and precision should be reported, and its comment warns that total scores can be consistent while subscores have unacceptably low reliability. Standard 2.4 says the same for differences between two scores, as quoted earlier. Standard 1.14 asks for the rationale and evidence behind any interpretation of subscores, score differences or profiles. Read together, they say that a test taker should be able to ask of any gap in a report what its precision is and what evidence supports reading it.

The APA Guidelines for Psychological Assessment and Evaluation, approved by the APA Council of Representatives in March 2020, speak to professionals but are useful to anyone reading a profile. They say psychologists strive to understand the conceptual meaning of scores and the technical range of interpretation of any given set of individual scores, and that accurate interpretation depends on integrating multiple sources of data. They list overinterpretation, selective interpretation and misinterpretation among the errors in reporting assessment results. Picking the single largest gap out of fifteen is selective interpretation in exactly that sense.

What follows for a reader is practical. Treat the overall score and its interval as the main result. Treat a gap you chose in advance, that exceeds its critical value and that is rare for that pair as worth a second look. Treat every other gap as the ordinary scatter of a normal profile, as the studies of Carroll, Carrasco, Schretlen, Binder and Grégoire all indicate. If everyday difficulties are the reason you are looking at a profile, a qualified clinician who can combine a supervised assessment with an interview and history is the appropriate source, and the page on where to take an IQ test lists the options for each purpose. An online score report is one data point, and the guidelines are clear that data points are to be integrated and not read alone.

13 Sources Behind This Page

Every figure on this page traces to one of the sources below, or is labeled as our own arithmetic. The pair counts, the probability of at least one significant pair under independence, the critical value check against the sample report, the standard deviation of a difference, the 3.8 point percentile step and every number in Table 3 (a simulation of 3 million equally correlated profiles, rounded to whole numbers) are our arithmetic and not the work of any author or of any test publisher. The invented profile in the worked example is not a real person and not an ACIS result. Carroll (2011) is a conference abstract, read on the NSU Works page on October 13, 2026, and we cite only the figures it prints.

• American Educational Research Association, American Psychological Association and National Council on Measurement in Education. Standards for Educational and Psychological Testing. AERA, 2014, Standards 1.14, 2.3 and 2.4 and their comments.
• American Psychological Association, APA Task Force on Psychological Assessment and Evaluation Guidelines. APA Guidelines for Psychological Assessment and Evaluation, approved by the APA Council of Representatives in March 2020, the passages on interpretation and on integration of multiple sources of data.
• Binder L, Iverson G and Brooks B. To err is human: "Abnormal" neuropsychological scores and variability are common in healthy adults. Archives of Clinical Neuropsychology, 2009, volume 24, issue 1, pages 31 to 46.
• Blum D and Holling H. Spearman's law of diminishing returns. A meta-analysis. Intelligence, 2017, volume 65, pages 60 to 66.
• Brooks B, Holdnack J and Iverson G. Advanced clinical interpretation of the WAIS-IV and WMS-IV: Prevalence of low scores varies by level of intelligence and years of education. Assessment, 2011, volume 18, issue 2, pages 156 to 167.
• Canivez G. Incremental criterion validity of WAIS-IV factor index scores: Relationships with WIAT-II and WIAT-III subtest and composite scores. Psychological Assessment, 2013, volume 25, issue 2, pages 484 to 495.
• Carrasco R, Grups J, Evans B, Simco E and Mittenberg W. Apparently abnormal Wechsler Memory Scale index score patterns in the normal population. Applied Neuropsychology: Adult, 2015, volume 22, issue 1, pages 1 to 6.
• Carroll C. Rates of apparently abnormal WAIS-4 patterns in the normal population. Abstract, 31st Annual Meeting of the National Academy of Neuropsychology, Marco Island, Florida, November 16 to 19, 2011, NSU Works, read October 13, 2026.
• Crawford J, Garthwaite P and Gault C. Estimating the percentage of the population with abnormally low scores (or abnormally large score differences) on standardized neuropsychological test batteries: A generic method with applications. Neuropsychology, 2007, volume 21, issue 4, pages 419 to 430.
• Crawford J, Garthwaite P, Longman R and Batty A. Some supplementary methods for the analysis of WAIS-IV index scores in neuropsychological assessment. Journal of Neuropsychology, 2012, volume 6, issue 2, pages 192 to 211.
• Grégoire J, Coalson D and Zhu J. Analysis of WAIS-IV index score scatter using significant deviation from the mean index score. Assessment, 2011, volume 18, issue 2, pages 168 to 177.
• McGill R, Dombrowski S and Canivez G. Cognitive profile analysis in school psychology: History, issues, and continued concerns. Journal of School Psychology, 2018, volume 71, pages 108 to 121.
• Pearson. WAIS-5 sample score report for a demonstration examinee, dated September 16, 2024, pearsonassessments.com, read October 13, 2026.
• Pearson. WAIS-IV Technical and Interpretive Manual, excerpt including the discussion of base rates and the Sattler criterion, hosted by Pearson Clinical Australia, read October 13, 2026.
• Schretlen D, Testa S, Winicki J, Pearlson G and Gordon B. Frequency and bases of abnormal performance by healthy adults on neuropsychological testing. Journal of the International Neuropsychological Society, 2008, volume 14, issue 3, pages 436 to 445.

14 Frequently Asked Questions