What is educational therapy?

Educational therapy takes place within specialized, one-on-one sessions tailored to the specific academic needs of the individual student. Various methods are used to optimize the student's strengths so that they may be used to fortify weaknesses. Because many students need concepts broken into manageable chunks, the educational therapist approaches sessions with methodical organization and structure. Educational therapy also teaches compensatory strategies that allow the student to experience success in the classroom and beyond, and can improve underlying processing skills so that learning new material is easier.

How is educational therapy different from tutoring?

Educational therapy addresses underlying learning skills such as visual and auditory processing, attention and focus, and memory. Academic skills such as reading and writing are remediated by teaching the strategies necessary to read, write, calculate and problem solve. An educational therapist has completed graduate and often post-graduate training in working with all types of learners. Tutoring, by contrast, focuses on re-teaching academic subject matter and helping with homework, and a tutor can be anyone proficient in the subject at hand.

Who needs educational therapy?

When a child continues to struggle despite parent-teacher interventions or private academic tutoring, they should be evaluated for underlying learning deficits by a licensed neuropsychologist or clinical psychologist who specializes in learning issues. Children do not outgrow learning problems, and it is important to begin intervention as early as possible to mitigate and potentially prevent self-esteem problems and unnecessary daily stress.

How long are educational therapy sessions and how often should they happen?

Sessions are one-on-one and run 50 minutes, with the educational therapist and student working intensively together. A minimum of two sessions per week is recommended, though each student's plan is discussed on a case-by-case basis during the intake session.

What learning differences do you work with?

Our network of independent professionals brings extensive experience with ADHD, autism spectrum disorders, dyslexia, dyscalculia, dysgraphia, language-based learning differences, processing weaknesses and anxiety, helping students identify and develop their strengths.

Which areas of Los Angeles do you serve, and can sessions be virtual?

We serve Calabasas, Santa Monica, Beverly Hills, Sherman Oaks, Encino, the South Bay, Los Angeles and surrounding areas. Sessions are available in-office, in-home, in-school, in the community, in college settings, or virtually.

How are students matched with a specialist?

We assess each student's needs, learning preferences and personality, then refer them to the right specialist - a qualified educational therapist, learning specialist or executive functioning coach - rather than assigning whoever is available.

Standard Error of Measurement: What That Band Means

Andrea Chernin

3 days ago

23 min read

You have read the number a thousand times and you have probably never used it. It sits in a narrow column beside the standard score, two values with a dash between them, under a heading that says something like 90% confidence interval.

It is the only thing on the page that tells you how much to trust the number beside it, and it is derived from the standard error of measurement — the one statistic on a score report that describes the test rather than the student.

Here is the part nobody says out loud. That band is not one object. The confidence level it uses is a setting somebody chose, not a property of the child. Its width changes several-fold from one line of the same report to the next.

One publisher's glossary lists three standard confidence levels and another publisher's default is not among them. And the single question practitioners actually ask of two scores — are these two numbers different? — needs a completely different error term, one the band cannot supply and your report does not print.

The document that governs all of this is free to download, and it mentions the phrase "confidence interval" four times in a thousand pages.

The short version

The band comes from the standard error of measurement. The standard error of measurement is the test's unreliability expressed in the units of the score you are reading.

The confidence level — 68, 80, 90 or 95 percent — is a multiplier applied to that error. It is chosen in the scoring software, not by the data.

Within one instrument, the error is not constant. It differs by subtest, by composite and by grade, and the published figures differ by a factor of four or more.

Comparing two scores is a different problem with a different error term, and the governing standard says so in a clause of its own.

Nothing here is legal advice.

What the band on the report actually is

Start with what the thing is, because the vocabulary is genuinely inconsistent and that inconsistency is doing some of the damage.

The definition the governing document gives

The Standards for Educational and Psychological Testing, published jointly by the American Educational Research Association, the American Psychological Association and the National Council on Measurement in Education, is the document every publisher cites. Its glossary is terse:

"confidence interval: An interval within which the parameter of interest will be included with a specified probability."

Note what that sentence is about. It is about a parameter — a property of the measurement — not about a student.

The conditional version of the error gets its own entry, defined as "the standard deviation of measurement errors that affect the scores of test takers at a specified test score level." That phrase — at a specified test score level — is the one to hold on to.

And in the background text of its reliability chapter, the Standards explains the relationship between the two in one sentence:

"The standard error of measurement can be used to generate confidence intervals around reported scores. It is therefore generally more informative than a reliability or generalizability coefficient, once a measurement procedure has been adopted and the interpretation of scores has become the user's primary concern."

That is the whole logic. A reliability coefficient of .93 tells you nothing you can act on. The same information expressed in score points tells you how far apart two numbers have to be before you should treat them as different.

Riverside publishes the arithmetic, and it is worth seeing

Most practitioners have never seen the formula, which is a shame, because it is one line. Riverside Insights publishes it in its own Glossary of Testing, Measurement, and Statistical Terms:

"Confidence Interval Lower Limit = Student's Score - (Z)(SEM) Confidence Interval Upper Limit = Student's Score + (Z)(SEM)"

The glossary then gives the multipliers: Z is 1.00 at a 68 percent confidence level, 1.28 at 80 percent, and 1.65 at 90 percent.

It also works the example, and the worked example is the thing to keep. With a standard error of 3.0 and a score of 10, Riverside shows the 68 percent interval as 7 to 13, the 80 percent interval as roughly 6 to 14, and the 90 percent interval as 5.05 to 14.95.

Same test. Same student. Same standard error. One band six points wide and another ten points wide. Nothing about the child changed between those three lines.

The same glossary also tells you that the two words you see on reports are the same thing: "Confidence Band – see Confidence Interval." Riverside's own WJ V Score Report Interpretation guide lists "confidence bands" among the elements you can switch on when you generate a report, alongside percentile ranks and relative proficiency indexes.

The width of the band is a setting, not a finding

This is the first thing that is genuinely useful to know, and it takes about a minute to verify on any publisher's own documentation.

Pearson offers two confidence levels and prints one by default

Pearson's Q-global help page for configuring WIAT-4 reports states the setting plainly. For the Score Report, the instruction is to "Select the confidence interval to be used for the report: 90% or 95%". The same wording appears in the settings for the Parent Report.

Pearson's own published WIAT-4 sample score report prints columns headed "90% Confidence interval" — on the core composite summary, on the supplemental composite summary and in the subtest tables.

So the band you are most likely to see on a WIAT-4 is the narrower of the two available. That is not a criticism of Pearson. It is a fact about what you are holding.

Riverside names three levels, and 95 percent is not among them

Riverside's glossary describes the confidence level associated with a score interval as "usually 68%, 80%, or 90%". It gives Z values for exactly those three.

Ninety-five percent — one of Pearson's two WIAT-4 options — does not appear in that list at all.

What that means when you read somebody else's report

Two reports can show bands of visibly different widths on scores of identical precision, purely because two pieces of software were configured differently. And two reports can show bands of identical width on scores of genuinely different precision, for the same reason in reverse.

A band is not a measurement. It is a measurement multiplied by a number somebody selected from a dropdown.

The practical consequence is small but real: when you compare a band on a report from last year against a band on a report from this year, check the column heading before you conclude anything about the child's consistency. If one says 90 and one says 95, the widths are not comparable and the apparent change may be entirely an artefact of the setting.

This is the same class of problem as the one in grade equivalent scores, where the unit itself is unequal, and the one in outdated test norms, where the comparison group has quietly moved. In all three cases the number looks like a property of the student and is partly a property of the paperwork.

Within one test, the band is not one width

The second useful fact is that precision varies inside a single instrument, and publishers show you this if you look.

Pearson's own sample report runs from plus or minus three to plus or minus thirteen

Every interval printed in the WIAT-4 sample score report is symmetric about the standard score, so the half-width is easy to read off. On that one document, the half-widths range from three points to thirteen points.

A standard score of 85 is printed with an interval of 82 to 88 — three points either side. A standard score of 160 is printed with an interval of 147 to 173 — thirteen points either side.

On the same report, for the same student, the least precise score carries a band more than four times wider than the most precise one. If you were treating the band as a uniform fuzziness you add to every number, you were wrong by a factor of four.

DIBELS publishes the same pattern in raw units

The DIBELS 8th Edition Technical Manual from the University of Oregon does something unusually transparent: it reports the standard error of measurement for every score, in every grade, at every benchmark period, in Table 2.34. It also states its method, which is the classical one — the standard deviation multiplied by the square root of one minus the reliability.

Read the narrative and the pattern is immediate. Nonsense Word Fluency correct letter sounds has a standard error rising from 5 to 7 in kindergarten, to 10 to 14 in first grade, to 12 to 14 in second grade, and finally to 14 to 17 in third grade.

Oral reading fluency accuracy runs the other way — 5 to 10 percentage points in first grade, falling to 1 to 2 by eighth grade.

The manual explains why in one clause: "as variability in students' scores increases, SEMs will naturally become larger." The error is not a flaw that someone failed to fix. It is partly a consequence of how spread out the scores are at that age.

The Standards asked for exactly this, and it has a name

Two clauses are doing the work here.

Standard 2.13 requires that "the standard error of measurement, both overall and conditional (if reported), should be provided in units of each reported score."

Standard 2.14 goes further: "When possible and appropriate, conditional standard errors of measurement should be reported at several score levels unless there is evidence that the standard error is constant across score levels."

That second clause is the one with teeth for a practitioner. It is an instruction to publishers that a single average error figure is not good enough, because precision is not constant. The commentary adds that where cut scores are used for selection or classification, the standard errors should be reported near each cut score.

What the Standards require, and where to read them free

A detail that changes how usable all of this is: the Standards is not a paywalled artefact you need a university library for.

It is open access, and has been since 2021

The American Educational Research Association, the American Psychological Association and the National Council on Measurement in Education announced on 1 March 2021 that the current edition was available as a free download, in English and Spanish, as a PDF and as an ePub. The current edition is the one published in 2014, and the open-access files sit at testingstandards.net.

If you read assessment reports for a living and you have never opened the full text, that is the single highest-value hour available to you. Chapter 2 is forty pages and it is the whole subject.

Three clauses that do most of the work

Standard 2.3 is the one that covers subtests, and it is blunt in the commentary:

"It is not sufficient to report estimates of reliabilities and standard errors of measurement only for total scores when subscores are also interpreted."

That matters because subtest-level interpretation is exactly where practitioners work. If a report draws your attention to a relative weakness on one subtest, the precision of that subtest — not of the composite it sits inside — is the relevant figure.

Standard 2.11 and Standard 2.12 extend the same logic to subgroups and to age and grade bands, requiring reliability and precision data for each age or grade-level subgroup "not just for all grades or ages combined."

The one clause about the band itself uses the word "might"

Here is the finding that surprised me, and it is worth sitting with.

Chapter 6 holds the reporting standards. Standard 6.10 requires that score interpretations "describe in simple language what the test covers, what scores represent, the precision/reliability of the scores, and how scores are intended to be used."

Its commentary is the only place in the volume that describes the thing you are looking at on a report:

"Score precision might be depicted by error bands or likely score ranges, showing the standard error of measurement."

Might. The band on your report — the artefact the whole industry prints, the one this article is about — appears in the governing document as a permissive example inside a comment, not as a requirement.

Four mentions in a thousand pages

The phrase "confidence interval" appears four times in the entire 2014 Standards. One of those is in Standard 1.20, about effect sizes in validity research, where the volume states that "standard errors or confidence intervals provide more information and thus are preferred in place of, or as supplements to, significance testing."

The phrase "standard error of measurement" appears sixteen times. The word "reliability" appears more than three hundred times.

And the phrase "estimated true score" appears zero times. So does "score band."

The field's own rulebook talks about reliability constantly, about the standard error of measurement often, and about the band on the report almost not at all. The band is a convention of the score-report industry, resting on a measurement concept the Standards does specify in detail. Those are two different things and it is useful to know which one you are holding.

The question the band cannot answer

This is the section that changes practice, and it is the reason the title of this piece is about a number nobody uses.

Standard 2.4, in full

"When a test score interpretation emphasizes differences between two observed scores of an individual or two averages of a group, reliability/precision data, including standard errors, should be provided for such differences."

The commentary names the use case precisely, and it is yours: "Differences between verbal and performance scores on tests of intelligence and scholastic ability are often employed in the diagnosis of cognitive impairment and learning problems. Psychodiagnostic inferences are frequently drawn from the differences between subtest scores."

It also warns that "in some cases, the reliability/precision of change scores can be much lower than the reliabilities of the separate scores involved."

So the Standards anticipated the exact thing practitioners do with reports — read two subtest scores against each other — and said that activity needs its own error term. The phrase "standard error of the difference" appears three times in the volume.

And here is the trap. Overlapping confidence bands do not tell you that two scores are the same, and non-overlapping bands do not tell you that they are different. The bands are built from each score's own error. The difference between two scores has an error of its own, which depends on both errors and on how strongly the two measures correlate. Eyeballing the overlap is not a shortcut to it.

What your report prints instead, and it is a different machine

The reassuring part is that publishers do supply the difference machinery. It is just not the band.

Pearson's Q-global configuration page for the WIAT-4 shows it as a separate set of options. There are panels for composite standard score differences and subtest standard score differences, with room for up to twenty custom composite comparisons and up to thirty custom subtest comparisons. For those tables, the instruction is to "Select the significance level to be used for the report: 0.05 or 0.10".

Two further analyses sit alongside them, both restricted to age-based norms: an ability–achievement discrepancy analysis, with a "difference method (predicted or simple), and significance level (0.01 or 0.05)", and a pattern of strengths and weaknesses analysis at 0.01 or 0.05.

Notice the vocabulary shift. The band is a confidence interval at 90 or 95 percent. The difference tables are significance tests at 0.05, 0.10 or 0.01. These are different statistical objects with different thresholds, printed on the same page, and the report does not explain that to you.

If a report you are reading draws a conclusion from the gap between two subtests, the question to ask is which of those two machines produced it. If the answer is neither — if someone eyeballed the overlap — you have learned something about the report.

Two different tests is a harder case, and Standard 12.12 says so

Practitioners compare across instruments constantly, because the reports arrive from different sources. Standard 12.12 addresses it directly:

"When an individual student's scores from different tests are compared, any educational decision based on the comparison should take into account the extent of overlap between the two constructs and the reliability or standard error of the difference score."

The commentary adds two conditions most cross-report comparisons do not meet. The two tests should be "placed on a common scale, either by standardization or by some other means" and, if appropriate, "normed on the same population at about the same time."

Normed at about the same time. That clause connects straight to the norms problem, and it is the measurement-side argument for why two scores from instruments with twenty years between their normative samples are not a comparison at all.

Change scores carry more error than the scores they are built from

Standard 12.11 covers growth for individual students, and its commentary asks for "the standard error of the difference between scores on the pretest and posttest."

Standard 13.2 covers change or gain scores. Its commentary states the consequence in a clause worth memorising: "it is important to consider that the error associated with change scores is higher than the error associated with the original scores on which they are based."

That is the measurement answer to the most common question in a progress review. A pre-score and a post-score each carry error, and the difference between them carries more than either. A gain you can see is not automatically a gain you can defend.

Progress monitoring is where this bites hardest

Everything above concerns the standardised report that arrives on your desk. The numbers you generate yourself, week by week, are where the error term is both largest and least visible.

The fluency norms table publishes no error term at all

The oral reading fluency norms practitioners cite are compiled in Technical Report 1702, An Update to Compiled ORF Norms, available in full from ERIC and from Behavioral Research and Teaching.

I searched the document. The word "confidence" appears zero times.

The phrase "standard error" appears exactly once, and only in the reference list, as the title of a cited article: Christ, T. J., and Silberglitt, B. (2007), "Curriculum-based measurement of oral reading fluency: The standard error of measurement," School Psychology Review, 36, 130–146.

The most widely reproduced table in reading practice cites a paper about its own measurement error in the bibliography and never applies it in the body.

That is consistent with what the report is — a compilation of norms rather than an interpretive guide. It is also the measurement half of the finding in our piece on oral reading fluency norms, which looked at what the technical report does and does not tell you to do with the table.

The published standard error of an oral reading fluency score

The cited paper is worth knowing in its own right. Its ERIC record gives the figures: across grades, the median standard error of measurement was 10 words read correctly per minute, with a range of 5 to 15, and the authors identify 5 to 9 as the most likely estimates. The study analysed 63,207 curriculum-based measurement probes from 8,200 students over eight years. The journal record carries the full citation.

Hold that figure next to the decision rules that circulate in practice, which are commonly expressed in units of roughly ten words per minute. A median standard error of 10 words per minute means that a rule of thumb at that scale is operating at about the width of one standard error of the measurement it is applied to.

Two boundaries belong in the same breath. These standard error estimates come from a different dataset than the compiled norms, so this is not a correction to anybody's table. And a standard error is not a claim about any individual student's reading.

It is a statement about the precision of that kind of measure, which is exactly why a single probe is a weak basis for a decision and a slope across many probes is a stronger one.

DIBELS 8 publishes it score by score and grade by grade

The contrast with DIBELS 8 is instructive, because the same construct is handled with the error term attached.

From the technical manual's narrative, oral reading fluency standard errors run 5 to 8 in first grade, 9 to 11 in second, 10 to 11 in third, 9 to 13 in fourth, 10 to 11 in fifth, 10 to 12 in sixth, 10 to 13 in seventh and 9 to 10 in eighth. Composite score standard errors run 17 to 25 in kindergarten and 9 to 10 in eighth grade.

Those figures sit in the same neighbourhood as Christ and Silberglitt's, from an independent dataset and a different method, which is the kind of convergence that makes a figure worth trusting as an order of magnitude.

The practical move is unglamorous and it works: find out whether the system you are using publishes a standard error for the score you are reading, and if it does, write the number on the inside cover of the manual.

For the tools in our comparison of progress monitoring tools, the answer differs by system. Knowing which movement on your own graph is noise is the difference between a decision rule and a superstition.

The clearinghouses already read the lower bound

There is one more finding here and it is the one I would put on a poster.

Progress monitoring: reliability and validity of slope

The National Center on Intensive Intervention rates progress-monitoring tools on its Academic Progress Monitoring chart. Read its rating rubric and you find that the ratings are not assigned on the coefficient. They are assigned on the bottom of the coefficient's confidence interval.

For Reliability of Slope, a full bubble requires that "the lower bound of the confidence interval around the median coefficient met or exceeded 0.50", and a half bubble that the lower bound "fell below 0.50 but met or exceeded 0.40". The rubric also defines what counts as enough data: "at least 10 regularly collected measurements over a period of at least 20 weeks."

For Validity of Slope, a full bubble requires "the lower bound of the confidence interval around each coefficient met or exceeded 0.40".

Screening: classification accuracy and reliability

The Academic Screening chart rubric does the same thing. A full bubble for Classification Accuracy requires "the lower bound of the confidence interval around the Area Under the Curve (AUC) estimate ≥ 0.80 and Sensitivity ≥ 0.80 and Specificity ≥ 0.80."

For Reliability, a full bubble requires that "for each type of reliability reported the lower bound of the confidence interval around the median estimate met or exceeded 0.70."

The asymmetry worth noticing

The clearinghouse that rates your tools judges them on the lower bound of an interval. The report that rates a student hands you a point estimate and a band, and almost everyone reads the point.

That asymmetry is the whole argument of this article in two sentences. The discipline already exists in the field, is published openly, and is applied rigorously — to instruments. The same discipline applied to a child's score means asking what the least favourable plausible value is before you build a plan on the most likely one.

It also cuts the other way, which is the honest version. The lower bound of a band around a weak score is not evidence of a weaker student; it is the reason to be slow about concluding anything from one administration. The direction of caution depends on what decision the number is being asked to carry.

What a band does not tell you

Two misreadings are common enough to name.

It is not a statement about this child in the ordinary sense

Riverside's glossary spells out the logic honestly, and reading it slowly is clarifying:

"The confidence level associated with the score interval, usually 68%, 80%, or 90%, indicates the percentage of times, given repeated sampling, that the interval will contain the student's true score."

Given repeated sampling. The probability attaches to the procedure of constructing intervals, not to this particular interval around this particular child. Riverside's worked illustration spells it out — if the test were administered a hundred times, in theory and assuming no practice effects, the true score would fall inside the interval on 68 of them at a 68 percent confidence level.

That is a subtler claim than "there is a 68 percent chance this child's real ability is in this range," and the difference matters when you are writing it into a report that a parent will read.

It cannot be converted into a percentage of right decisions

The temptation is to turn the error into a confidence about a decision. The Standards closes that door in the commentary to Standard 2.16:

"the standard error cannot be translated into the expected percentage of consistent or accurate decisions without strong assumptions about the distributions of measurement errors and true scores."

Which is why that standard asks for decision consistency to be estimated and reported separately, rather than inferred from the error. If you want to know how often a classification would repeat, that is a different statistic and somebody has to have computed it.

Where the ethics land

Our pieces on reading a psychoeducational evaluation and on achievement test qualification levels both turn on where the professional boundary sits. This one is simpler than either, because the Association of Educational Therapists says it in a single clause.

One word, once

The AET Code of Ethics, Revision #9, 2025 requires, at II.I.B, that educational therapists:

"select and use appropriate assessment instruments, recognizing their limitations with respect to reliability, validity, and bias."

I searched the Code. The word "reliability" appears exactly once in the entire document, in that clause. The phrase "standard error" appears zero times. So do the words "confidence", "score", "percentile", "measurement" and "statistic."

One word, once, is the whole of the professional body's instruction on measurement precision. That is not a gap to complain about — a code of ethics is not a psychometrics text, and the AET Fact Sheet describes the role in terms of formal and informal educational assessment rather than in terms of statistics.

But it does mean the clause carries more weight than its length suggests. Recognising an instrument's limitations with respect to reliability, in practice, means knowing its standard error in the units of the score you are reporting.

And a second clause that makes it your job

II.II.E asks educational therapists to "develop effective communication with parents/guardians, avoiding or interpreting technical terminology," and II.II.I to "facilitate the understanding among parents/guardians, school personnel, and other professionals regarding the realistic limitations of each one's function and role."

The confidence interval is the most technical object on a score report and the one most often skipped in a parent meeting. Those two clauses, read together, put explaining it inside the role rather than outside it — while II.I.D still directs you to "seek interpretation of assessment data from professionals in related fields," which is where the diagnostic question belongs and stays.

There is published evidence that this is hard for educators generally, not just for you. An ETS research memorandum on teachers' understanding of score-report graphics notes that "Research shows that many educators have trouble understanding and making appropriate use of score reports."

That is a statement about score reports as a whole rather than about error bands specifically. The measurement-error question has a research line of its own, including Zapata-Rivera, Zwick and Vezzu's 2016 study of a measurement-error tutorial for teachers in Educational Assessment.

I could not retrieve that article's findings from behind its publisher's access controls, so I am naming it as existing research rather than reporting what it concluded. If the question is load-bearing for you, the DOI is the place to start.

A sequence, not a decision

As with our other assessment pieces, this is an order of operations rather than an answer. It tells you what to ask, not what to conclude.

Read the column heading. Find the confidence level on the report in front of you. If it is not stated, you do not know the width of anything.
Find the error in score units. Look for the standard error of measurement for the specific score you care about, in the technical manual, not for the composite it belongs to. Standard 2.13 asks publishers to give it in the units of each reported score.
Check whether the error is conditional. If the manual publishes errors by score level or by grade, use the one that matches your student rather than the overall average.
Separate the two machines. If a conclusion rests on a gap between two scores, find out whether a difference test produced it or whether somebody compared two bands by eye.
Treat change with more suspicion than status. Standard 13.2 says the error on a change score exceeds the error on the scores it came from.
Ask the lower-bound question before you plan. Not to pick a pessimistic number, but to know how much of your plan depends on the point estimate being exactly right.
Then stop. Whether a pattern of scores indicates a disorder is not a measurement question, and it is not yours to answer.

What is out of scope here

Three things deliberately.

Eligibility and identification decisions are not covered. Whether a score or a discrepancy supports a classification is a question answered by statute, regulation and a qualified evaluator, not by a confidence interval, and not by this article. Nothing here is legal advice. If that is your question, it belongs with your state education agency and, for independent practice, with an attorney.

Diagnostic interpretation is not covered. Nothing above tells you what any score or any gap between scores means about a student, and AET II.I.D directs that question to professionals in related fields.

The psychometrics are not covered to any depth. This is a practitioner's reading of published requirements and published figures, not a measurement tutorial. The Standards is free and Chapter 2 does the job properly.

Where the published record runs out

Worth stating plainly, because the gaps are part of the picture.

The universe of primary sources for this subject is narrow: the 2014 Standards, a handful of publishers' own glossaries and report-configuration pages, two publicly posted technical manuals, the two NCII rating rubrics, and a small research literature on score-report comprehension.

There are no fifty-state findings here and no industry survey. If this article cites fewer domains than our comparisons of spelling assessment tools or reading comprehension assessment tools, that is because the sources genuinely are fewer, and padding the list would mean citing secondary material.

Several publishers do not publish, on the open web, which score their confidence intervals are centred on or which error term they use. I could confirm from Pearson's own sample report that every WIAT-4 interval on it is symmetric about the standard score, which is informative about that report.

I could not establish a comparable fact for every publisher from public documentation, so this article does not assert one. If that distinction matters for an instrument you use, the technical manual is where it is answered and the publisher's support line is where to ask.

I could not retrieve the findings of the ETS measurement-error tutorial study named above, and have said so rather than summarising a paper I did not read.

And on the research literature generally: the comprehension studies concern teachers and parents reading score reports, not educational therapists specifically. Whether the finding transfers to a practitioner who reads reports as a core professional task is an open question, and I am not going to assert that it does.

Frequently asked questions

What is the standard error of measurement, in one sentence?

It is the test's unreliability expressed in the units of the score you are reading — the statistic that tells you how much a student's score would be expected to bounce around across repeated administrations of the same instrument, holding the student's underlying ability constant.

Does a 95 percent confidence interval mean the test is less accurate than a 90 percent one?

No. The confidence level is a multiplier, not a measurement. Riverside's published formula uses a Z of 1.00 at 68 percent and 1.65 at 90 percent applied to the same standard error, so a higher confidence level produces a wider band on an identically precise score. Pearson's WIAT-4 reports let you choose 90 or 95 percent and default to 90.

If two subtest confidence intervals overlap, are the scores the same?

Overlap is not a test of difference. Standard 2.4 of the 2014 Standards requires that reliability and precision data, "including standard errors, should be provided for such differences," because the difference between two scores has its own error term that depends on both scores' errors and on how strongly the two measures correlate.

On a WIAT-4 report, difference tables with their own significance levels of 0.05 or 0.10 are the correct tool, and they are a separate option from the confidence interval.

Is the band the same width for every score on a report?

No. On Pearson's own published WIAT-4 sample score report, the printed intervals range from three points either side of the standard score to thirteen points either side. Standard 2.14 of the Standards asks publishers to report conditional standard errors at several score levels precisely because precision is not constant.

Where can I read the testing standards without paying for them?

AERA, APA and NCME announced the open-access release on 1 March 2021. The current 2014 edition is downloadable free, in English and Spanish, from testingstandards.net. Chapter 2 covers reliability and errors of measurement and Chapter 6 covers reporting.

Do progress monitoring systems publish a standard error for their scores?

Some do and some do not, and it is worth checking for the system you use. The DIBELS 8th Edition Technical Manual publishes standard errors for every score, grade and benchmark period, with oral reading fluency running from 5 to 8 words per minute in first grade to 9 to 10 in eighth.

The compiled oral reading fluency norms in Technical Report 1702 publish none, and mention the phrase "standard error" only once, in a reference-list entry.

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