Teaching · For Teachers · Assessment

Every score is
a range. Here is
how wide.

Type the standard deviation and reliability from the test manual, then the scores you are reading. The calculator gives the standard error of measurement, the band each score sits in, and whether a change or a gap between two students is bigger than the test’s own noise.

Find the bandWhat you get
$12one-time · every device you sign in on
Buy · $12

Included with Caveat Classroom and Whole-school licenses. Or get it in the For Teachers toolkit, $79 for 72 items.

The SEM calculator

The worked example is made up: standard scores with a standard deviation of 15 and a reliability of .91. Use codes, not names. Nothing you type leaves this browser.

Loading the calculator. If nothing appears, turn on JavaScript.

What you get

Teaching · For Teachers$12 · included with Classroom and Whole-school licenses

What you finish with
The standard error of measurement, the band around each observed score at the level you choose, the standard error of a difference and a note on each pair of scores. It prints as a summary and downloads as a spreadsheet.
Who it is for
School psychologists and diagnosticians, special educators reading evaluation reports, assessment coordinators and teachers interpreting standardized scores.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. Up to 40 scores. Prints a summary; downloads a spreadsheet (.csv); export and import a file.
Access
$12 one-time, yours on every device you sign in on; the tool opens once you are signed in with it. Included with Caveat Classroom and Whole-school licenses. Also in the For Teachers toolkit ($79) and the Teaching Suite pass ($199), and 1 more bundle. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The For Teachers space in Caveat Teaching.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Name the test and type its standard deviation and reliability from the manual.
  2. Choose a band: 68, 90 or 95 percent.
  3. Add the observed scores you want to read.
  4. Read each band and the note on each pair.
  5. Print the summary or download the spreadsheet.

Find the band

How the band is worked out

Reliability turned into points on the score scale.

The worked example, from reliability to a bandUnreliable share1 − .91 = .09from the manualSEM4.5015 × √.0990% band± 7.401.645 × SEMS-07 fall, 8678.6 to 93.4the true score is likely hereThe worked example, from reliability to a bandUnreliable share1 − .91 = .09from the manualSEM4.5015 × √.0990% band± 7.401.645 × SEMS-07 fall, 8678.6 to 93.4the true score is likely here
A reliability of .91 leaves 9% of the score variance as error; its square root times the SD, 4.50 points, is the typical distance between an observed and a true score.

The arithmetic

Reliability is the share of score variance that is consistent. One minus reliability is the share that is error, and the SEM converts it to score points: SD × √(1 − reliability). About 68 percent of the time the true score lies within one SEM of the observed score, 90 percent within 1.645 and 95 percent within 1.96. Two scores on the same test have more error between them than either alone, SEM × √2.

Which numbers to use

Use the SD of the score scale you are reading (15 for most standard scores, 10 for T-scores, 3 for scaled scores) and the reliability the publisher reports for that score and age. Manuals sometimes report several reliabilities; internal consistency gives narrower bands than test-retest. Many manuals center bands on an estimated true score rather than the observed score; if yours does, use its tables.

Sources

  1. American Educational Research Association, American Psychological Association, and National Council on Measurement in Education. (2014). Standards for Educational and Psychological Testing, chapter 2: reliability and errors of measurement.
  2. Harvill, L. M. (1991). Standard error of measurement. Educational Measurement: Issues and Practice, 10(2), 33–41 (NCME instructional module).
  3. Individuals with Disabilities Education Act regulations, 34 CFR 300.304(c): assessments must be valid and reliable for the purpose used.
  4. Crocker, L., and Algina, J. (2008). Introduction to Classical and Modern Test Theory. Cengage: the standard error of the difference.

The worked example is made up. This page does arithmetic on the SD and reliability you type; it supplies no norms. A score band is one piece of evidence, never a diagnosis. Your figures stay in this browser. Support: team@caveatacademic.com.