# Standard error of measure: Definition and calculations

Document created by Community User on Jul 29, 2016Last modified by Community User on Sep 8, 2020
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Introduction
A definition of standard error of measure (SEM) and why it is important.

Information
The standard error of measure (SEM) indicates a score's precision. If a student takes the same test twice within the same term, the test with the lowest standard error is determined to be the more reliable and precise of the two tests and will be highlighted in reports.

In some instances this may be the score with the lower RIT. A student with a high standard error is one who may have more erratic answering patterns. The lower standard error indicates we are able to predict with greater precision the student's true score as they answered within a specific, predictable pattern.

Typical SEM values for the MAP Growth test test range from 2.8 to 3.5, although the assessment is considered valid up to an SEM of 5.5. If a student took two mathematics tests in the fall and scored 200 on one with a standard error of 3, and 205 on the other with a standard error of 4, the first score with the lower standard error would be reported.

## Why is it important to include SEM information with assessment data?

All achievement test scores are estimates of a student's status on a trait (such as "science knowledge"). Since the trait cannot be seen, it is frequently referred to as a latent trait. And since the trait cannot be seen, neither can a student's status on the trait. At best, we can infer where the student stands with respect to the trait by having the student answer a range of questions that have been anchored to the trait in terms of their relative difficulty. However, we always know that this inference is not conclusive – it must always be qualified by the noise that is inherent in any assessment, for example: idiosyncrasies in test content, imperfect item difficulty estimates, poorly targeted test items, careless errors by the student, lucky guesses by the student, and distractions in the testing environment. These noise sources are captured and summarized in the form of SEMs. When the SEM accompanies the test score, we present a more complete picture of the student's test performance. At the most basic level, the SEM allows the consumer of the test score to get a sense of not only how precise the estimate of achievement is, but also how much confidence can be placed in the score.

## Considerations for placement testing and other high-stakes testing:

Any time you are making a placement decision or another high-stakes decision for a student, we recommend using the RIT range with the SEM, rather than a single RIT score, to determine whether the student meets criteria established by your district. We also recommend using no less than three points of data to make important decisions about students. For more information, see Multiple Measures and Data Triangulation – A Balanced Assessment Approach.