# Explain briefly the meaning and use of the term "standard error of measurement

### October 27, 2019 Explain briefly the meaning and use of the term "standard error of measurement
The standard error of measurement (SEm) is a measure of how much-measured test scores are spread around a “true” score. The SEm is especially meaningful to a test taker because it applies to a single score and it uses the same units as the test. The standard error of measurement (SEm) estimates how repeated measures of a person on the same instrument tend to be distributed around his or her “true” score. The true score is always an unknown because no measure can be constructed that provides a perfect reflection of the true score.
What is the Standard Error of Measurement?
The standard error of measurement (SEm) is a measure of how much-measured test scores are spread around a “true” score. The SEm is especially meaningful to a test taker because it applies to a single score and it uses the same units as the test.
Making Sense of Standard Error of Measurement If you want to track student progress over time, it’s critical to use an assessment that provides you with accurate estimates of student achievement— assessments with a high level of precision. When we refer to measures of precision, we are referencing something known as the Standard Error of Measurement (SEM).

Before we define SEM, it’s important to remember that all test scores are estimates of a student’s true score. That is, irrespective of the test being used, all observed scores include some measurement error, so we can never really know a student’s actual achievement level (his or her true score). But we can estimate the range in which we think a student’s true score likely falls; in general the smaller the range, the greater the precision of the assessment.

SEM put in simple terms, is a measure of the precision of the assessment—the smaller the SEM, the more precise the measurement capacity of the instrument. Consequently, smaller standard errors translate to more sensitive measurements of student progress. On MAP assessments, student RIT scores are always reported with an associated SEM, with the SEM often presented as a range of scores around a student’s observed RIT score. On some reports, it looks something like this:
Student Score Range: 185-188-191
So what information does this range of scores provide? First, the middle number tells us that an RIT score of 188 is the best estimate of this student’s current achievement level. It also tells us that the SEM associated with this student’s score is approximately 3 RIT—this is why the range around the student’s RIT score extends from 185 (188 – 3) to 191 (188 + 3). An SEM of 3 RIT points is consistent with typical SEMs on the MAP tests (which tend to be approximately 3 RIT for all students).

The observed score and its associated SEM can be used to construct a “confidence interval” to any desired degree of certainty. For example, a range of ± 1 SEM around the observed score (which, in the case above, was a range from 185 to 191) is the range within which there is a 68% chance that a student’s true score lies, with 188 representing the most likely estimate of this student’s score. Intuitively, if we specified a larger range around the observed score—for example, ± 2 SEM, or approximately ± 6 RIT—we would be much more confident that the range encompassed the student’s true score, as this range corresponds to a 95% confidence interval.

So, to this point we’ve learned that smaller SEMs are related to greater precision in the estimation of student achievement, and, conversely, that the larger the SEM, the less sensitive is our ability to detect changes in student achievement.   FB Page

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