Standard Error of Measurement

The term standard error of measurement indicates the spread of measurement errors when estimating an examinee’s true score from the observed score. Standard error of measurement is most frequently useful in test reliability. An observed score is an examinee’s obtained score, or raw score, on a particular test. A true score would be determined if this particular test was then given to a group of examinees 1,000 times, under identical conditions. The average of those observed scores would yield the best estimate of the examinees’ true abilities. Standard deviation is applied to the average of those scores across persons and administrations to determine the standard error of measurement. Observed score and true score can be used together to determine the amount of error:

$${\text{Score}}_{\text{true}}={\text{ Score}}_{\text{observed}}+{\text{ Score}}_{\text{error}}.$$

However, this true score is purely hypothetical and is not a practical way to estimate error. Therefore, other estimates of error must be used, including standard deviation and reliability.

Standard error of measurement applies to a single score and should be applied more frequently than a reliability coefficient to interpret individual score meaning. Standard error is used in conjunction with the normal distribution in order to make decisions about individual test scores. Accordingly, standard error can be used to estimate a range of scores around a specified cut point when determining an examinee’s ability or potential. The normal distribution can aid in the interpretation of scores that fall above, below, or between specific points on the distribution. This concept is particularly important, as it relates to standardized testing and promotion or retention criteria. For example, if the cut point for failing is a 50, and administrators want to be 68% sure of their decision, standard error of measurement indicates that examinees who are within one standard error (SE) of the cut point (i.e., 50 ± SEmeasurement) may fluctuate above or below the cut point if the test were administered again. In situations such as this, it is imperative that more data be gathered, such as class performance indicators or growth scores, to determine promotion or retention.

A large standard error indicates a large amount of variability between different samples; therefore, the sample may not accurately represent the population. This occurs when sample means are spread far along the y-axis, in the tails of the normal distribution. When sample means are grouped closer to the population mean, standard error will be smaller.

This entry first discusses the distinction between standard error and standard deviation, as these concepts are often confused. Then, standard error is applied to confidence intervals and other assessment situations.