Question

if a test has a standard deviation of 20 and a reliability of .90, what is the standard error of measurement?

Answer 1

The standard error of this measurement is 6.32

How to determine the standard error of measurement?

The standard error of measurement is simply the estimate of how repeated measures of an entity on the same instrument tend to be distributed around the entity' “true” score.

In this case, we have the following parameters

Standard deviation = 20

Reliability = 0.90

The standard error of measurement from the standard deviation and the reliability is calculated using the following formula

Standard error of measurement = Standard deviation * √1 - reliability

Substitute the known values in the above equation, so, we have the following representation

Standard error of measurement = 20 * √1 - 0.90

This gives

Standard error of measurement = 20 * √0.10

Evaluate

Standard error of measurement = 6.32

Hence, the standard error in this case is 6.32

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