Enter the standard deviation and the reliability coefficient into the calculator to determine the standard error of measurement (SEM).
Standard Error Of Measurement Formula
The following formula is used to calculate the standard error of measurement (SEM):
SEM = σ * √(1 - r)
Variables:
- SEM is the standard error of measurement
- σ (sigma) is the standard deviation of the test scores
- r is the reliability coefficient of the test
To calculate the standard error of measurement, multiply the standard deviation (σ) by the square root of one minus the reliability coefficient (r).
What is Standard Error Of Measurement?
The standard error of measurement (SEM) is a measure of the precision of an assessment or test. It represents the standard deviation of error inherent in the test scores, which arises from various sources of measurement error. The SEM is used to estimate how repeated measures of a person on the same instrument tend to be distributed around their “true” score. A lower SEM indicates a more precise measurement.
How to Calculate Standard Error Of Measurement?
The following steps outline how to calculate the Standard Error Of Measurement (SEM).
- First, determine the standard deviation (σ) of the test scores.
- Next, determine the reliability coefficient (r) of the test.
- Next, gather the formula from above = SEM = σ * √(1 – r).
- Finally, calculate the Standard Error Of Measurement (SEM).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Standard Deviation (σ) = 15
Reliability Coefficient (r) = 0.90
