The formula to calculate the Standard Error of Measurement is:
\[ \text{SEM} = \sigma \times \sqrt{1 - r} \]
Where:
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.
Let's consider an example:
Using the formula to calculate the Standard Error of Measurement:
\[ \text{SEM} = 5 \times \sqrt{1 - 0.8} = 5 \times \sqrt{0.2} \approx 2.24 \]
This means that the standard error of measurement for this scenario is approximately 2.24.