Standard Error of Measurement
The standard error of measurement (SEM) is an estimate of error to use in interpreting an individual’s test score. A test score is an estimate of a person’s “true” test performance. Using a reliability coefficient and the test’s standard deviation, we can calculate this value:
SEM = s Ö( 1 – r)
Where:
S = the standard deviation for the test
r = the reliability coefficient for the test
For
example,
A Wechsler test with a split-half reliability coefficient of .96 and a standard deviation of 15 yields a SEM of 3
SEM = s Ö( 1 – r ) = 15 Ö ( 1-.96) = 15 Ö.04 = 15 x .2 = 3
Now that we have a SEM of 3 we can apply it to a real life situation.
Example: Joe took the Wechsler test and received a score of 100.
Let’s build a “band of error”add a definition here around Joe’s test score of 100, using a 68% interval. A 68% interval is approximately equal to 1 standard deviation on either side of the mean.
For a 68%
interval, use the following formula:
Test score ±
1(SEM)
Where:
= 100 ± (1 x 3) = 100 ± 3
Why
the “±
1”? Because we are adopting the normal distribution for our theoretical
distribution of error, and 68% of the values lie within the area between 1
standard deviation below the mean and 1 standard deviation above the mean.
Chances
are 68 out of 100 that Joe’s true score falls within the range of 97 and 103.
What
about a 95% confidence interval?
Test
score ±
2(SEM) = 100
±
(2 x 3) =
100 ±
6
Chances
are 95 out of 100 that Joe’s true score falls within the range of 94 and 106.
The
higher a test’s reliability coefficient, the smaller the test’s SEM.
Try another example
Jane has a score of 110. Find the "band of error" for a 68% interval.
With a 68% interval the true score will fall between 107 and 113. ± 3 points on either side of her score of 110.
Now try a 95% interval
With a 95% interval the true score will fall between 104 and 116. ± 6 points on either side of her score
