**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

**
**