Biomedical Engineering Reference
In-Depth Information
random or unsystematic sources in any individual object's score. This error
estimate is known as the standard error of measurement and is defined
more precisely in the next section. Also, knowledge of the reliability of a
measurement process can help us understand to what degree errors of mea-
surement are contributing to a possible underestimate of group differences
in demonstration studies.
Quantifying Reliability and Measurement Errors
One important goal of a measurement study is to quantify the reliability of
a measurement process. We have seen that quantification can be accom-
plished by two general methods. Using a representative sample of objects
we can employ a measurement process using multiple co-occurring obser-
vations to estimate internal consistency reliability; or we can repeat a mea-
surement process on separate occasions, which enables estimation of
test-retest reliability. A key aspect of reliability, from a measurement per-
spective, is that
any measurement process consisting of multiple observations
can reveal the magnitude of its own reliability.
This contrasts with estima-
tion of validity, that, as we will see later, requires collection of additional
data.
For either the test-retest or internal consistency approach, we can
compute a reliability coefficient with a maximum value of 1.0. The reliabil-
ity coefficient (
) is defined, somewhat abstractly, as the fraction of the total
variability in the scores of all objects that is attributable to differences in
the true scores of the objects themselves. That is,
r
V
V
total
•
r=
where
V
•
=
variability due to true score differences
V
total
=
total variability in the measurements
This formula, as it stands, is not helpful. The true score variability cannot
be observed directly from the results of a measurement process because the
true scores themselves are unknown. However, by using measurement
theory and performing some algebra not shown here, we can put this
formula in a more useful form. Using the assumption that the errors reduc-
ing reliability of measurement are random and thus uncorrelated with true
scores, we can conclude that the true score variability is equal to the total
variability minus the variability due to measurement error. We may thus
write:
VV
V
-
total
error
r=
total
This is more helpful because both quantities on the right side of the formula
can be computed directly from the data generated by a measurement study.
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