Several articles have discussed the curious fact that
a difference score with zero reliability can nonetheless
allow a powerful test of change. This statistical legerdemain
should not be overemphasized for three reasons.
First, although the reliability of the difference score
may be unrelated to power, the reliabilities of the variables
used to create the difference scores are directly
related to the power of the test. Second, with what
some will regard as additional legerdemain, it is possible
to define reliability in the context of a difference
score in such a way that power is a direct function of
reliability. The third and most serious objection to the
conclusion that the reliability of a difference score is
unimportant is that the underlying statistical model
used in its derivation is rarely appropriate for psychological
data. Index terms: control of individual differences,
difference scores, reliability, reliability of
the marginal distribution, statistical power, within-group
Humphreys, Lloyd G & Drasgow, Fritz. (1989). Some comments on the relation between reliability and statistical power. Applied Psychological Measurement, 13, 419-425. doi:10.1177/014662168901300407
Humphreys, Lloyd G.; Drasgow, Fritz.
Some comments on the relation between reliability and statistical power.
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