The properties of gain scores are linearly determined
by the properties of their components. Thus,
the reliability of a gain is uniquely determined by the
reliabilities of the components, the correlation between
them, and their standard deviations. Reliability
is not inherently low, but the components of gains
used in many investigations make low reliability
likely. Correlations of the difference between two
measures and a third variate are also determined
uniquely by three correlations and two standard deviations.
Raw score standard deviations frequently
tell more about the measurement metric and how it is
used than about the psychological processes underlying
the measurements. Correlations involving gains/
differences cannot be understood adequately unless
the essential sample statistics of the components are
known and reported. Index terms: change scores,
classical test theory, difference scores, gain scores,
intraindividual differences, measurement of growth,
reliability, test theory, validity.
Humphreys, Lloyd G. (1996). Linear dependence of gain scores on their components imposes constraints on their use and interpretation: Comment on "Are simple gain scores obsolete?" Applied Psychological Measurement, 20, 293-294. doi:10.1177/014662169602000309
Humphreys, Lloyd G..
Linear dependence of gain scores on their components imposes constraints on their use and interpretation: Comment on "Are simple gain scores obsolete?".
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