By writing the familiar equation for the correlation of gains and initial status in a form which reveals that the correlation does not depend on the standard deviations of pretest and posttest scores separately, but only on their ratio, it is possible to exhibit a one-parameter family of functions which throws new light on this relationship. The same family of functions provides information about the correlation between the true components of gains and initial status, as well as information about the correlation between the error components of gains and initial status.
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