"Lord's Paradox" is a term applied to a hypothetical situation illustrated by Frederic M. Lord in which Gain Score Analysis (GSA) and the Analysis of Covariance (ANCOVA) yield conflicting results in testing differential treatment effects for natural groups. This paper demonstrates that GSA and ANCOVA will always yield conflicting results unless the slopes of within group regression lines of posttest on pretest equal one. It is also pointed out that in Lord's specific hypothetical example, trait instability accounts for regression line slopes not equaling one and invalidates the ANCOVA. An analysis that corrects for this problem is demonstrated.
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