The objective of this paper is to examine the relationship between the unreliability of difference scores and the power of tests of significance in an attempt to determine the validity of the paradox for the measurement of change presented by Overall and Woodward: that the power of tests of significance is maximum when the reliability of the difference scores is zero. It is concluded that this paradox is more superficial than real. A negative covariation between power and reliability of difference may occur if subject-by-time interaction variance is significantly greater than measurement error variance, and a positive relationship if the opposite is true. (Author/BW)