The present note examines the tables in May and Hittner's 1997 informative article and suggests an alternative interpretation of their meaning. The basic idea of appending two new scenarios to the one introduced by Williams, Zimmerman, and Cummings in 1996 is quite helpful, but one should not overlook the fact that assumptions about the relative size of pretest and posttest observed score variances are not independent of assumptions about the relative size of pretest and posttest validity and reliability coefficients. For this reason, the parameters in May and Hittner's scenarios II and III may be less likely to occur in practice than the parameters in their scenario I.
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