The five-parameter strategy developed by Edwards (1994) and Edwards and Cable (2009) has been widely used in congruence research for testing the perfect fit effect. This classical testing strategy, however, has a vulnerability: it includes the curvature of the surface along the misfit line (a4) and the intercept of the first principal axis (p10) but excludes the slope of the surface along the misfit line (a3). We argue that other things being equal, the combination of a4 and p10 is less reliable for testing the variation of the outcome along the misfit line, compared to the combination of a4 and a3. Due to this limitation, this popular five-parameter strategy, when used to close the empirical loop for congruence research, may lead to misleading conclusions, rather than accurate inferences and precise practical implications. To improve this situation, we propose to refine this classical testing strategy. Specifically, the new testing strategy we propose replaces p10 with a3, while retaining the other four parameters suggested by Edwards and Cable (2009). This one small change to the classical testing strategy allows a giant leap for congruence research, promising more robust theory development and scientific rigor.
