The Delphi method is a means of structuring group communication process so that a group of experts can gather information or forecast future problems effectively. A primary objective of a Delphi study is to obtain consensual and consistent opinions from a group of experts in two or more successive rounds on a given research subject. Consensus and consistency are presumed to have been reached when a stopping criterion used for determining a consensus has been met. This study examined two nonparametric statistical methods: the McNemar change test (Q. McNemar, 1969) and the Binomial test for setting stopping rules in the context of Delphi studies. Simulation results indicate that the McNemar change test could be robust even if the correction for continuity was not made, and the McNemar test was not as conservative as the Binomial test. Discussions on how to apply both tests to Delphi studies are included. (Contains 4 tables and 19 references.) (Author/SLD)