AbstractThere has been rapid progress in developing effective and easy‐to‐use tests of the order of a finite mixture model. The EM‐test is the latest to join the rank. It has a relatively simple limiting distribution and enjoys broad applicability. Based on asymptotic theory, the P‐value of the EM‐test is approximated via its limiting distribution. The built‐in tuning parameter has an important influence on the approximation precision. Thus, choosing an appropriate value for this parameter is important for fully realizing the advantages of the EM‐test. In this article, we develop a novel computer‐experiment approach to address this issue. Through designed experiments, we derive a number of empirical formulas for the tuning parameter. Extensive validation simulation shows that these formulas work well in terms of providing accurate type I errors. The Canadian Journal of Statistics 39: 389–404; 2011 © 2011 Statistical Society of Canada