The mixed model analysis of variance assumes a mathematical property known as sphericity. Several preliminary tests have been proposed to detect departures from the sphericity assumption. The logic of the preliminary testing procedure is to conduct the mixed model analysis of variance if the preliminary test suggests that the sphericity assumption is tenable, or alternatively, to conduct another analysis of variance which does not assume sphericity. This paper examines the value of basing the analysis strategy upon the outcome of the preliminary test on the sphericity assumption. The examination is divided into four parts: (1) sphericity and its relationship to the mixed model analysis are reviewed; (2) five sphericity tests are reviewed, and the appearance of these tests in three popular statistical packages is described; (3) the performances of these tests in a Monte Carlo Type 1 error study are reported; and (4) the danger of depending upon a preliminary test to make analysis decisions is emphasized using an example data set. (BAE)