Critical regions at the level of significance &agr;=1%, 5%, 10%, and 20% have been calculated for testing whether or not a sample ofNsingle, cubic crystals is randomly oriented. The stereographic triangle has been divided into five cells in two different ways, one with respect to important crystallographic directions in fcc crystals and one with respect to those in bcc crystals. Representative tables forN=10 for fcc and for bcc crystals and forN=20 bcc crystals are presented.