Romanowicz <1993> suggested that great earthquake alternate in a predictable fashion between strike-slip and dip-slip mechanisms on a 20--30 year cycle. We investigate whether or not the observed pattern of shifting predominance between strike slip and dip slip is capable of frequent reproduction by random simulation. To accomplish this, we randomly drew strike-slip and dip-slip events in the same proportion as in the historic record and determined how frequently a pattern of predominance similar to the historic record is generated. Out of 1000 simulations a pattern similar to the historic record was observed 183 times. This throws considerable doubt on Romanowicz's <1993> conclusion that a mechanism is at work producing the distribution she observed of great earthquakes. The difficulty in coming to conclusions from data of the type used by Romanowicz <1993> is explored, along with the psychological literature on the difficulty of detecting random and nonrandom patterns from relatively small amounts of information.¿ 1997 American Geophysical Union