Most of the easily accessible statistical models for estimating chance performance assume random sampling with replacement, but the objectives of psychological experiments commonly require sampling without replacement. It is often desirable, for example, to administer a repeated series of measurements to the same individual while balancing conditions, types of stimulus event, or types of response alternative. Since both human and nonhuman subjects can detect the nonrandom effects of sampling without replacement (Jenkins, 1965), a precise estimate of chance performance must take this into account. Consider the following experimental example generated by a well-known and hotly-disputed theoretical question. Gardner and Gardner (1978) reared five chimpanzees, Washoe, Moja, Pili, Tatu, and Dar, under conditions that closely simulated the rearing conditions of human infants. Where earlier experiments in cross-fostering such as Kellogg and Kellogg (1933) and Hayes and Hayes (1951) used speech, Gardner and Gardner used American Sign Language (ASL), the gestural language of the deaf in North America. Naturalistic observations of the young chimpanzees yielded results that closely approximate the results of similar observations of very young human children. While other developmental similarities were accepted without dispute, the evidence for verbal skills generated heated controversy (e.g., Umiker-Sebeok & Sebeok, 1980). One of the more pertinent arguments that have been raised concerns the validity of adventitious, naturalistic observations, particularly in the case of verbal behavior. Under the rich, informal conditions of cross-fostering, observers may read more meaning than is actually present in the signs. The fact that the remarkable linguistic skills that have been attributed to very young human children are based on equally informal observations (c.f. Bloom, 1970; Brown, 1973) only serves to underscore the need for more stringent evidence. Early in Project Washoe, Gardner and Gardner (1971, pp. 158-161) began a series of vocabulary tests designed to demonstrate that cross-fostered chimpanzees could communicate to a human observer under conditions in which the only information available to the observer was the sign language of the chimpanzees. To accomplish this, exemplars of nameable objects were photographed on 35-mm slides which were back-projected on a screen that could be seen by the chimpanzee subject, but could not be seen by the observers. A second objective was to demonstrate that independent observers agreed with each other. To accomplish this, there were two observers. The first observer served as interlocutor in the testing room with the chimpanzee.