We present statistical tests for departures from random expectation in spatial memory tasks. We consider two common protocols for spatial memory experiments. In the first one, subjects are allowed to search a fixed number of sites. In the second protocol, subjects are allowed to search until they achieve a fixed number of successes. In either of these protocols, the subjects involved mayor may not revisit sites that have been previously searched or exploited. This yields four situations to consider: fixed number of sites searched or fixed number of successes, with or without revisits. We derive analytical expressions for the probability mass functions, expectations, and variances associated with each type of null hypothesis. Wepresent three statistical tests of these hypotheses: the Kolmogorov-Smirnov test, the ordinary sign test, and the Z test. Weuse our results to demonstrate a priori calculation of sample sizes and statistical power and to consider a mixed model of sampling with and without replacement.The basis for experiments investigating spatial memory capabilities ofanimals is that animals are able to perform spatial memory tasks better than expected by chance. In spatial memory experiments, such as radial maze experiments, a fixed number of sites is used. Some sites contain food, and others do not. Moreover, two experimental protocols can be used. In the first protocol, animals can explore a fixed number of sites. We shall refer to this protocol as the fixed-number-of-samples/trials protocol. The data that result from this protocol are the number of visited sites containing food. In the second protocol, animals can explore until they have found a fixed number of sites containing food. We shall refer to this second protocol as thefixed-number-of-successes protocol. The data that result from this protocol are the total number ofsites visited.One relevant null hypothesis is that the animals search at random until they find food-storage sites. In many cases, animals search without revisiting locations previously searched; in other cases (e.g., rats that have had their hippocampus lesioned), the animals do revisit previously searched or exploited sites. Again, two cases must be distinguished. In the first case, the hypothesis is that animals explore the sites at random and without replacement. In the second case, we can suppose that animals explore at random with replacement. Four different situations must thus be examined. Animals can search with or without replacement in a protocol where either the number of trials or the number of successes is fixed. In order to test the hypothesis that animals search better than at random, it is necessary to know the probability mass functions of the number of successes (in the fixed-number-of-trials protocol) or of the number of trials (in the fixed-numberof-successes protocol) when animals search at random with or without replacement.At first sight, this problem looks simple and classic. One might think that when an animal searches at random with replacement, the solu...