New tests for departures from random behavior in spatial memory experiments

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 may or 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. We present three statistical tests of these hypotheses: the Kolmogorov-Smirnov test, the ordinary sign test, and the Z test. We use 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.