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Aim: Conservation practitioners use biological surveys to ascertain whether or not a site is occupied by a particular species. Widely used statistical methods estimate the probability that a species will be detected in a survey of an occupied site. However, these estimates of detection probability are alone not sufficient to calculate the probability that a species is present given that it was not detected. The aim of this paper is to demonstrate methods for correctly calculating (1) the probability a species occupies a site given one or more non-detections, and (2) the number of sequential non-detections necessary to assert, with a pre-specified confidence, that a species is absent from a site. Location: Occupancy data for a tree frog in eastern Australia serve to illustrate methods that may be applied anywhere species' occupancy data are used and detection probabilities are < 1. Methods: Building on Bayesian expressions for the probability that a site is occupied by a species when it is not detected, and the number of non-detections necessary to assert absence with a pre-specified confidence, we estimate occupancy probabilities across tree frog survey locations, drawing on information about where and when the species was detected during surveys. Results: We show that the number of sequential non-detections necessary to assert that a species is absent increases nonlinearly with the prior probability of occupancy, the probability of detection if present, and the desired level of confidence about absence. Main conclusions: If used more widely, the Bayesian analytical approaches illustrated here would improve collection and interpretation of biological survey data, providing a coherent way to incorporate detection probability estimates in the design of minimum survey requirements for monitoring, impact assessment and distribution modelling.