The Uniformly Most Powerful Invariant Test for the Shoulder Condition in Point Transect Sampling

Estimating population abundance is of primary interest in wildlife population studies. Point transect sampling is a well established methodology for this purpose. The usual approach for estimating the density or the size of the population of interest is to assume a particular model for the detection function (the conditional probability of detecting an animal given that it is at a given distance from the observer). The two most popular models for this function are the half-normal model and the negative exponential model. However, it appears that the estimates are extremely sensitive to the shape of the detection function, particularly to the so-called shoulder condition, which ensures that an animal is almost certain to be detected if it is at a small distance from the observer. The half-normal model satisfies this condition whereas the negative exponential does not. Therefore, testing whether such a hypothesis is consistent with the data at hand should be a primary concern in every study concerning the estimation of animal abundance. In this paper we propose a test for this purpose. This is the uniformly most powerful test in the class of the scale invariant tests. The asymptotic distribution of the test statistic is calculated by utilising both the half-normal and negative exponential model while the critical values and the power are tabulated via Monte Carlo simulations for small samples. Finally, the procedure is applied to two datasets of chipping sparrows collected at the Rocky Mountain Bird Observatory, Colorado..