Design-based inference from on-site samples

On-site sampling is used in surveys where a frame of the population of interest is not near at hand. The population may for instance consist of individuals visiting some fishing-waters or a shopping mall. We demonstrate how general conclusions can be drawn from on-site sample data by use of design-based sampling theory. For an on-site sample of individuals, firstand second-order inclusion probabilities are derived, thus making point and variance estimation possible. The performances of some alternative estimators of the population mean are compared in a simulation, based on real survey data on anglers visiting the Kaitum river. The derived inclusion probabilities are also used to evaluate an often-made on-site sampling assumption: that the individuals’ inclusion probabilities are proportional to their number of visits to a site. It is shown that for the sampling design under study, the assumption holds for at least one special case, but not in general.