Incorporating prior knowledge in environmental sampling: ranked set sampling and other double sampling procedures

Environmental sampling can be difficult and expensive to carry out. Those taking the samples would like to integrate their knowledge of the system of study or their judgment about the system into the sample selection process to decrease the number of necessary samples. However, mere convenience or non-random sampling can severely limit statistical inference. Methods do exist that integrate prior knowledge into a random sampling procedure that allows for valid statistical inference. Double sampling methods use this extra information to select samples for measurement, thus reducing the number of necessary samples (in order to achieve a desired objective) and thereby reducing sampling costs. The level of prior information required can range from a linear relationship with a known auxiliary variable to simple ranking based on auxiliary information. We examine three types of double sampling methods (ranked set sampling, weighted double sampling and double sampling with ratio estimation), with accompanying examples from Oregon stream habitat data. All three methods can provide increased precision and/or lower sampling costs over simple random sampling. The appropriate double sampling method for the data and research situation depends upon the type of prior information available. The categories of prior information are summarized in a table and illustrated using the example data. Copyright (C) 2002 John Wiley Sons, Ltd.