Evaluation of Ranked Set Sampling for Estimating Shrub Phytomass in Appalachian Oak Forests

Abstract

Ranked set sampling was introduced by McIntyre (1952) in estimating pasture yields. As described by McIntyre, the ranked set sampling procedure is implemented by first selecting a set of n elements at random from a population, and then raking those elements from lowest to highest by inspection of the variable of interest. The lowest ranked element is then measured. A second set of n elements is selected and ranked, and the second lowest element is measured. This process is continued until n such sets have been selected and n elements have been measured. The entire procedure can be repeated as many times as deemed necessary. McIntyre claimed that the ranked set estimator of the population mean was unbiased regardless of errors in ranking, and that with perfect ranking the variance of the mean from ranked set sampling would be less than that of random sampling when the number of measured elements is the same for both methods. Halls and Dell (1966) concluded that ranked set sampling was more efficient than simple random sampling in estimating pasture yields. A theoretical underpinning for ranked set sampling was provided by Dell and Clutter (1972), who also demonstrated that ranked set sampling is more efficient than random sampling even when errors in ranking are present. Ranked set sampling is clearly advantageous when measurement of an element is time consuming or costly and sample elements can be reliably ranked. The effectiveness of this technique has already been demonstrated for estimating forage and pasture yields. The objective of this study is to evaluate the effectiveness of ranked set sampling for estimating shrub phytomass in forest stands.