Using ‘found’ data to augment a probability sample: Procedure and case study

Abstract

While probability sampling has the advantage of permitting unbiased population estimates, many past and existing monitoring schemes do not employ probability sampling. We describe and demonstrate a general procedure for augmenting an existing probability sample with data from nonprobability-based surveys ('found' data). The procedure, first proposed by Overton (1990), uses sampling frame attributes to group the probability and found samples into similar subsets. Subsequently, this similarity is assumed to reflect the representativeness of the found sample for the matching subpopulation. Two methods of establishing similarity and producing estimates are described: pseudo-random and calibration. The pseudo-random method is used when the found sample can contribute additional information on variables already measured for the probability sample, thus increasing the effective sample size. The calibration method is used when the found sample contributes information that is unique to the found observations. For either approach, the found sample data yield observations that are treated as a probability sample, and population estimates are made according to a probability estimation protocol. To demonstrate these approaches, we applied them to found and probability samples of stream discharge data for the southeastern US.

Combining Existing Monitoring Sites with a Probability Survey Design--Examples from U.S. EPA's National Coastal Assessment

“…Incorporation of state monitoring sites that were probability-based (e.g., stratified random samples) was straightforward. Using the concepts introduced by Overton et al [4] for combining nonprobability samples with probability samples, criteria were developed for evaluating existing nonprobability sites for possible incorporation into the NCA design. The states of Massachusetts, Rhode Island, and Connecticut conduct fish trawl surveys using stratified random samples.…”

“…For existing monitoring program sites that were not selected using a probability design, the process to determine if sites could be incorporated into the NCA design was based on the two concepts identified in Overton et al [4]:…”

“…Over the past few years, there has been a growing literature on combining nonprobability and probability sites [4][5][6][7][8]. Some insight into characterizing a population by combining nonprobability samples with probability samples has been provided by Overton et al [6] and summarized by Cox and Piegorsch [5].…”

“…To complete characterization of the whole population, the nonprobability sample partition subsequently would be combined with the probability sample partition. Overton et al [4] suggest that similarity is a reasonable criterion for the nonprobability sample to be treated as representative. Here, we take similarity to mean that the two sets of sites have at least one indicator in common, and that the two distributions for the indicators are indistinguishable.…”

On the Estimation of Detection Probabilities for Sampling Stream-Dwelling Fishes.

“…I caution, however, that this is an analysis of 'found data' (sensu Overton et al 1993). That is, the data were collected for a variety of purposes and site selection was nonrandom.…”