Use of a Web-Based Convenience Sample to Supplement a Probability Sample
Published in: Survey methodology, v. 33, no. 2, Dec. 2007, p. 211-215
Posted on RAND.org on January 01, 2007
In this paper the authors describe a methodology for combining a convenience sample with a probability sample in order to produce an estimator with a smaller mean squared error (MSE) than estimators based on only the probability sample. The authors then explore the properties of the resulting composite estimator, a linear combination of the convenience and probability sample estimators with weights that are a function of bias. The authors discuss the estimator's properties in the context of web-based convenience sampling. Their analysis demonstrates that the use of a convenience sample to supplement a probability sample for improvements in the MSE of estimation may be practical only under limited circumstances. First, the remaining bias of the estimator based on the convenience sample must be quite small, equivalent to no more than 0.1 of the outcome's population standard deviation. For a dichotomous outcome, this implies a bias of no more than five percentage points at 50 percent prevalence and no more than three percentage points at 10 percent prevalence. Second, the probability sample should contain at least 1,000-10,000 observations for adequate estimation of the bias of the convenience sample estimator. Third, it must be inexpensive and feasible to collect at least thousands (and probably tens of thousands) of web-based convenience observations. The conclusions about the limited usefulness of convenience samples with estimator bias of more than 0.1 standard deviations also apply to direct use of estimators based on that sample.