Screening tests are used in forensic science for field testing and directing laboratory analysis of physical evidence. These tests are often binary in that the data produced is interpreted as yes/no or present/absent. The utility of screening assays can be improved by evaluating a relevant background population and incorporating prior knowledge to refine the decision boundary. In the current study, each participant completed a questionnaire helpful in analyzing positive results when they did occur. Pattern matching was undertaken using neural networks, and decision thresholds were established using likelihood ratios derived from the population study. This approach significantly reduced the background positive rates compared to an arbitrary decision threshold technique. This methodology could be extended to other pattern-recognition algorithms used with instrumental data. This article also reports the largest population study to date focused on the organic residues of firearms discharge. The proportion of positives found in the population sample were less than 5 percent; when a likelihood ratio of 10:1 (shooter/not shooter) was used, the frequency of positives fell below 2 percent. The results suggest that background levels of organic gunshot residue will not be a significant analytic concern for assay development. (Publisher abstract modified)