Mathematical characterization of dose uncertainty effects on functions summarizing findings of community noise attitudinal surveys

Abstract

Previous Monte Carlo simulations have quantified the extent to which dose (sound level) uncertainty in community noise dose–response surveys can bias the shape of inferred dose–response functions. The present work extends the prior findings to create a mathematical model of the biasing effect. The exact effect on any particular data set depends on additional attributes (situational variables) beyond dose uncertainty itself. Several variables and their interaction effects are accounted for in the model. The model produced identical results to the prior Monte Carlo simulations and thereby demonstrated the same slope reduction effect. This model was further exercised to demonstrate the nature and extent of situational variable interaction effects related to the range of doses employed and their distribution across the range. One manifestation was a false asymptotic behavior in the observed dose–response relationship. The mathematical model provides a means to not only predict dose uncertainty effects but also to serve as a foundation for correcting for such effects in regression analyses of transportation noise dose–response relationships.