A membrane-based assay device for detecting the presence or quantity of an analyte residing in a test sample is provided. The device utilizes conjugated probes that contain a specific binding member for the analyte of interest. The specific binding member preferentially complexes with the analyte within a test sample when contacted therewith. Excess analyte that remains uncomplexed with the specific binding member undergoes non-specific binding, such as to a hydrophobic domain. As a result, the ability of the uncomplexed analyte to compete with the complexed analyte at the detection zone of the device is restricted. Thus, the incidence of “false negatives” is limited in a simple, efficient, and relatively inexpensive manner.