Some bulk properties of interstellar dust are known through infrared and X-ray observations of the interstellar medium. However, the properties of individual interstellar dust particles are largely unconstrained, so it is not known whether individual interstellar dust particles can be definitively distinguished from interplanetary dust particles in the Stardust Interstellar Dust Collector (SIDC) based only on chemical, mineralogical or isotopic analyses. It was therefore understood from the beginning of the Stardust Interstellar Preliminary Examination (ISPE) that identification of interstellar dust candidates would rest on three criteria - broad consistency with known extraterrestrial materials, inconsistency with an origin as secondary ejecta from impacts on the spacecraft, and consistency, in a statistical sense, of observed dynamical properties - that is, trajectory and capture speed - with an origin in the interstellar dust stream. Here we quantitatively test four interstellar dust candidates, reported previously [1], against these criteria