Experimental investigation is fundamental to theory-building in cognitive science, but its value depends on the linking assumptions made by researchers about the mapping between empirical measurements and theoretical constructs. We argue that sufficient clarity and justification are often lacking for linking assumptions made in visual world eye-tracking, a widely used experimental method in psycholinguistic research. We test what we term the Referential Belief linking assumption: that the proportion of looks to a referent in a time window reflects participants’ degree of belief that the referent is the in- tended target in that time window. We do so by comparing eye-tracking data against explicit beliefs collected in an incremental decision task (Exp. 1), which replicates a scalar implicature processing study (Exp. 3 of Sun & Breheny, 2020). In Exp. 2, we replicate Sun and Breheny (2020) in a web-based eye-tracking paradigm using WebGazer.js. The results provide support for the Referential Belief link and cautious optimism for the prospect of conducting web-based eye-tracking. We discuss limitations on both fronts.