title: On the relativity of relative frequencies.
abstract: The most prominent models of numerical representation posit that numerical symbols are converted into a single internal, abstract representation prior to estimation and comparison processing. Here, we (1) provide a mathematical analysis of the predictions of the abstract-representation hypothesis, assuming the validity of the analog-representation hypothesis, (2) run a simulation to assess the patterns of data that result from our mathematical analysis, and (3) conduct two experiments to test the predictions of our model, using relative frequencies as inputs. We assess relative frequencies in a typical numerical distance task, whereby participants are presented with two relative frequencies and asked to identify the one that represents the larger quantity. Our data reveal that relative frequencies' numerical representations (1) are analog and (2) are scale-specific (i.e., nonabstract).
authors.affiliation: Department of Psychology, University of North Carolina Wilmington, 601 South College Road, Wilmington, NC 28403-5612, USA.
authors.forename: Erin
authors.initials: E
authors.lastname: Warren
authors.forename: Dale J
authors.initials: DJ
authors.lastname: Cohen
mesh_terms: D000704:Analysis of Variance; D001307:Auditory Perception / Q000502:physiology*; D006801:Humans; D008433:Mathematics; D008960:Models, Psychological; D012660:Semantics; D013561:Symbolism; D013997:Time Factors