title: Efficient estimation of Weber's W.
abstract: Many studies rely on estimation of Weber ratios (W) in order to quantify the acuity an individual's approximate number system. This paper discusses several problems encountered in estimating W using the standard methods, most notably low power and inefficiency. Through simulation, this work shows that W can best be estimated in a Bayesian framework that uses an inverse (1/W) prior. This beneficially balances a bias/variance trade-off and, when used with MAP estimation is extremely simple to implement. Use of this scheme substantially improves statistical power in examining correlates of W.
authors.affiliation: Department of Brain and Cognitive Sciences, University of Rochester, Rochester, NY, USA. spiantado@gmail.com.
authors.forename: Steven T
authors.initials: ST
authors.lastname: Piantadosi
mesh_terms: D001499:Bayes Theorem; D013223:Statistics as Topic
keywords: Bayesian statistics; Numerical cognition; Statistical estimation; Weber ratio