The problem of meaningfulness: Weber's law, Guilford's power law, and the near-miss-to-Weber's law

The present paper provides reformulations of common models of discrimination, like for instance, Weber's law, Guilford's power law, and the near-miss-to-Weber's law. All models are based on the assumption that the model parameters might depend on the underlying physical stimulus scale by which the physical intensities are measured. By discussing the meaningfulness of the model parameters, we come to the conclusion that the near-miss-to-Weber's law can be applied to physical quantities which are measured on a ratio-, interval-, or log-interval scale, whereas applications of Weber's law and Guilford's power law are necessarily restricted to physical ratio scales. Finally, we discuss the meaningfulness of an empirically based submodel of the near-miss-to-Weber's law, referred to as fixed-point model. The results show that, from a theoretical point of view, the fixed-point model is superior to Guilford's power law and the near-miss-to-Weber's law.