Abstract
An algebraic model of bisection —a special case of Pfanzagl’s general measurement system-was tested for brightness. Nonparametric scalability, a condition derived from reflexivity, commutativity, and bisymmetry, was disconfirmed, leading to a rejection of the commutativity axiom, and necessitating the incorporation of a response bias parameter. The systematic bias in the data was substantially reduced by the introduction of the response bias parameter-interpreted as “position” bias, not hysteresis. The data are generally supportive of Pfanzagl’s bisection system, although the failure of commutativity requires the incorporation of a response bias parameter.
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This research was supported by the Advanced Research Projects Agency of the Department of Defense and was monitored by the Air Force Office of Scientific Research under Contract No. F44620-67-C-0099. We are indebted to Robyn Dawes for helpful comments.
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Fagot, R.F., Stewart, M.R. Test of a response bias model of bisection. Perception & Psychophysics 7, 257–262 (1970). https://doi.org/10.3758/BF03210160
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DOI: https://doi.org/10.3758/BF03210160