Symmetry, direct measurement, and Torgerson's conjecture

Journal of Mathematical Psychology

Volumn 50, Issue 3, 2006, Pages 290-301

  Narens, Louis ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bisection; Direct measurement; Measurement theory; Psychophysics; Symmetry; Torgerson's conjecture

Indexed keywords

EID: 33646787485     PISSN: 00222496     EISSN: 10960880     Source Type: Journal    
DOI: 10.1016/j.jmp.2005.12.007     Document Type: Article

References (29)

1. Birnbaum, M.H. (1978). Differences and ratios in psychophysical measurement. In N.J. Castellan Jr., & F. Restle (Eds.), Cognitive Theory (Vol. 3). Hillsdale, NJ: Erlbaum.
2. Birnbaum M.H. Controversies in psychological measurement. In: Wegener B. (Ed). Social attitudes and psychological measurement (1982), Erlbaum, Hillsdale, NJ 401-485
3. Birnbaum H.H., and Elmasian R. Loudness ratios and differences involve the same psychophysical operation. Perception and Psychophysics 22 (1977) 383-391
4. Ekman G. Measurement of moral judgments: A comparison of scaling methods. Perceptual and Motor Skills 15 (1962) 3-9
5. Ekman G., and Künnapas T. Scales of aesthetic value. Perceptual and Motor Skills 14 (1962) 19-26
6. Ekman G., and Künnapas T. Measurement of aesthetic value by "direct" and "indirect" methods. Scandinavian Journal of Psychology 3 (1962) 33-39
7. Ellermeier W., and Faulhammer G. Empirical evaluation of axioms fundamental to Stevenss ratio-scaling approach: I. Loudness production. Perception and Psychophysics 62 8 (2000) 1505-1511
8. Ellermeier, W., Narens, L., & Dielmann, B. (2003). Perceptual ratios, differences, and the underlying scale. In B. Berglund, & E. Borg (Eds.), Fechner Day 2003. Proceedings of the 19th annual meeting of the international society for psychophysics (pp. 71-76). Stockholm, Sweden: International Society for Psychophysics.
9. Falmagne J.-C. Elements of psychophysical theory (1985), Oxford University Press, New York
10. Garner W.R. A technique and a scale for loudness measurement. Journal of Acoustical Society America 26 (1954) 73-88
11. Hagerty M., and Birnbaum M.H. Nonmetric tests of ratio vs. subtractive theories of stimulus comparison. Perception and Psychophysics 24 (1978) 121-129
12. Krantz, D. H., Luce, R.D., Suppes, P., & Tversky, A., (1971). Foundations of measurement (Vol. I). New York: Academic Press.
13. Luce R.D. A psychophysical theory of intensity proportions joint presentations and matches. Psychological Review 109 (2002) 520-532
14. Luce R.D. Symmetric and asymmetric matching of joint presentations. Psychological Review 111 (2004) 446-454
15. Luce R.D., and Narens L. Classification of concatenation structures by scale type. Journal of Mathematical Psychology 29 (1985) 1-72
16. Mellers B.A., Davis D., and Birnbaum M.H. Weight of evidence supports one operation for "ratios" and "differences" of heaviness. Journal of Experimental Psychology: Human Perception and Performance 10 (1984) 216-230
17. Miyamoto J.M. An axiomatization of the ratio/difference representation. Journal of Mathematical Psychology 27 (1983) 439-455
18. Narens L. Abstract measurement theory (1985), MIT Press, Cambridge, MA
19. Narens L. The measurement theory of dense threshold structures. Journal of Mathematical Psychology 38 (1994) 301-321
20. Narens L. A theory of magnitude estimation. Journal of Mathematical Psychology 40 (1996) 109-129
21. Peißner, M., 1999. Experimente zur direkten Skalierbarkeit von gesehenen Helligkeiten. Unpublished master's thesis, Universität Regensburg.
22. Pfanzagl J. Theory of measurement (1968), Wiley, New York
23. Plateau M.J. Sur la measure des sensations physiques, et sur la loi qui lie l'intensité de ces sensations à l'intensité de la cause excitante. Bulletin de l'Académie Royale des Sciences es Lettres, et des Beaux Arts de Belgique 33 (1872) 376-388
24. Schneider B.A. A technique for the nonmetric analysis of paired comparisons of psychological intervals. Psychometrika 45 (1980) 357-372
25. Steingrimsson, R., & Luce, R. D. (2005a). Empirical evaluation of a model of global psychophysical judgments: I. Behavioral properties of summations and productions. Journal of Mathematical Psychology, submitted for publication.
26. Steingrimsson, R., & Luce, R. D. (2005b). Empirical evaluation of a model of global psychophysical judgments: II. Behavioral properties linking summations and productions. Journal of Mathematical Psychology, submitted for publication.
27. Torgerson W.S. Distances and ratios in psychological scaling. Acta Psychologica 19 (1961) 201-205
28. Veit C.T. Ratio and subtractive processes in psychophysical judgment. Journal of Experimental Psychology: General 107 (1978) 81-107
29. Zimmer K. Examining the validity of numerical ratios in loudness fractionation. Perception and Psychophysics 67 (2005) 569-579