The do’s and don’ts of psychophysical methods for interpretability of psychometric functions and their descriptors

  1. Miguel Ángel García-Pérez 1
  2. Rocío Alcalá-Quintana 1
  1. 1 Universidad Complutense de Madrid
    info

    Universidad Complutense de Madrid

    Madrid, España

    ROR 02p0gd045

Revista:
The Spanish Journal of Psychology

ISSN: 1138-7416

Año de publicación: 2019

Número: 22

Páginas: 1-30

Tipo: Artículo

DOI: 10.1017/SJP.2019.49 DIALNET GOOGLE SCHOLAR lock_openAcceso abierto editor

Otras publicaciones en: The Spanish Journal of Psychology

Resumen

Many areas of research require measuring psychometric functions or their descriptors (thresholds, slopes, etc.). Data for this purpose are collected with psychophysical methods of various types and justification for the interpretation of results arises from a model of performance grounded in signal detection theory. Decades of research have shown that psychophysical data display features that are incompatible with such framework, questioning the validity of interpretations obtained under it and revealing that psychophysical performance is more complex than this framework entertains. This paper describes the assumptions and formulation of the conventional framework for the two major classes of psychophysical methods (single- and dual-presentation methods) and presents various lines of empirical evidence that the framework is inconsistent with. An alternative framework is then described and shown to account for all the characteristics that the conventional framework regards as anomalies. This alternative process model explicitly separates the sensory, decisional, and response components of performance and represents them via parameters whose estimation characterizes the corresponding processes. Retrospective and prospective evidence of the validity of the alternative framework is also presented. A formal analysis also reveals that some psychophysical methods and response formats are unsuitable for separation of the three components of observed performance. Recommendations are thus given regarding practices that should be avoided and those that should be followed to ensure interpretability of the psychometric function, or descriptors (detection threshold, difference limen, point of subjective equality, etc.) obtained with shortcut methods that do not require estimation of psychometric functions.

Referencias bibliográficas

  • Alcalá-Quintana R., & García-Pérez M. A. (2011). A model for the time-order error in contrast discrimination. Quarterly Journal of Experimental Psychology, 64, 1221–1248. https://doi.org/10.1080/17470218.2010.540018
  • Alcalá-Quintana R., & García-Pérez M. A. (2013). Fitting model-based psychometric functions to simultaneity and temporal-order judgment data: MATLAB and R routines. Behavior Research Methods, 45, 972–998. https://doi. org/10.3758/s13428-013-0325-2
  • Allan L. G. (1977). The time-order error in judgments of duration. Canadian Journal of Psychology, 31, 24–31. https://doi.org/10.1037/h0081647
  • Allan L. G. (2002). The location and interpretation of the bisection point. The Quarterly Journal of Experimental Psychology Section B, 55, 43–60. https://doi. org/10.1080/02724990143000162
  • Bausenhart K. M., Bratzke D., & Ulrich R. (2016). Formation and representation of temporal reference information. Current Opinion in Behavioral Sciences, 8, 46–52. https://doi.org/10.1016/j.cobeha.2016.01.007
  • Bausenhart K. M., Dyjas O., & Ulrich R. (2015). Effects of stimulus order on discrimination sensitivity for short and long durations. Attention, Perception, & Psychophysics, 77, 1033–1043. https://doi.org/10.3758/s13414-015-0875-8
  • Bausenhart K. M., Dyjas O., Vorberg D., & Ulrich R. (2012). Estimating discrimination performance in two-alternative forced choice tasks: Routines for MATLAB and R. Behavior Research Methods, 44, 1157–1174. https://doi.org/10.3758/ s13428-012-0207-z
  • Bruno A., Ayhan I., & Johnston A. (2012). Effects of temporal features and order on the apparent duration of a visual stimulus. Frontiers in Psychology, 3, 90. https://doi.org/10.3389/fpsyg.2012.00090
  • Cai M. B., & Eagleman D. M. (2015). Duration estimates within a modality are integrated sub-optimally. Frontiers in Psychology, 6, 1041. https://doi.org/10.3389/fpsyg.2015.01041
  • Capstick G. (2012). Audiovisual prior entry: Evidence from the synchrony comparison judgment task (Doctoral dissertation), University of Ottawa, Canada. Retrieved from https://www.ruor.uottawa.ca/bitstream/10393/23100/1/Capstick_Gary_2012_thesis.pdf
  • Christensen R. H. B., & Brockhoff P. B. (2009). Estimation and inference in the same–different test. Food Quality and Preference, 20, 514–524. https://doi.org/10.1016/j.foodqual.2009.05.005
  • Church R. M., & Gibbon J. (1982). Temporal generalization. Journal of Experimental Psychology: Animal Behavior Processes, 8, 165–186. https://doi.org/10.1037/00977403.8.2.165
  • Clark T. K., Yi Y., Galvan-Garza R. C., Bermúdez Rey M. C., & Merfeld D. M. (2017). When uncertain, does human self-motion decision-making fully utilize complete information? Journal of Neurophysiology, 119, 1485–1496. https://doi.org/10.1152/jn.00680.2017
  • Diederich A., & Colonius H. (2015). The time window of multisensory integration: Relating reaction times and judgments of temporal order. Psychological Review, 122, 232–241. https://doi.org/10.1037/a0038696
  • Dyjas O., Bausenhart K. M., & Ulrich R. (2012). Trial-bytrial updating of an internal reference in discrimination tasks: Evidence from effects of stimulus order and trial sequence. Attention, Perception, & Psychophysics, 74, 1819–1841. https://doi.org/10.3758/s13414-012-0362-4
  • Dyjas O., Bausenhart K. M., & Ulrich R. (2014). Effects of stimulus order on duration discrimination sensitivity are under attentional control. Journal of Experimental Psychology: Human Perception and Performance, 40, 292–307. https://doi.org/10.1037/a0033611
  • Dyjas O., & Ulrich R. (2014). Effects of stimulus order on discrimination processes in comparative and equality judgments: Data and models. Quarterly Journal of Experimental Psychology, 67, 1121–1150. https://doi.org/10.1080/17470218.2013.847968
  • Dzhafarov E. N., & Colonius H. (1999). Fechnerian metrics in unidimensional and multidimensional stimulus spaces. Psychonomic Bulletin & Review, 6, 239–268. https://doi.org/10.3758/BF03212329
  • Dzhafarov E. N., & Colonius H. (2006). Reconstructing distances among objects from their discriminability. Psychometrika, 71, 365–386. https://doi.org/10.1007/s11336-003-1126-9
  • Ellinghaus R., Ulrich R., & Bausenhart K. M. (2018). Effects of stimulus order on comparative judgments across stimulus attributes and sensory modalities. Journal of Experimental Psychology: Human Perception and Performance, 44, 7–12. https://doi.org/10.1037/xhp0000495
  • Ellinghaus R., Gick M., Ulrich R., & Bausenhart K. M. (2019). Decay of internal reference information in duration discrimination: Intertrial interval modulates the Type B effect. Quarterly Journal of Experimental Psychology, 72, 1578–1586. https://doi.org/10.1177/1747021818808187
  • Ellis A. W., Klaus M. P., & Mast F. W. (2017). Vestibular cognition: The effect of prior belief on vestibular perceptual decision making. Journal of Neurology, 264, S74–S80. https://doi.org/10.1007/s00415-017-8471-6
  • Ehrenstein W. H., & Ehrenstein A. (1999). Psychophysical methods. In U. Windhorst & H. Johansson (Eds.), Modern techniques in neuroscience research (pp. 1211–1241). Berlin, Germany: Springer.
  • Faes F., Nollo G., Ravelli F., Ricci L., Vescovi M., Turatto M., … Antolini R. (2007). Small-sample characterization of stochastic approximation staircases in forced-choice adaptive threshold estimation. Perception & Psychophysics, 69, 254−262. https://doi.org/10.3758/BF03193747
  • Fechner G. T. (1860/1966). Elements of Psychophysics, Vol. 1. New York, NY: Holt. (Original work published 1860).
  • Fernberger S. W. (1913). On the relation of the methods of just perceptible differences and constant stimuli. The Psychological Monographs, 14, i–81. https://doi.org/10.1037/h0093068
  • Fernberger S. W. (1914a). A simplification of the practice of the method of constant stimuli. The American Journal of Psychology, 25, 121–130. https://doi.org/10.2307/1413025
  • Fernberger S. W. (1914b). On the elimination of the two extreme intensities of the comparison stimuli in the method of constant stimuli. Psychological Review, 21, 335–355. https://doi.org/10.1037/h0072494
  • Fernberger S. W. (1916). The influence of mental and physical work on the formation of judgments in lifted weight experiments. Journal of Experimental Psychology, 1, 508–532. https://doi.org/10.1037/h0075134
  • Fernberger S. W. (1920). Interdependence of judgments within the series for the method of constant stimuli. Journal of Experimental Psychology, 3, 126–150. https://doi.org/10.1037/h0065212
  • Fernberger S. W. (1921). An experimental study of the “stimulus error”. Journal of Experimental Psychology, 4, 63–76. https://doi.org/10.1037/h0071167
  • Fernberger S. W. (1930). The use of equality judgments in psychophysical procedures. Psychological Review, 37, 107–112. https://doi.org/10.1037/h0074662
  • Fernberger S. W. (1931). On absolute and relative judgments in lifted weight experiments. The American Journal of Psychology, 43, 560–578. https://doi.org/10.2307/1415158
  • Galanter E., & Messick S. (1961). The relation between category and magnitude scales of loudness. Psychological Review, 68, 363–372. https://doi.org/10.1037/h0038690
  • García-Pérez M. A. (1998). Forced-choice staircases with fixed step sizes: Asymptotic and small-sample properties. Vision Research, 38, 1861–1881. https://doi.org/10.1016/S0042-6989(97)00340-4
  • García-Pérez M. A. (2000). Optimal setups for forced-choice staircases with fixed step sizes. Spatial Vision, 13, 431–448. https://doi.org/10.1163/156856800741306
  • García-Pérez M. A. (2001). Yes−no staircases with fixed step sizes: Psychometric properties and optimal setup. Optometry and Vision Science, 78, 56–64. https://doi.org/10.1097/00006324-200101010-00015
  • García-Pérez M. A. (2002). Properties of some variants of adaptive staircases with fixed step sizes. Spatial Vision, 15, 303–321. https://doi.org/10.1163/15685680260174056
  • García-Pérez M. A. (2011). A cautionary note on the use of the adaptive up−down method. The Journal of the Acoustical Society of America, 130, 2098–2107. https://doi.org/10.1121/1.3628334
  • García-Pérez M. A. (2014a). Does time ever fly or slow down? The difficult interpretation of psychophysical data on time perception. Frontiers in Human Neuroscience, 8, 415. https://doi.org/10.3389/fnhum.2014.00415
  • García-Pérez M. A. (2014b). Adaptive psychophysical methods for nonmonotonic psychometric functions. Attention, Perception, & Psychophysics, 76, 621–641. https:// doi.org/10.3758/s13414-013-0574-2
  • García-Pérez M. A., & Alcalá-Quintana R. (2005). Sampling plans for fitting the psychometric function. The Spanish Journal of Psychology, 8, 256–289. https://doi.org/10.1017/S113874160000514X
  • García-Perez M. A., & Alcala-Quintana R. (2010a). The difference model with guessing explains interval bias in two-alternative forced-choice detection procedures. Journal of Sensory Studies, 25, 876–898. https://doi.org/10.1111/j.1745-459X.2010.00310.x
  • García-Pérez M. A., & Alcalá-Quintana R. (2010b). Reminder and 2AFC tasks provide similar estimates of the difference limen: A reanalysis of data from Lapid, Ulrich, and Rammsayer (2008) and a discussion of Ulrich and Vorberg (2009). Attention, Perception, & Psychophysics, 72, 1155–1178. https://doi.org/10.3758/APP.72.4.1155
  • García-Pérez M. A., & Alcalá-Quintana R. (2011a). Interval bias in 2AFC detection tasks: Sorting out the artifacts. Attention, Perception, & Psychophysics, 73, 2332–2352. https://doi.org/10.3758/s13414-011-0167-x
  • García-Pérez M. A., & Alcala-Quintana R. (2011b). Improving the estimation of psychometric functions in 2AFC discrimination tasks. Frontiers in Psychology, 2, Article 96. https://doi.org/10.3389/fpsyg.2011.00096
  • García-Pérez M. A., & Alcalá-Quintana R. (2012a). On the discrepant results in synchrony judgment and temporalorder judgment tasks: A quantitative model. Psychonomic Bulletin & Review, 19, 820–846. https://doi.org/10.3758/s13423-012-0278-y
  • García-Pérez M. A., & Alcalá-Quintana R. (2012b). Response errors explain the failure of independent-channels models of perception of temporal order. Frontiers in Psychology, 3, Article 94. https://doi.org/10.3389/fpsyg.2012.00094
  • García-Pérez M. A., & Alcalá-Quintana R. (2013). Shifts of the psychometric function: Distinguishing bias from perceptual effects. Quarterly Journal of Experimental Psychology, 66, 319–337. https://doi.org/10.1080/17470218.2012.708761
  • García-Pérez M. A., & Alcalá-Quintana R. (2015a). Converging evidence that common timing processes underlie temporal-order and simultaneity judgments: A model-based analysis. Attention, Perception, & Psychophysics, 77, 1750–1766. https://doi.org/10.3758/s13414-015-0869-6
  • García-Pérez M. A., & Alcalá-Quintana R. (2015b). The left visual field attentional advantage: No evidence of different speeds of processing across visual hemifields. Consciousness and Cognition, 37, 16–26. https://doi.org/10.1016/j.concog.2015.08.004
  • García-Pérez M. A., & Alcalá-Quintana R. (2015c). Visual and auditory components in the perception of asynchronous audiovisual speech. I-Perception, 6(6). https://doi.org/10.1177/2041669515615735
  • García-Pérez M. A., & Alcalá-Quintana R. (2017). The indecision model of psychophysical performance in dual-presentation tasks: Parameter estimation and comparative analysis of response formats. Frontiers in Psychology, 8, 1142. https://doi.org/10.3389/fpsyg.2017.01142
  • García-Pérez M. A., & Alcalá-Quintana R. (2018). Perceived temporal order and simultaneity: Beyond psychometric functions. In A. Vatakis, F. Balcı, M. Di Luca, & Á. Correa (Eds.), Timing and time perception: Procedures, measures, and applications (pp. 263–294). Leiden, The Netherlands: Brill.
  • García-Pérez M. A., & Núñez-Antón V. (2018). Nonparametric tests for equality of psychometric functions. Behavior Research Methods, 50, 2226–2255. https://doi.org/10.3758/s13428-0170989-0
  • García-Pérez M. A., & Peli E. (2014). The bisection point across variants of the task. Attention, Perception, & Psychophysics, 76, 1671–1697. https://doi.org/10.3758/s13414-014-0672-9
  • García-Pérez M. A., & Peli E. (2015). Aniseikonia tests: The role of viewing mode, response bias, and size–color illusions. Translational Vision Science & Technology, 4(3), Article 9. https://doi.org/10.1167/tvst.4.3.9
  • García-Pérez M. A., & Peli E. (2019). Psychophysical tests do not identify ocular dominance consistently. I-Perception, 10(2). https://doi.org/10.1177/2041669519841397
  • Gibbon J. (1981). On the form and location of the psychometric bisection function for time. Journal of Mathematical Psychology, 24, 58–87. http://doi.org/10.1016/0022-2496(81)90035-3
  • Gil S., & Droit-Volet S. (2011). “Time flies in the presence of angry faces”...depending on the temporal task used! Acta Psychologica, 136, 354–362. https://doi.org/ 10.1016/j.actpsy.2010.12.010
  • Green D. M., & Swets J. A. (1966). Signal Detection Theory and Psychophysics. New York, NY: Wiley.
  • Greenberg M. G. (1965). A modification of Thurstone’s law of comparative judgment to accommodate a judgment category of “equal” or “no difference”. Psychological Bulletin, 64, 108–112. https://doi.org/10.1037/h0022283
  • Hegelmaier F. (1852). Ueber das Gedächtniss für Linearanschauungen. Archiv für Physiologische Heilkunde, 11, 844–853.
  • Hellström Å. (1977). Time errors are perceptual. Psychological Research, 39, 345–388. https://doi.org/10.1007/BF00308933
  • Hellström Å. (1978). Factors producing and factors not producing time errors: An experiment with loudness comparisons. Perception & Psychophysics, 23, 433–444. https://doi.org/10.3758/BF03204147
  • Hellström Å. (1979). Time errors and differential sensation weighting. Journal of Experimental Psychology: Human Perception and Performance, 5, 460–477. https://doi. org/10.1037/0096-1523.5.3.460
  • Hellström Å. (1985). The time-order error and its relatives: Mirrors of cognitive processes in comparing. Psychological Bulletin, 97, 35–61. https://doi.org/10.1037/0033-2909.97.1.35
  • Hellström Å. (2003). Comparison is not just subtraction: Effects of timeand space-order on subjective stimulus difference. Perception & Psychophysics, 65, 1161–1177. https://doi.org/10.3758/BF03194842
  • Hellström Å., & Rammsayer T. H. (2015). Time-order errors and standard-position effects in duration discrimination: An experimental study and an analysis by the sensationweighting model. Attention, Perception, & Psychophysics, 77, 2409–2423. https://doi.org/10.3758/s13414-015-0946-x
  • James W. (1886). The perception of time. Journal of Speculative Philosophy, 20, 374–407.
  • Jamieson D. G., & Petrusic W. M. (1975). Presentation order effects in duration discrimination. Perception & Psychophysics, 17, 197–202. https://doi.org/10.3758/BF03203886
  • Johnson D. M., Watson C. S., & Kelly W. J. (1984). Performance differences among the intervals in forcedchoice tasks. Perception & Psychophysics, 35, 553–557. https://doi.org/10.3758/BF03205952
  • Kim M.-A., Lee Y.-M., & Lee H.-S. (2010). Comparison of d’ estimates produced by three versions of a duo-trio test for discriminating tomato juices with varying salt concentrations: The effects of the number and position of the reference stimulus. Food Quality and Preference, 21, 504–511. https://doi.org/10.1016/j.foodqual.2010.01.005
  • Kingdom F. A. A., & Prins N. (2010). Psychophysics: A practical introduction. New York, NY: Academic Press.
  • Kornbrot D. E. (2016). Human psychophysical functions, an update: Methods for identifying their form; estimating their parameters; and evaluating the effects of important predictors. Psychometrika, 81, 201–216. https://doi. org/10.1007/s11336-014-9418-9
  • Laming D., & Laming J. (1992). F. Hegelmaier: On memory for the length of a line. Psychological Research, 54, 233–239. https://doi.org/10.1007/BF01358261
  • Lapid E., Ulrich R., & Rammsayer T. (2008). On estimating the difference limen in duration discrimination tasks: A comparison of the 2AFC and the reminder task. Perception & Psychophysics, 70, 291–305. https://doi. org/10.3758/PP.70.2.291
  • Lapid E., Ulrich R., & Rammsayer T. (2009). Comparisons of two variants of the method of constant stimuli for estimating difference thresholds. Swiss Journal of Psychology, 68, 189–192. https://doi.org/10.1024/1421-0185.68.4.189
  • Levison M., & Restle F. (1968). Invalid results from the method of constant stimuli. Perception & Psychophysics, 4, 121–122. https://doi.org/10.3758/BF03209522
  • Lim K., Wang W., & Merfeld D. M. (2017). Unbounded evidence accumulation characterizes subjective visual vertical forced-choice perceptual choice and confidence. Journal of Neurophysiology, 118, 2636–2653. https://doi. org/10.1152/jn.00318.2017
  • Lyon D. O., & Eno H. L. (1914). A time experiment in psychophysics. Part II. Psychological Review, 21, 9–22. https://doi.org/10.1037/h0076086
  • Macmillan N. A., & Creelman C. D. (2005). Detection Theory: A user’s guide (2nd Ed.). Mahwah, NJ: Erlbaum.
  • Macmillan N. A., Kaplan H. L., & Creelman C. D. (1977). The psychophysics of categorical perception. Psychological Review, 84, 452–471. https://doi. org/10.1037/0033-295X.84.5.452
  • Magnotti J. F., Ma W. J., & Beauchamp M. S. (2013). Causal inference of asynchronous audiovisual speech. Frontiers in Psychology, 4, Article 798. https://doi.org/10.3389/ fpsyg.2013.00798
  • Marks L. E., & Algom D. (1998). Psychophysical scaling. In M. H. Birnbaum (Ed.), Handbook of perception and cognition. Measurement, judgment, and decision making (2nd Ed., pp. 81–178). New York, NY: Academic Press.
  • Marks L. E., & Gescheider G. A. (2002). Psychophysical scaling. In J. Wixted (Ed.), Stevens’ handbook of experimental psychology. Vol. 4, Methodology in experimental psychology (3rd Ed., pp. 91–138). New York, NY: Wiley.
  • Morgan M., Dillenburger B., Raphael S., & Solomon J. A. (2012). Observers can voluntarily shift their psychometric functions without losing sensitivity. Attention, Perception, & Psychophysics, 74, 185–193. https://doi.org/10.3758/ s13414-011-0222-7
  • Nachmias J. (2006). The role of virtual standards in visual discrimination. Vision Research, 46, 2456–2464. https://doi. org/10.1016/j.visres.2006.01.029
  • Olk B., & Harvey M. (2002). Effects of visible and invisible cueing on line bisection and Landmark performance in hemispatial neglect. Neuropsychologia, 40, 282–290. https:// doi.org/10.1016/S0028-3932(01)00095-1
  • Olk B., Wee J., & Kingstone A. (2004). The effect of hemispatial neglect on the perception of centre. Brain and Cognition, 55, 365–367. https://doi.org/10.1016/j. bandc.2004.02.048
  • Olson C. L., & Ogilvie J. C. (1972). The method of constant stimuli with two or more categories of response. Journal of Mathematical Psychology, 9, 320–338. https://doi. org/10.1016/0022-2496(72)90022-3
  • Patching G. R., Englund M. P., & Hellström Å. (2012). Timeand space-order effects in timed discrimination of brightness and size of paired visual stimuli. Journal of Experimental Psychology: Human Perception and Performance, 38, 915–940. https://doi.org/10.1037/a0027593
  • Peirce C. S., & Jastrow J. (1885). On small differences of sensation. Memoirs of the National Academy of Sciences, 3, 75–83.
  • Pelli D. G., & Farell B. (1995). Psychophysical methods. In M. Bass, E. W. van Stryland, D. R. Williams, & W. L. Wolfe (Eds.), Handbook of Optics. Vol. I, Fundamentals, techniques, and design (2nd Ed., pp. 29.1–29.13). New York, NY: McGraw-Hill.
  • Pfaffmann C. (1935). An experimental comparison of the method of single stimuli and the method of constant stimuli in gustation. The American Journal of Psychology, 47, 470–476. https://doi.org/10.2307/1416339
  • Rammsayer T., & Ulrich R. (2001). Counting models of temporal discrimination. Psychonomic Bulletin & Review, 8, 270–277. https://doi.org/10.3758/BF03196161
  • Rammsayer T., & Ulrich R. (2012). The greater temporal acuity in the reminder task than in the 2AFC task is independent of standard duration and sensory modality. Canadian Journal of Experimental Psychology, 66, 26–31. https://doi.org/10.1037/a0025349
  • Raslear T. G. (1985). Perceptual bias and response bias in temporal bisection. Perception & Psychophysics, 38, 261–268. https://doi.org/10.3758/BF03207153
  • Ross H. E., & Gregory R. L. (1964). Is the Weber fraction a function of physical or perceived input? Quarterly Journal of Experimental Psychology, 16, 116–122. https://doi. org/10.1080/17470216408416356
  • Schneider K. A., & Bavelier D. (2003). Components of visual prior entry. Cognitive Psychology, 47, 333–366. https://doi. org/10.1016/S0010-0285(03)00035-5
  • Schneider K. A., & Komlos M. (2008). Attention biases decisions but does not alter appearance. Journal of Vision, 8(15), 3. https://doi.org/10.1167/8.15.3
  • Self M. W., Mookhoek A., Tjalma N., & Roelfsema P. R. (2015). Contextual effects on perceived contrast: Figure– ground assignment and orientation contrast. Journal of Vision, 15(2), Article 2. https://doi.org/10.1167/15.2.2
  • Thurstone L. L. (1928). The phi-gamma hypothesis. Journal of Experimental Psychology, 11, 293–305. https:// doi.org/10.1037/h0070939
  • Treisman M., & Watts T. R. (1966). Relation between signal detectability theory and the traditional procedures for measuring sensory thresholds: Estimating d’ from results given by the method of constant stimuli. Psychological Bulletin, 66, 438–454. https://doi.org/10.1037/h0020413
  • Tünnermann J., & Scharlau I. (2018). Stuck on a plateau? A model-based approach to fundamental issues in visual temporal-order judgments. Vision, 2(3), Article 29. https:// doi.org/10.3390/vision2030029
  • Ulrich R. (1987). Threshold models of temporal-order judgments evaluated by a ternary response task. Perception & Psychophysics, 42, 224–239. https://doi. org/10.3758/BF03203074
  • Ulrich R., & Vorberg D. (2009). Estimating the difference limen in 2AFC tasks: Pitfalls and improved estimators. Attention, Perception, & Psychophysics, 71, 1219–1227. https://doi.org/10.3758/APP.71.6.1219
  • Urban F. M. (1908). The application of statistical methods to the problems of psychophysics. Philadelphia, PA: The Psychological Clinic Press.
  • Urban F. M. (1910). The method of constant stimuli and its generalizations. Psychological Review, 17, 229–259. https:// doi.org/10.1037/h0074515
  • Van Eijk R. L. J., Kohlrausch A., Juola J. F., & van de Par S. (2008). Audiovisual synchrony and temporal order judgments: Effects of experimental method and stimulus type. Perception & Psychophysics, 70, 955–968. https://doi. org/10.3758/PP.70.6.955
  • Vickers D. (1975). Where Angell feared to tread: Response time and frequency in three-category discrimination. In P. M. A. Rabbitt, & S. Dornic (Eds.), Attention and performance V (pp. 455–469). New York, NY: Academic Press.
  • Vickers D. (1979). Decision processes in visual perception. New York, NY: Academic Press.
  • Volkmann J. (1932). The method of single stimuli. The American Journal of Psychology, 44, 808–809. https://doi. org/10.2307/1414554
  • Watson C. S., Kellogg S. C., Kawanishi D. T., & Lucas P. A. (1973). The uncertain response in detection-oriented psychophysics. Journal of Experimental Psychology, 99, 180–185. https://doi.org/10.1037/h0034736
  • Wearden J. H., & Grindrod R. (2003). Manipulating decision processes in the human scalar timing system. Behavioural Processes, 61, 47–56. https://doi. org/10.1016/S0376-6357(02)00159-6
  • Weiß K., & Scharlau I. (2011). Simultaneity and temporal order perception: Different sides of the same coin? Evidence from a visual prior-entry study. Quarterly Journal of Experimental Psychology, 64, 394–416. https://doi.org/ 10.1080/17470218.2010.495783
  • Wever E. G., & Zener K. E. (1928). The method of absolute judgment in psychophysics. Psychological Review, 35, 466–493. https://doi.org/10.1037/h0075311
  • Wichmann F. A., & Jäkel F. (2018). Methods in psychophysics. In J. T. Wixted (Ed.), Stevens’ handbook of experimental psychology and cognitive neuroscience. Vol. 5, Methodology (4th Ed., pp. 265–306). Hoboken, NJ: Wiley.
  • Wickelgren W. A. (1968). Unidimensional strength theory and component analysis of noise in absolute and comparative judgments. Journal of Mathematical Psychology, 5, 102–122. https://doi.org/10.1016/00222496(68)90059-X
  • Woodrow H. (1935). The effect of practice upon time-order errors in the comparison of temporal intervals. Psychological Review, 42, 127–152. https://doi.org/10.1037/h0063696
  • Woodrow H., & Stott L. H. (1936). The effect of practice on positive time-order errors. Journal of Experimental Psychology, 19, 694–705. https://doi.org/10.1037/h0055057
  • Yi Y., & Merfeld D. M. (2016). A quantitative confidence signal detection model: 1. Fitting psychometric functions. Journal of Neurophysiology, 115, 1932–1945. https://doi. org/10.1152/jn.00318.2015
Fuente de los datos: Dialnet