The accumulator model of two-choice discrimination
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
Several formalisms propose that a representation of noisy evidence is evaluated against a criterion to produce a decision.
“Several formalisms propose that a representation of noisy evidence is evaluated against a criterion to produce a decision4-8.”
From Changes of mind in decision-making (2009) · cites this paper as [8]
Cites
An introduction to probability theory and its applications
(1958) · Journal of the Franklin Institute · doi:10.1016/0016-0032(58)90688-4 · Cited by 29,620 · see citing works
A Simplex Method for Function Minimization
Nelder, J. A., & Mead, R. (1965) · The Computer Journal · doi:10.1093/comjnl/7.4.308 · Cited by 28,905 · see citing works
A law of comparative judgment.
Thurstone, L. (1994) · Psychological Review · doi:10.1037/h0070288 · Cited by 5,077 · see citing works
Ratcliff, R. (1978) · Psychological Review · doi:10.1037/0033-295x.85.2.59 · Cited by 4,513 · see citing works
<i>The Theory of Stochastic Processes</i>
Cox, D. R., Miller, H. D., Weiss, G., & Shuler, K. (1966) · Physics Today · doi:10.1063/1.3047872 · Cited by 3,324 · see citing works
Stochastic Modeling of Elementary Psychological Processes
Snodgrass, J. G., Townsend, J. T., & Ashby, F. G. (1985) · The American Journal of Psychology · doi:10.2307/1422636 · Cited by 1,513 · see citing works
Kornblum, S. (1973) · Academic Press eBooks · Cited by 1,424 · see citing works
The Theory of Stochastic Processes.
Bartholomew, D. J., Cox, D., & Miller, H. D. (1966) · Journal of the Royal Statistical Society Series A (General) · doi:10.2307/2343509 · Cited by 1,201 · see citing works
Optimum Character of the Sequential Probability Ratio Test
Wald, A., & Wolfowitz, J. (1948) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177730197 · Cited by 1,162 · see citing works
Bergum, B. O., & Requin, J. (1980) · The American Journal of Psychology · doi:10.2307/1422120 · Cited by 1,045 · see citing works
Group reaction time distributions and an analysis of distribution statistics.
Ratcliff, R. (1979) · Psychological Bulletin · doi:10.1037/0033-2909.86.3.446 · Cited by 1,025 · see citing works
Information theory of choice-reaction times
Laming, D. (1968) · Medical Entomology and Zoology · Cited by 952 · see citing works
Models for choice-reaction time
Stone, M. (1960) · Psychometrika · doi:10.1007/bf02289729 · Cited by 696 · see citing works
Decision Processes in Visual Perception
(1979) · Elsevier eBooks · doi:10.1016/c2013-0-11654-6 · Cited by 511 · see citing works
A Sequential Theory of Psychological Discrimination
Link, S. W., & Heath, R. A. (1975) · Psychometrika · doi:10.1007/bf02291481 · Cited by 492 · see citing works
Katz, L., Johnson, N. L., & Kotz, S. (1970) · Journal of the American Statistical Association · doi:10.2307/2284307 · Cited by 375 · see citing works
Evidence for an Accumulator Model of Psychophysical Discrimination
VICKERS, D. (1970) · Ergonomics · doi:10.1080/00140137008931117 · Cited by 369 · see citing works
Self-citationTheoretical interpretations of the speed and accuracy of positive and negative responses.
Ratcliff, R. (1985) · Psychology Review · doi:10.1037/0033-295x.92.2.212 · Cited by 294 · see citing works
Vickers, D., Nettelbeck, T., & Willson, R. J. (1972) · Perception · doi:10.1068/p010263 · Cited by 269 · see citing works
Self-citationA theory of order relations in perceptual matching.
Ratcliff, R. (1981) · Psychological Review · doi:10.1037/0033-295x.88.6.552 · Cited by 265 · see citing works
Choice reaction performance following an error
Laming, D. (1979) · Acta Psychologica · doi:10.1016/0001-6918(79)90026-x · Cited by 263 · see citing works
The relative judgment theory of two choice response time
Link, S. W. (1975) · Journal of Mathematical Psychology · doi:10.1016/0022-2496(75)90053-x · Cited by 251 · see citing works
How old and young subjects monitor and control responses for accuracy and speed
Rabbitt, P. (1979) · British Journal of Psychology · doi:10.1111/j.2044-8295.1979.tb01687.x · Cited by 209 · see citing works
A Recruitment Theory of Simple Behavior
LaBerge, D. (1962) · Psychometrika · doi:10.1007/bf02289645 · Cited by 193 · see citing works
Correction for fast guessing and the speed-accuracy tradeoff in choice reaction time
Yellott, J. I. (1971) · Journal of Mathematical Psychology · doi:10.1016/0022-2496(71)90011-3 · Cited by 186 · see citing works
The Theory of Generalised Functions
Jones, D. S. (1982) · Cambridge University Press eBooks · doi:10.1017/cbo9780511569210 · Cited by 180 · see citing works
Fast guesses in choice reaction time
Ollman, R. (1966) · Psychonomic Science · doi:10.3758/bf03328004 · Cited by 154 · see citing works
SOME ALTERNATIVE STOCHASTIC MODELS OF CHOICE1
Audley, R., & Pike, A. (1965) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.1965.tb00342.x · Cited by 147 · see citing works
Response latency models for signal detection.
Pike, R. (1973) · Psychological Review · doi:10.1037/h0033871 · Cited by 147 · see citing works
Cognition, information processing, and motivation
Ydewalle, G. D. (1985) · Elsevier eBooks · Cited by 145 · see citing works
Vickers, D., & Packer, J. (1982) · Acta Psychologica · doi:10.1016/0001-6918(82)90006-3 · Cited by 139 · see citing works
Self-citationEvidence from auditory simple reaction times for both change and level detectors
Burbeck, S. L., & Luce, R. D. (1982) · Perception & Psychophysics · doi:10.3758/bf03204271 · Cited by 136 · see citing works
Some Experiments on Simple and Choice Reaction Time.
Snodgrass, J. G., Luce, R. D., & Galanter, E. (1967) · Journal of Experimental Psychology · doi:10.1037/h0021280 · Cited by 100 · see citing works
A biased random walk model for two choice reaction times
Ashby, F. G. (1983) · Journal of Mathematical Psychology · doi:10.1016/0022-2496(83)90011-1 · Cited by 85 · see citing works
LATENCY AND RELATIVE FREQUENCY OF RESPONSE IN PSYCHOPHYSICAL DISCRIMINATION
Pike, A. R. (1968) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.1968.tb00407.x · Cited by 67 · see citing works
Correction for guessing in choice reaction time
Yellott, J. I. (1967) · Psychonomic Science · doi:10.3758/bf03331682 · Cited by 62 · see citing works
Pike, A. R. (1966) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.1966.tb00351.x · Cited by 59 · see citing works
Experimental paradigms emphasising state or process limitations: II effects on confidence
Vickers, D., Smith, P. L., Burt, J. S., & Brown, M. (1985) · Acta Psychologica · doi:10.1016/0001-6918(85)90018-6 · Cited by 50 · see citing works
Self-citationModeling evidence accumulation with partial loss in expanded judgment.
Smith, P. L., & Vickers, D. (1989) · Journal of Experimental Psychology Human Perception & Performance · doi:10.1037/0096-1523.15.4.797 · Cited by 45 · see citing works
Self-citationReaction-Time Distributions in the Detection of Weak Signals in Noise
Carterette, E. C., Friedman, M. P., & Cosmides, R. (1965) · The Journal of the Acoustical Society of America · doi:10.1121/1.1909737 · Cited by 42 · see citing works
Accumulator and Random-Walk Models of Psychophysical Discrimination: A Counter-Evaluation
Vickers, D., & Smith, P. L. (1985) · Perception · doi:10.1068/p140471 · Cited by 29 · see citing works
Self-citationInspection Time and Mild Mental Retardation
Nettelbeck, T. (1985) · International review of research in mental retardation · doi:10.1016/s0074-7750(08)60234-7 · Cited by 20 · see citing works
A critical comparison of two random-walk models for two-choice reaction time
Laming, D. (1979) · Acta Psychologica · doi:10.1016/0001-6918(79)90001-5 · Cited by 17 · see citing works
On the relations between random walk models for two-choice response times
Swensson, R. G., & Green, D. M. (1977) · Journal of Mathematical Psychology · doi:10.1016/0022-2496(77)90034-7 · Cited by 12 · see citing works
Fourier analysis of reaction time data
Green, D. M. (1971) · Behavior Research Methods · doi:10.3758/bf03209931 · Cited by 8 · see citing works
Masking Effects of Similar and Dissimilar Letters: A Test of the Interactive Channels Model
Townsend, J. T., & Snodgrass, J. G. (1977) · Perceptual and Motor Skills · doi:10.2466/pms.1977.44.3c.1219 · Cited by 6 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
The time course of perceptual choice: The leaky, competing accumulator model.
Usher, M., & McClelland, J. L. (2001) · Psychological Review · doi:10.1037/0033-295x.108.3.550 · Cited by 2,152 · see citing works
Diffusion decision model: Current issues and history
Ratcliff, R., Smith, P. L., Brown, S. D., & McKoon, G. (2016) · Trends in Cognitive Sciences · doi:10.1016/j.tics.2016.01.007 · Cited by 1,630 · see citing works
“Instead, they were better described by a version of the Vickers accumulator model [98], in which only large stimulus elements are accumulated and small ones are ignored.”
Self-citationModeling Response Times for Two-Choice Decisions
Ratcliff, R., & Rouder, J. N. (1998) · Psychological Science · doi:10.1111/1467-9280.00067 · Cited by 1,478 · see citing works
Psychology and neurobiology of simple decisions
Smith, P. L., & Ratcliff, R. (2004) · Trends in Neurosciences · doi:10.1016/j.tins.2004.01.006 · Cited by 1,051 · see citing works
Self-citationRepresentation of Confidence Associated with a Decision by Neurons in the Parietal Cortex
Kiani, R., & Shadlen, M. N. (2009) · Science · doi:10.1126/science.1169405 · Cited by 1,027 · see citing works
Ratcliff, R., & Tuerlinckx, F. (2002) · Psychonomic Bulletin & Review · doi:10.3758/bf03196302 · Cited by 838 · see citing works
A supramodal accumulation-to-bound signal that determines perceptual decisions in humans
O'Connell, R. G., Dockree, P. M., & Kelly, S. P. (2012) · Nature Neuroscience · doi:10.1038/nn.3248 · Cited by 755 · see citing works
Changes of mind in decision-making
Resulaj, A., Kiani, R., Wolpert, D. M., & Shadlen, M. N. (2009) · Nature · doi:10.1038/nature08275 · Cited by 678 · see citing works
The effect of stimulus strength on the speed and accuracy of a perceptual decision
Palmer, J., Huk, A. C., & Shadlen, M. N. (2005) · Journal of Vision · doi:10.1167/5.5.1 · Cited by 691 · see citing works
Internal and External Influences on the Rate of Sensory Evidence Accumulation in the Human Brain
Kelly, S. P., & O'Connell, R. G. (2013) · The Journal of Neuroscience · doi:10.1523/jneurosci.3355-13.2013 · Cited by 455 · see citing works
Kiani, R., Hanks, T. D., & Shadlen, M. N. (2008) · The Journal of Neuroscience · doi:10.1523/jneurosci.4761-07.2008 · Cited by 500 · see citing works
Choice Certainty Is Informed by Both Evidence and Decision Time
Kiani, R., Corthell, L., & Shadlen, M. N. (2014) · Neuron · doi:10.1016/j.neuron.2014.12.015 · Cited by 470 · see citing works
The classic P300 encodes a build‐to‐threshold decision variable
Twomey, D. M., Murphy, P. R., Kelly, S. P., & O'Connell, R. G. (2015) · European Journal of Neuroscience · doi:10.1111/ejn.12936 · Cited by 376 · see citing works
Confidence as Bayesian probability: From neural origins to behavior
Meyniel, F., Sigman, M., & Mainen, Z. F. (2015) · Neuron · doi:10.1016/j.neuron.2015.09.039 · Cited by 349 · see citing works
Ploran, E. J., Nelson, S. M., Velanova, K., Donaldson, D. I., Petersen, S. E., & Wheeler, M. E. (2007) · The Journal of Neuroscience · doi:10.1523/jneurosci.3522-07.2007 · Cited by 282 · see citing works
“Accumulator models (Audley and Pike, 1965; Link and Heath, 1975; Ratcliff, 1978; Ratcliff and McKoon, 1982; Smith and Vickers, 1988; Usher and McClelland, 2001) describe evidence gathering as a gradual process in which evidence supporting different choices accrues over time.”
BackgroundEffects of cortical microstimulation on confidence in a perceptual decision
Fetsch, C. R., Kiani, R., Newsome, W. T., & Shadlen, M. N. (2014) · Neuron · doi:10.1016/j.neuron.2014.07.011 · Cited by 185 · see citing works
Motor effort alters changes of mind in sensorimotor decision making
Burk, D., Ingram, J. N., Franklin, D. W., Shadlen, M. N., & Wolpert, D. M. (2014) · PLoS ONE · doi:10.1371/journal.pone.0092681 · Cited by 117 · see citing works
Visual attention modulates the integration of goal-relevant evidence and not value
Sepulveda, P., Usher, M., Davies, N., Benson, A. A., Ortoleva, P., & De Martino, B. (2020) · eLife · doi:10.7554/elife.60705 · Cited by 121 · see citing works
Facial Trust Appraisal Negatively Biased in Borderline Personality Disorder
Fertuck, E. A., Grinband, J., & Stanley, B. (2013) · Psychiatry Research · doi:10.1016/j.psychres.2013.01.004 · Cited by 104 · see citing works
Brumby, D. P., Cox, A. L., Back, J., & Gould, S. J. J. (2013) · Journal of Experimental Psychology: Applied · doi:10.1037/a0032696 · Cited by 103 · see citing works
Unconscious information changes decision accuracy but not confidence
Vlassova, A., Donkin, C., & Pearson, J. (2014) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1403619111 · Cited by 70 · see citing works
A note on the distribution of response times for a random walk with Gaussian increments
Smith, P. L. (1990) · Journal of Mathematical Psychology · doi:10.1016/0022-2496(90)90023-3 · Cited by 51 · see citing works
Self-citationExtended LATER model can account for trial-by-trial variability of both pre- and post-processes
Nakahara, H., Nakamura, K., & Hikosaka, O. (2006) · Neural Networks · doi:10.1016/j.neunet.2006.07.001 · Cited by 45 · see citing works
Dissociating early and late error signals in perceptual recognition
Wheeler, M. E., Petersen, S. E., Nelson, S. M., Ploran, E. J., & Velanova, K. (2008) · Journal of Cognitive Neuroscience · doi:10.1162/jocn.2008.20155 · Cited by 30 · see citing works
- Authors
- Smith, P. L., & Vickers, D.
- Affiliations
- The University of Adelaide (AU)
- Corresponding author
- Smith, Philip L
- ORCID
- Smith, Philip L
- Venue
- Journal of Mathematical Psychology
- Publisher
- Elsevier BV
- Published
- 1988-06
- Volume
- 32
- Issue
- 2
- Pages
- 135-168
- ISSN
- 0022-2496 (ISSN-L)
- OpenAlex
- W2077632748
- Cited by
- 223
- References
- 46
- Citations by year
- 2026: 3 · 2025: 5 · 2024: 9 · 2023: 8 · 2022: 7 · 2021: 8 · 2020: 17 · 2019: 8 · 2018: 13 · 2017: 5 · 2016: 14 · 2015: 8 · 2014: 12 · 2013: 10 · 2012: 7
- FWCI
- 1.95
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Mathematical Psychology (publishedVersion)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural and Behavioral Psychology Studies
- Social Sciences › Decision Sciences › General Decision Sciences › Decision-Making and Behavioral Economics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Visual perception and processing mechanisms
- Keywords
- accumulator model, two-choice discrimination, decision-making, race model, first passage time distribution, response confidence, discriminability, decision criterion, sampling time, reaction time (psychology)
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review