A selective summary of visual averaging research and issues up to 2000.

Ariely's (2001) "Seeing Sets: Representation by Statistical Properties" (Psychological Science, 12, 157-162) rekindled interest in summary-value estimation for visual ensembles (groups of similar items). Revisiting and reinvigorating research on the "intuitive statistician" has prompted a new set of insights and debates concerning how and why the visual system might benefit from a compact representation of the optic array and how this might relate to crowding, sparse representation, efficiency coding, and processing limits. New research tools and imaging techniques coupled with solid psychophysical work have added substantially to the large base of work done in the 20th century. The present brief review acts as a summary of the ensemble of work prior to Ariely's (2001) landmark paper to encourage a comprehensive continuity of knowledge and reintroduce some of the contemporaneous concerns to help inform ongoing research and modeling.

[1]  D. Spalding.  The Principles of Psychology , 1873, Nature.

[2]  J. Jastrow.  Studies from the University of Wisconsin: On the Judgment of Angles and Positions of Lines , 1892 .

[3]  C. H. Judd.  A study of geometrical illusions. , 1899 .

[4]  J. Wallin.  The estimation of the midrate between two tempos. , 1912 .

[5]  E. S. Pearson.  ON THE VARIATIONS IN PERSONAL EQUATION AND THE CORRELATION OF SUCCESSIVE JUDGMENTS , 1922 .

[6]  H. K. Wolfe.  On the Estimation of the Middle of Lines , 1923 .

[7]  M. Pratt.  The visual estimation of angles. , 1926 .

[8]  A preliminary study of bisection of lines. , 1935 .

[9]  H. Helson.  Adaptation-level as frame of reference for prediction of psychophysical data. , 1947, The American journal of psychology.

[10]  T. Reese,et al.  The Effect of Differential Reinforcement on the Discrimination of Visual Number , 1951 .

[11]  Philip Br.  Effect of length of series upon generalization and central tendency in the discrimination of a series of stimuli. , 1952 .

[12]  R. Gottsdanker.  The accuracy of prediction motion. , 1952, Journal of experimental psychology.

[13]  B. Philip.  Effect of length of series upon generalization and central tendency in the discrimination of a series of stimuli. , 1952, Canadian journal of psychology.

[14]  D. R. Brown,et al.  Stimulus-similarity and the anchoring of subjective scales. , 1953, The American journal of psychology.

[15]  C. Slack.  Some characteristics of the 'Range effect'. , 1953, Journal of experimental psychology.

[16]  F. Attneave.  Some informational aspects of visual perception. , 1954, Psychological review.

[17]  H. Helson,et al.  The use of comparative rating scales for the evaluation of psychophysical data. , 1954, The American journal of psychology.

[18]  J. Deese.  Some problems in the theory of vigilance. , 1955, Psychological review.

[19]  W. Estes.  Statistical theory of spontaneous recovery and regression. , 1955, Psychological review.

[20]  F. W. Irwin,et al.  Further tests of theories of decision in an expanded judgment situation. , 1956, Journal of experimental psychology.

[21]  R. Gottsdanker.  The ability of human operators to detect acceleration of target motion. , 1956, Psychological bulletin.

[22]  F. W. Irwin,et al.  Further tests of theories of decision in an expanded judgment situation. , 1956, Journal of experimental psychology.

[23]  F. W. Irwin,et al.  Tests of two theories of decision in an expanded judgment situation. , 1956, Journal of experimental psychology.

[24]  S. S. Stevens,et al.  Ratio scales and category scales for a dozen perceptual continua. , 1957, Journal of experimental psychology.

[25]  C. H. Baker.  Towards a theory of vigilance. , 1959, Canadian journal of psychology.

[26]  N. Anderson,et al.  Likelihood judgments and sequential effects in a two-choice probability learning situation. , 1960, Journal of experimental psychology.

[27]  R. Calfee,et al.  Context effects in judgment: adaptation level as a function of the mean, midpoint, and median of the stimuli. , 1960, Journal of experimental psychology.

[28]  W. Edwards.  Behavioral decision theory. , 1961, Annual review of psychology.

[29]  C. H. Baker.  On temporal extrapolation. , 1962 .

[30]  N. Anderson.  Application of an Additive Model to Impression Formation , 1962, Science.

[31]  J. Spencer.  A FURTHER STUDY OF ESTIMATING AVERAGES , 1963 .

[32]  C. Peterson,et al.  MODE, MEDIAN, AND MEAN AS OPTIMAL STRATEGIES. , 1964, Journal of experimental psychology.

[33]  N. Anderson.  Test of a model for number-averaging behavior , 1964 .

[34]  R. S. Rodger,et al.  EFFECT OF "APPARENT" INSTRUCTIONS ON BRIGHTNESS JUDGMENTS. , 1964, Journal of experimental psychology.

[35]  A. Parducci.  Category judgment: a range-frequency model. , 1965, Psychological review.

[36]  N. Anderson.  Averaging versus adding as a stimulus-combination rule in impression formation. , 1965, Journal of experimental psychology.

[37]  M. Teghtsoonian.  THE JUDGMENT OF SIZE. , 1965, The American journal of psychology.

[38]  L. Beach,et al.  Intuitive estimation of means , 1966 .

[39]  Changes in perceived size of angle as a function or orientation in the frontal plane. , 1966, Journal of experimental psychology.

[40]  T. Engen,et al.  Effect of reference number on magnitude estimation , 1966 .

[41]  L. Beach,et al.  Man as an Intuitive Statistician , 2022 .

[42]  R. Swensson,et al.  Instructions about randomness and run dependency in two-choice learning. , 1967, Journal of experimental psychology.

[43]  The frequency principle for comparative judgments) , 1967 .

[44]  N. Anderson.  Application of a weighted average model to a psychophysical averaging task , 1967 .

[45]  N. Anderson,et al.  Further data on a weighted average model for judgment in a lifted weight task , 1968 .

[46]  M. Mashhour,et al.  On the new “psychophysical law”: A validation study , 1968 .

[47]  K. E. Beery.  Estimation of Angles , 1968, Perceptual and motor skills.

[48]  N. Anderson.  Averaging of space and number stimuli with simultaneous presentation. , 1968, Journal of experimental psychology.

[49]  P. Stoloff.  Detection and scaling of statistical differences between visual textures , 1969 .

[50]  S. J. Rule.  Subject difference in exponents from circle size, numerousness, and line length , 1969 .

[51]  A. Miller,et al.  Magnitude estimation of average length and average inclination. , 1969, Journal of experimental psychology.

[52]  G. Lowe,et al.  Presentation time and the intuitive estimation of means , 1969 .

[53]  N. Anderson,et al.  Subjective averaging of length with serial presentation , 1969 .

[54]  D. Massaro.  The effects of feedback in psychophysical tasks , 1969 .

[55]  The intuitive estimation of means with auditory presentation , 1969 .

[56]  G. H. Fisher.  An Experimental Study of Angular Subtension , 1969, The Quarterly journal of experimental psychology.

[57]  J. Baird,et al.  Test of a Cognitive Theory of Psychophysics: Size Discrimination , 1970, Perceptual and motor skills.

[58]  John E. Laestadius.  Tolerance for errors in intuitive mean estimations , 1970 .

[59]  M. Teghtsoonian,et al.  Two varieties of perceived length , 1970 .

[60]  Magnitude Estimation of Average Length: A Follow-up , 1970 .

[61]  W. Groman,et al.  Some evidence for a visual slant averaging mechanism , 1970 .

[62]  J. Baird,et al.  Relative frequencies of numerical responses in ratio estimation1 , 1970 .

[63]  L. E. Krueger.  Apparent combined length of two-line and four-line sets , 1970 .

[64]  C. Hendrick,et al.  Number averaging behavior: A primacy effect , 1970 .

[65]  N. Anderson.  Functional measurement and psychophysical judgment. , 1970, Psychological review.

[66]  B. Stacey,et al.  Judgment of angle size: An experimental appraisal , 1971 .

[67]  Paul Slovic,et al.  Comparison of Bayesian and Regression Approaches to the Study of Information Processing in Judgment. , 1971 .

[68]  M. Birnbaum,et al.  Contextual effects in information integration. , 1971, Journal of experimental psychology.

[69]  E. Abravanel.  The synthesis of length within and between perceptual systems , 1971 .

[70]  V. Lollo,et al.  Judgment and response in magnitude estimation. , 1971 .

[71]  D. Weiss.  Averaging: An empirical validity criterion for magnitude estimation , 1972 .

[72]  R. Sekuler,et al.  Changes in visual spatial organization: response frequency equalization versus adaptation level. , 1973, Journal of experimental psychology.

[73]  N. Anderson.  Serial position curves in impression formation. , 1973 .

[74]  M. Birnbaum,et al.  Subjective correlation and the size-numerosity illusion. , 1974, Journal of experimental psychology.

[75]  N. Anderson,et al.  Performance = Motivation × Ability: An integration-theoretical analysis. , 1974 .

[76]  I. Levin.  Averaging processes in ratings and choices based on numerical information , 1974, Memory & cognition.

[77]  I. Levin.  Averaging processes and intuitive statistical judgments , 1974 .

[78]  M. Birnbaum.  The nonadditivity of personality impressions. , 1974, Journal of experimental psychology.

[79]  Norman H. Anderson,et al.  Integration of semantic constraints , 1974 .

[80]  N. Anderson,et al.  Cognitive algebra of the equation: Gift size = generosity = income , 1974 .

[81]  G Stanley,et al.  Adding and averaging angles: comparison of haptic-visual and visual-visual information integration. , 1974, Acta psychologica.

[82]  E. Poulton.  Range Effects in Experiments on People , 1975 .

[83]  J. Bettman,et al.  Multiattribute Measurement Models and Multiattribute Attitude Theory: A Test of Construct Validity , 1975 .

[84]  B. Fischhoff,et al.  Attribution Theory and Judgment under Uncertainty , 1975 .

[85]  Distribution Characteristics as Predictors of Error in Intuitive Estimation of Means , 1975 .

[86]  James Shanteau,et al.  Do Consumers Evaluate Products by Adding or Averaging Attribute Information , 1976 .

[87]  A. Lovie,et al.  Teaching intuitive statistics I: Estimating means and variances , 1976 .

[88]  T. Indow,et al.  Scaling of dot numerosity , 1977 .

[89]  I. Levin,et al.  The processing of deviant information in prediction and evaluation , 1977, Memory & cognition.

[90]  S. Runeson.  On the possibility of "smart" perceptual mechanisms. , 1977, Scandinavian journal of psychology.

[91]  M. Morgan.  Differential visual persistence between the two eyes: a model for the Fertsch-Pulfrich effect. , 1977, Journal of experimental psychology. Human perception and performance.

[92]  N. Anderson,et al.  Integration Theory Applied to Children's Judgments of Equity. , 1978 .

[93]  E. Simms.  Averaging Model of Information Integration Theory Applied in the Classroom. , 1978 .

[94]  N. Anderson.  Algebraic Rules in Psychology Measurement , 1979 .

[95]  L. Hasher,et al.  Automatic and effortful processes in memory. , 1979 .

[96]  E. Poulton.  Models for biases in judging sensory magnitude. , 1979, Psychological bulletin.

[97]  I. Levin,et al.  Information Variability and Reliability Effects in Evaluating Student Performance. , 1980 .

[98]  R. Neill.  Spatio-temporal averaging and the dynamic visual noise stereophenomenon , 1981, Vision Research.

[99]  R. Hogarth.  Beyond discrete biases: Functional and dysfunctional aspects of judgmental heuristics. , 1981 .

[100]  I. Eggleton.  Intuitive Time-Series Extrapolation , 1982 .

[101]  L. E. Krueger,et al.  Single judgments of numerosity , 1982, Perception & psychophysics.

[102]  J. Zwislocki.  Group and individual relations between sensation magnitudes and their numerical estimates , 1983, Perception & psychophysics.

[103]  David J. Samson,et al.  Intuitive averaging of categorized numerical stimuli , 1983 .

[104]  G. Murphy,et al.  The utility of theories in intuitive statistics: The robustness of theory-based judgments. , 1984 .

[105]  L Hasher,et al.  Automatic processing of fundamental information: the case of frequency of occurrence. , 1984, The American psychologist.

[106]  P. Pollard.  Intuitive judgments of proportions, means, and variances: A review , 1984 .

[107]  L. Beach,et al.  The citation bias: Fad and fashion in the judgment and decision literature. , 1984 .

[108]  W. Wiest,et al.  Stevens's exponent for psychophysical scaling of perceived, remembered, and inferred distance. , 1985, Psychological bulletin.

[109]  D. Algom,et al.  Integration of stimulus dimensions in perception and memory: composition rules and psychophysical relations. , 1985, Journal of experimental psychology. General.

[110]  D. W. Heeley.  Spatial frequency discrimination for sinewave gratings with random, bandpass frequency modulation: evidence for averaging in spatial acuity. , 1987, Spatial vision.

[111]  L. M. Ward,et al.  Remembrance of sounds past: memory and psychophysical scaling. , 1987, Journal of experimental psychology. Human perception and performance.

[112]  N. Anderson.  Contributions To Information Integration Theory: Volume 1: Cognition , 1991 .

[113]  J. Gibbon,et al.  Human bisection at the geometric mean , 1991 .

[114]  J. Wearden.  Human Performance on an Analogue of an Interval Bisection Task , 1991, The Quarterly journal of experimental psychology. B, Comparative and physiological psychology.

[115]  Scott N. J. Watamaniuk,et al.  Temporal and spatial integration in dynamic random-dot stimuli , 1992, Vision Research.

[116]  Andrew P. Duchon,et al.  The human visual system averages speed information , 1992, Vision Research.

[117]  R. Siegler,et al.  Metrics and mappings: a framework for understanding real-world quantitative estimation. , 1993, Psychological review.

[118]  Robert S. Siegler,et al.  Metrics and Mappings: A Framework for Understanding Real-World Quantitative Estimation. , 1993 .

[119]  S. Runeson.  Psychophysics: The failure of an elementaristic dream , 1994, Behavioral and Brain Sciences.

[120]  L. Myaskovsky,et al.  The Easy Path From Many To Much: the Numerosity Heuristic , 1994, Cognitive Psychology.

[121]  J. Wearden,et al.  Stimulus Range Effects in Temporal Bisection by Humans , 1996, The Quarterly journal of experimental psychology. B, Comparative and physiological psychology.

[122]  P. Atchley,et al.  Discrimination of speed distributions: Sensitivity to statistical properties , 1995, Vision Research.

[123]  P. Verghese,et al.  Combining speed information across space , 1995, Vision Research.

[124]  Preeti Verghese,et al.  Perceived visual speed constrained by image segmentation , 1996, Nature.

[125]  L. Cosmides,et al.  Are humans good intuitive statisticians after all? Rethinking some conclusions from the literature on judgment under uncertainty , 1996, Cognition.

[126]  M. Spetch,et al.  Averaging temporal duration and spatial position. , 1996, Journal of experimental psychology. Animal behavior processes.

[127]  D. Laming,et al.  J. Plateau: On the measurement of physical sensations and on the law which links the intensity of these sensations to the intensity of the source , 1996, Psychological research.

[128]  J. Wearden,et al.  Stimulus range effects in temporal bisection by humans. , 1996, The Quarterly journal of experimental psychology. B, Comparative and physiological psychology.

[129]  Joachim Meyer,et al.  Correlation estimates as perceptual judgments. , 1997 .

[130]  P. Verghese,et al.  Spatial Layout Affects Speed Discrimination , 1997, Vision Research.

[131]  R. Watt,et al.  The computation of orientation statistics from visual texture , 1997, Vision Research.

[132]  Steven C. Dakin,et al.  The detection of structure in glass patterns: Psychophysics and computational models , 1997, Vision Research.

[133]  J. Wearden,et al.  Temporal Bisection in Humans with Longer Stimulus Durations , 1997, The Quarterly journal of experimental psychology. B, Comparative and physiological psychology.

[134]  Temporal Bisection in Humans with Longer Stimulus Durations , 1997, The Quarterly journal of experimental psychology. B, Comparative and physiological psychology.

[135]  M. Dougherty,et al.  Averaging expectancies and perceptual experiences in the assessment of quality. , 1999, Acta psychologica.

[136]  S. McKee,et al.  The use of an implicit standard for measuring discrimination thresholds , 2000, Vision Research.

[137]  O. Braddick,et al.  Speed and direction of locally-paired dot patterns , 2000, Vision Research.

[138]  D Purves,et al.  Why are angles misperceived? , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[139]  D. Ariely.  Seeing Sets: Representation by Statistical Properties , 2001, Psychological science.

[140]  H Barlow,et al.  Redundancy reduction revisited , 2001, Network.

[141]  I. Kuriki.  Testing the Possibility of Average-Color Perception from Multi-Colored Patterns , 2004 .

[142]  Ian Spence,et al.  The Apparent and Effective Dimensionality of Representations of Objects , 2004, Hum. Factors.

[143]  G. Gigerenzer.  Mindless statistics , 2004 .

[144]  The Perception of Number , 2009 .

[145]  F. Urban.  The Central Tendency of Judgment. , 2022 .