Sensory scaling: Unanswered questions

Despite the range of literature he refers to, Krueger fails adequately to consider alternative interpretations and this limits the weight that can be given to his conclusions. His argument relies on underlying assumptions that can be questioned and have not been justified. In the space available I shall attempt a brief discussion of some of these difficulties. (1) What Is It that Is measured? Krueger refers to "subjective magnitude (conscious sensation)" and proposes that "sensations are phenomenally experienced (i.e., introspectable via direct magnitude estimation and category ratings)." In normal scientific practice, the claim that a procedure delivers a measure of a variable requires that we define the variable and offer some validation of the proposed measurement procedure. Thus, "motivation" might be defined as the determinant of certain aspects of behavior, and a presumed measure of motivation would be validated by examining correlations with behavior. But we have no clear definition of "subjective magnitude" and we are not offered any procedure for validating proposed measures of it. Instead, discussion in this area usually rests on intuitive convictions. To illustrate, suppose that a loud noise is presented to a subject and he responds by emitting the number "ten"; a low noise is presented and his response is "five." It may seem intuitively evident that each noise produced a unique subjective experience; the sensory experience produced by the loud noise is different from that produced by the low noise; and "ten" and "five" capture the difference between the former and the latter. But this subjectivist view (SV) is at best an intuitive correlation, and we know that correlation does not guarantee a causal relation. The leading proponent of this view was Stevens (1957b; 1960); Krueger's arguments follow the same line. But other views are possible. If, to avoid relying on the untestable basis of intuition, we follow the example of attempts to define the concept of "intelligence" and define the sensory scale as that which sensory-scaling procedures measure, we arrive at an information-processing view (IPV) of sensory scaling (Treisman 1962; 1964a; 1964b). According to this view, the response "ten" is determined by underlying neural processes consequent on the physical stimulus processes that at best parallel in some intuitive sense the corresponding "subjective experiences"; any scale we derive from such responses can only refer to the underlying physical processes. In a procedure such as magnitude estimation, the data are in the form of a table of correspondences between stimulus intensities, /, and corresponding mean responses R. An empirical relationship is found between the two, such as R = alp. The IPV rests on the observation that any such relationship can be expanded into a pair of equations that include an intermediate measure S. Then S = f{I), R = g(S), where/and g are any functions (out of an infinite set of possible pairs) such that g[/(/)] = O/P. (More than two stages are of course possible.)

[1]  J C Baird,et al.  Studies of the cognitive representation of spatial relations: II. A familiar environment. , 1979, Journal of experimental psychology. General.

[2]  L E Marks,et al.  Binaural summation of the loudness of pure tones. , 1978, The Journal of the Acoustical Society of America.

[3]  R. Shepard Metric structures in ordinal data , 1966 .

[4]  R. Hellman,et al.  Growth of loudness at 1000 and 3000 Hz. , 1976, The Journal of the Acoustical Society of America.

[5]  N I Durlach,et al.  Intensity perception. I. Preliminary theory of intensity resolution. , 1969, The Journal of the Acoustical Society of America.

[6]  Vincent Di Lollo,et al.  A consistent failure of the power law for lifted weight , 1970 .

[7]  D. M. Green,et al.  Variability and sequential effects in cross-modality matching of area and loudness. , 1980, Journal of experimental psychology. Human perception and performance.

[8]  S. S. Stevens,et al.  Saturation of red: A prothetic continuum , 1966 .

[9]  H. Fletcher,et al.  Loudness, its definition, measurement and calculation. , 1933 .

[10]  Neal F. Viemeister,et al.  Intensity Discrimination of Pulsed Sinusoids: The Effects of Filtered Noise , 1972 .

[11]  N. Guttman,et al.  Discriminability and stimulus generalization. , 1956, Journal of experimental psychology.

[12]  Donald Laming,et al.  A reexamination of Sensory Analysis , 1988, Behavioral and Brain Sciences.

[13]  S S Stevens,et al.  To Honor Fechner and Repeal His Law: A power function, not a log function, describes the operating characteristic of a sensory system. , 1961, Science.

[14]  G S Wasserman,et al.  Intensity dependence of perceived duration: data, theories, and neural integration. , 1989, Psychological bulletin.

[15]  E Galanter,et al.  Dual loudness scales in individual subjects. , 1986, Journal of experimental psychology. Human perception and performance.

[16]  Willem A. Wagenaar,et al.  Stevens vs Fechner: A plea for dismissal of the case , 1975 .

[17]  ROBERT S. MOYER,et al.  Time required for Judgements of Numerical Inequality , 1967, Nature.

[18]  J. Baird,et al.  When Power Functions Fail: A Theoretical Explanation , 1970 .

[19]  J. Baird Psychophysical study of numbers , 1975 .

[20]  D. M. Green,et al.  The bow and sequential effects in absolute identification , 1982, Perception & psychophysics.

[21]  E. Tulving,et al.  Estimations of loudness by a group of untrained observers. , 1957, The American journal of psychology.

[22]  S S Stevens,et al.  Operations or words? , 1966, Psychological monographs.

[23]  E. Zwicker,et al.  A MODEL OF LOUDNESS SUMMATION. , 1965, Psychological review.

[24]  Norman H. Anderson,et al.  Cross-task validation of functional measurement , 1972 .

[25]  S. S. Stevens,et al.  Brightness function: effects of adaptation. , 1963, Journal of the Optical Society of America.

[26]  Miguelina Guirao,et al.  Loudness, reciprocality, and partition scales. , 1962 .

[27]  A. H. Holway,et al.  On the Law for Minimal Discrimination of Intensities: III. , 1937, Proceedings of the National Academy of Sciences of the United States of America.

[28]  M. Wagner,et al.  The metric of visual space , 1985, Perception & psychophysics.

[29]  W. Levelt,et al.  Binaural additivity of loudness. , 1972, The British journal of mathematical and statistical psychology.

[30]  L. Marks Stimulus-range, number of categories, and form of the category-scale. , 1968, The American journal of psychology.

[31]  J J Zwislocki,et al.  Loudness determination at low sound frequencies. , 1968, The Journal of the Acoustical Society of America.

[32]  R. Eyman,et al.  A model for partitioning judgment error in psychophysics. , 1970, Psychological bulletin.

[33]  I. Good 342. Note: Correlation for Power Functions , 1972 .

[34]  M. A. Bouman,et al.  Spatiotemporal modulation transfer in the human eye. , 1967, Journal of the Optical Society of America.

[35]  S. Parker,et al.  The perceptual basis of loudness ratio judgments , 1976 .

[36]  L E Marks,et al.  Cross-modality matching functions generated by magnitude estimation , 1980, Perception & psychophysics.

[37]  Gordon E. Legge,et al.  Sensory analysis in vision and audition , 1988, Behavioral and Brain Sciences.

[38]  J. Baird,et al.  Psychophysical study of numbers , 1975 .

[39]  A. Fraioli,et al.  Sensation magnitude of vibrotactile stimuli , 1969 .

[40]  D. Hood,et al.  Comparison of changes in sensitivity and sensation: implications for the response-intensity function of the human photopic system. , 1979, Journal of experimental psychology. Human perception and performance.

[41]  W. Keidel,et al.  NEUROPHYSIOLOGICAL EVIDENCE FOR THE STEVENS POWER FUNCTION IN MAN. , 1965, The Journal of the Acoustical Society of America.

[42]  Hiroshi Ono,et al.  Difference threshold for stimulus length under simultaneous and nonsimultaneous viewing conditions , 1967 .

[43]  R. Mcbride Psychophysics: Could fechner's assumption be correct? , 1983 .

[44]  E. Boring,et al.  The derivation of subjective scales from just noticeable differences. , 1958, Psychological review.

[45]  G S Wasserman,et al.  The psychophysical function: harmonizing Fechner and Stevens. , 1979, Science.

[46]  Lawrence E. Marks,et al.  On scales of sensation: Prolegomena to any future psychophysics that will be able to come forth as science , 1974 .

[47]  S. Parker,et al.  Loudness and loudness discrimination , 1980, Perception & psychophysics.

[48]  M. Treisman,et al.  Relation between signal detectability theory and the traditional procedures for measuring sensory thresholds: Estimating d' from results given by the method of constant simuli. , 1966 .

[49]  W. H. Atkinson A general equation for sensory magnitude , 1982, Perception & psychophysics.

[50]  Gerald S. Wasserman,et al.  Direct intracellular measurement of non-linear postreceptor transfer functions in dark and light adaptation in Limulus , 1985, Brain Research.

[51]  H. F. Gaydos Sensitivity in the judgment of size by finger-span. , 1958, The American journal of psychology.

[52]  D. Laming Differential coupling of sensory discriminations inferred from a survey of stable decision models for Weber's law. , 1982, The British journal of mathematical and statistical psychology.

[53]  J. Phillips A Note on Treisman's Model , 1964 .

[54]  S. J. Rule Comparisons of intervals between subjective numbers , 1972 .

[55]  S. Parker,et al.  Ratio scale measurement of the perceived lengths of lines. , 1975, Journal of experimental psychology. Human perception and performance.

[56]  G. A. Miller THE PSYCHOLOGICAL REVIEW THE MAGICAL NUMBER SEVEN, PLUS OR MINUS TWO: SOME LIMITS ON OUR CAPACITY FOR PROCESSING INFORMATION 1 , 1956 .

[57]  R M Warren,et al.  Criterion shift rule and perceptual homeostasis. , 1985, Psychological review.

[58]  F. J. Pilgrim,et al.  Differential sensitivity in gustation. , 1957, Journal of experimental psychology.

[59]  R. Luce,et al.  Simultaneous conjoint measurement: A new type of fundamental measurement , 1964 .

[60]  R. B. Freeman Contrast interpretation of brightness constancy. , 1967, Psychological bulletin.

[61]  K H Norwich,et al.  The psychophysics of taste from the entropy of the stimulus , 1984, Perception & psychophysics.

[62]  R. Luce,et al.  On the possible psychophysical laws. , 1959, Psychological review.

[63]  Jozef J. Zwislocki,et al.  Loudness Function of a 1000‐cps Tone in the Presence of a Masking Noise , 1964 .

[64]  J. Baird Psychophysical study of Numbers , 1975 .

[65]  S. S. Stevens On the Validity of the Loudness Scale , 1959 .

[66]  R. M. Warren Visual intensity judgments: an empirical rule and a theory. , 1969, Psychological review.

[67]  W. R. Garner Advantages of the Discriminability Criterion for a Loudness Scale , 1958 .

[68]  H Eisler,et al.  Subjective duration and psychophysics. , 1975, Psychological review.

[69]  J. Beck,et al.  Ratio-estimations of loudness-intervals. , 1967, The American journal of psychology.

[70]  D. W. Curtis Magnitude estimations and category judgments of brightness and brightness intervals: a two-stage interpretation. , 1970, Journal of Experimental Psychology.

[71]  N I Durlach,et al.  Intensity perception. VIII. Loudness comparisons between different types of stimuli. , 1977, The Journal of the Acoustical Society of America.

[72]  D. W. Curtis,et al.  Conjoint scaling of subjective number and weight. , 1973, Journal of experimental psychology.

[73]  C T Veit,et al.  Ratio and subtractive processes in psychophysical judgment. , 1978, Journal of experimental psychology. General.

[74]  J C Baird,et al.  Studies of the cognitive representation of spatial relations: III. A hypothetical environment. , 1979, Journal of experimental psychology. General.

[75]  Roger N. Shepard,et al.  Psychological relations and psychophysical scales: On the status of “direct” psychophysical measurement ☆ , 1981 .

[76]  D. Raab,et al.  Visual reaction time and the Broca-Sulzer phenomenon. , 1961, Journal of experimental psychology.

[77]  Mark F. Lewis Category Judgments as Functions of Flash Luminance and Duration , 1965 .

[78]  J C Baird,et al.  A cognitive theory of psychophysics. I. Information transmission, partitioning, and Weber's Law. , 1970, Scandinavian journal of psychology.

[79]  R. Gregson,et al.  Psychophysical Power Law Exponent Value for Sucrose Intensity , 1965, Perceptual and motor skills.

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

[81]  Micheal Treisman,et al.  A statistical decision model for sensory discrimination which predicts Weber’s law and other sensory laws: Some results of a computer simulation , 1966 .

[82]  S. S. Stevens,et al.  Psychophysics: Introduction to Its Perceptual, Neural and Social Prospects , 1975 .

[83]  L. Marks,et al.  Ratio scaling of taste intensity by a matching procedure , 1979 .

[84]  K. O. Johnson,et al.  Peripheral neural determinants of temperature discrimination in man: a correlative study of responses to cooling skin. , 1973, Journal of neurophysiology.

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

[86]  M. Treisman Brightness contrast and the perceptual scale. , 1970, The British journal of mathematical and statistical psychology.

[87]  Warren S. Torgerson,et al.  Distances and ratios in psychophysical scaling , 1961 .

[88]  R. Mansfield Brightness function: effect of area and duration. , 1973, Journal of the Optical Society of America.

[89]  B. Mellers Evidence against “absolute” scaling , 1983, Perception & psychophysics.

[90]  James McKeen Cattell,et al.  On Errors of Observation , 1893 .

[91]  M. Treisman,et al.  Neural Effects and the Psychophysical Law , 1963, Nature.

[92]  N. Anderson Failure of additivity in bisection of length , 1977 .

[93]  W P Banks,et al.  Two subjective scales of number , 1981, Perception & psychophysics.

[94]  Donald A. Blankenship,et al.  Subjective duration: A functional measurement analysis , 1976 .

[95]  E C Poulton,et al.  Why unbiased numerical magnitude judgments of the loudness of noise are linear in decibels: A rejoinder to the Teghtsoonians , 1986, Perception & psychophysics.

[96]  R. Duncan Luce,et al.  Thurstone's discriminal processes fifty years later , 1977 .

[97]  M. Treisman Temporal discrimination and the indifference interval. Implications for a model of the "internal clock". , 1963, Psychological monographs.

[98]  B. Mellers Reply to Zwislocki’s views on “absolute” scaling , 1983, Perception & psychophysics.

[99]  R. J. Irwin,et al.  Auditory intensity discriminal scale I. Evidence derived from binaural intensity summation. , 1967, The Journal of the Acoustical Society of America.

[100]  D. Ja,et al.  Scales for perceived egocentric distance in a large open field: comparison of three psychophysical methods. , 1985 .

[101]  Malvin Carl Teich,et al.  A neural-counting model based on physiological characteristics of the peripheral auditory system. V. Application to loudness estimation and intensity discrimination , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[102]  Jozef J. Zwislocki,et al.  Monaural Loudness Function at 1000 cps and Interaural Summation , 1963 .

[103]  E. Carterette,et al.  Bisection of loudness , 1979, Perception & psychophysics.

[104]  G. B. Wetherill,et al.  SEQUENTIAL ESTIMATION OF POINTS ON A PSYCHOMETRIC FUNCTION. , 1965, The British journal of mathematical and statistical psychology.

[105]  D. Krantz Integration of just-noticeable differences , 1971 .

[106]  H. Helson Adaptation-level as a basis for a quantitative theory of frames of reference. , 1948, Psychological review.

[107]  J. C. Stevens Stimulus spacing and the judgment of loudness. , 1958, Journal of experimental psychology.

[108]  N. Anderson Cross-task validation of functional measurement using judgments of total magnitude. , 1974 .

[109]  H. Geissler Physical correlate theory versus the indirect calibration approach , 1983, Behavioral and Brain Sciences.

[110]  D. Weiss,et al.  The Impossible Dream of Fechner and Stevens , 1981, Perception.

[111]  Michel Treisman,et al.  The Magical Number Seven and Some Other Features of Category Scaling: Properties of a Model for Absolute Judgment , 1985 .

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

[113]  G. Legge Spatial frequency masking in human vision: binocular interactions. , 1979, Journal of the Optical Society of America.

[114]  N. I. Durlach,et al.  Intensity Perception. II. Resolution in One‐Interval Paradigms , 1972 .

[115]  G. Fechner,et al.  My own viewpoint on mental measurement (1887) , 1987 .

[116]  K. O. Johnson,et al.  Reconstruction of population response to a vibratory stimulus in quickly adapting mechanoreceptive afferent fiber population innervating glabrous skin of the monkey. , 1974, Journal of neurophysiology.

[117]  S. McKelvie,et al.  Comparisons of Intervals between Subjective Numbers, an Extension , 1977 .

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

[119]  M. Treisman Signal detection theory and Crozier's law: Derivation of a new sensory scaling procedure , 1965 .

[120]  D. W. Curtis,et al.  Magnitude judgments and difference judgments of lightness and darkness: a two-stage analysis. , 1974, Journal of experimental psychology.

[121]  H. Wallach,et al.  The perception of neutral colors. , 1963, Scientific American.

[122]  W. R. Garner,et al.  Operationism and the concept of perception. , 1956, Psychological review.

[123]  J J Zwislocki,et al.  On the relations of intensity jnd's to loudness and neural noise. , 1986, The Journal of the Acoustical Society of America.

[124]  S. S. Stevens Neural events and the psychophysical law. , 1970, Science.

[125]  Clairice T. Veit,et al.  Scale convergence as a criterion for rescaling: Information integration with difference, ratio, and averaging tasks , 1974 .

[126]  R. M. Warren,et al.  A basis for loudness-judgments. , 1958, The American journal of psychology.

[127]  W. E. Dawson,et al.  Inverse attribute functions and the proposed modifications of the power law , 1978, Perception & psychophysics.

[128]  D. M. Green,et al.  Intensity discrimination as a function of frequency and sensation level. , 1977, The Journal of the Acoustical Society of America.

[129]  L E Marks,et al.  On the cross-modal perception of intensity. , 1986, Journal of experimental psychology. Human perception and performance.

[130]  J. Baird,et al.  Psychophysical study of numbers , 1975 .

[131]  Lawrence E. Marks,et al.  A theory of loudness and loudness judgments. , 1979 .

[132]  L. Allan The perception of time , 1979 .

[133]  R. Shepard Geometrical approximations to the structure of musical pitch. , 1982, Psychological review.

[134]  Thomas L. Harrington,et al.  A test of a two-stage model of magnitude judgment , 1968 .

[135]  D. Cross,et al.  Stimulus range, number of categories, and the “virtual” exponent , 1983, Perception & psychophysics.

[136]  R. Hellman,et al.  Growth rate of loudness, annoyance, and noisiness as a function of tone location within the noise spectrum. , 1984, The Journal of the Acoustical Society of America.

[137]  R. Mcbride,et al.  A JND-scale/category-scale convergence in taste , 1983, Perception & psychophysics.

[138]  G. Ekman,et al.  Saltness, sweetness, and preference. A study of quantitative relations in individual subjects. , 1965, Scandinavian journal of psychology.

[139]  R M Nosofsky,et al.  Information integration and the identification of stimulus noise and criterial noise in absolute judgment. , 1983, Journal of experimental psychology. Human perception and performance.

[140]  J. Baird,et al.  Perception of psychophysical experiments , 1977 .

[141]  B. Rosner The Power Law and Subjective Scales of Number , 1965, Perceptual and Motor Skills.

[142]  D. Campbell,et al.  Separating perceptual and linguistic effects of context shifts upon absolute judgments. , 1961, Journal of experimental psychology.

[143]  B C Moore,et al.  Intensity discrimination: a severe departure from Weber's law. , 1984, The Journal of the Acoustical Society of America.

[144]  D. Krantz A theory of magnitude estimation and cross-modality matching☆ , 1972 .

[145]  J. Tukey On the Comparative Anatomy of Transformations , 1957 .

[146]  G. A. Miller,et al.  Sensitivity to Changes in the Intensity of White Noise and Its Relation to Masking and Loudness , 1947 .

[147]  K H Norwich,et al.  On the theory of Weber fractions , 1987, Perception & psychophysics.

[148]  B. Schneider,et al.  Individual loudness functions determined from direct comparisons of loudness intervals , 1980, Perception & psychophysics.

[149]  L. Marks,et al.  Twelve meanings of the measure constant in psychophysical power functions , 1983 .

[150]  C. I. Hovland A note on Guilford's generalized psychophysical law. , 1938 .

[151]  E. Poulton The new psychophysics: Six models for magnitude estimation. , 1968 .

[152]  Tarow Indow,et al.  An approach to geometry of visual space with no a priori mapping functions: Multidimensional mapping according to Riemannian metrics , 1982 .

[153]  Hannes Eisler,et al.  Magnitude scales, category scales, and Fechnerian integration. , 1963 .

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

[155]  G. Ekman,et al.  Is the Power Law a Special Case of Fechner's Law? , 1964, Perceptual and motor skills.

[156]  A. A. Collins,et al.  Absolute magnitude estimation of loudness by adults and children , 1987 .

[157]  L. Marks Brightness and equivalent intensity of intrinsic light. , 1973, Vision research.

[158]  J. Baird,et al.  Generation of multiple ratio scales with a fixed stitnulus attribute , 1971 .

[159]  M. Teghtsoonian,et al.  Range and regression effects in magnitude scaling , 1978, Perception & psychophysics.

[160]  B. Schneider The additivity of loudness across critical bands: A conjoint measurement approach , 1988, Perception & psychophysics.

[161]  N I Durlach,et al.  Intensity perception XI. Experimental results on the relation of intensity resolution to loudness matching. , 1980, The Journal of the Acoustical Society of America.

[162]  D Laming,et al.  Some principles of sensory analysis. , 1985, Psychological review.

[163]  John E. R. Staddon,et al.  THEORY OF BEHAVIORAL POWER FUNCTIONS , 1978 .

[164]  D. Bernoulli Exposition of a New Theory on the Measurement of Risk , 1954 .

[165]  L. Marks Binaural summation of loudness: Noise and two-tone complexes , 1980, Perception & psychophysics.

[166]  D. W. Curtis,et al.  Reevaluation of two models for judgments of perceptual intervals , 1973 .

[167]  S. S. Stevens The Psychophysics of Sensory Function. , 1960 .

[168]  J. Guilford A generalized psychophysical law. , 1932 .

[169]  A B Vallbo,et al.  Intensity of sensation related to activity of slowly adapting mechanoreceptive units in the human hand , 1980, The Journal of physiology.

[170]  H. Eisler EMPIRICAL TEST OF A MODEL RELATING MAGNITUDE AND CATEGORY SCALES , 1962 .

[171]  S. Parker,et al.  Intensity discrimination and loudness for tones in notched noise , 1987, Perception & psychophysics.

[172]  R. Hess,et al.  Spatial and temporal limits of vision in the achromat. , 1986, The Journal of physiology.

[173]  E. G. Heinemann,et al.  The relation of apparent brightness to the theshold for differences in luminance. , 1961, Journal of experimental psychology.

[174]  S. S. Stevens Issues in psychophysical measurement. , 1971 .

[175]  F. Campbell,et al.  Spatial-frequency discrimination in human vision. , 1970, Journal of the Optical Society of America.

[176]  R. Hellman,et al.  Loudness, annoyance, and noisiness produced by single-tone-noise complexes. , 1982, The Journal of the Acoustical Society of America.

[177]  G Borg,et al.  The relation between neural and perceptual intensity: a comparative study on the neural and psychophysical response to taste stimuli , 1967, The Journal of physiology.

[178]  S. Parker,et al.  A scale for the psychological magnitude of number , 1974 .

[179]  Response bias in category and magnitude estimation of difference and similarity for loudness and pitch. , 1978 .

[180]  R. Shepard The analysis of proximities: Multidimensional scaling with an unknown distance function. II , 1962 .

[181]  R. Luce,et al.  MAGNITUDE ESTIMATION OF HEAVINESS AND LOUDNESS BY INDIVIDUAL SUBJECTS: A TEST OF A PROBABILISTIC RESPONSE THEORY1 , 1965 .

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

[183]  J. Baird,et al.  Perception of psychophysical experiments: I. Scaling of methods , 1977 .

[184]  Harris Jd,et al.  The effect of sensation levels on intensive discrimination of noise. , 1950 .

[185]  H. Yilmaz Perceptual invariance and the psychophysical law , 1967 .

[186]  R. Shepard Stimulus and response generalization: tests of a model relating generalization to distance in psychological space. , 1958, Journal of experimental psychology.

[187]  R. Stelmack,et al.  Power functions of loudness magnitude estimations and auditory brainstem evoked responses , 1982, Perception & psychophysics.

[188]  R. R. Riesz Differential Intensity Sensitivity of the Ear for Pure Tones , 1928 .

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

[190]  S. Parker,et al.  Nomnetric scaling of loudness and pitch using similarity and difference estimates , 1974 .

[191]  A. Silberberg,et al.  Random monotone data fit simple algebraic models: Correlation is not confirmation. , 1988 .

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

[193]  N I Durlach,et al.  Intensity perception. XIII. Perceptual anchor model of context-coding. , 1984, The Journal of the Acoustical Society of America.

[194]  C. C. Pratt,et al.  The Weber ratio for intensive discrimination. , 1936 .

[195]  K. Pribram The cognitive revolution and mind/brain issues. , 1986, The American psychologist.

[196]  B. Leshowitz,et al.  Visual detection of signals in the presence of continuous and pulsed backqrounds , 1968 .

[197]  Edwin B. Newman,et al.  The Validity of the Just Noticeable Difference as a Unit of Psychological Magnitude , 1933 .

[198]  Michel Treisman,et al.  PSYCHOLOGICAL EXPLANATION: THE ‘PRIVATE DATA’ HYPOTHESIS* , 1962, The British Journal for the Philosophy of Science.

[199]  S S Stevens,et al.  On the Theory of Scales of Measurement. , 1946, Science.

[200]  N. Macmillan,et al.  Size judgment: The presence of a standard increases the exponent of the power law , 1974 .

[201]  G. H. Robinson Biasing power law exponents by magnitude estimation instructions , 1976 .

[202]  J. Hyvärinen,et al.  Cortical neuronal mechanisms in flutter-vibration studied in unanesthetized monkeys. Neuronal periodicity and frequency discrimination. , 1969, Journal of neurophysiology.

[203]  J C Baird,et al.  A cognitive theory of psychophysics. II. Fechner's Law and Stevens' Law. , 1970, Scandinavian journal of psychology.

[204]  S. S. Stevens Concerning the Form of the Loudness Function , 1957 .

[205]  Garner Wr,et al.  An equal discriminability scale for loudness judgments. , 1952 .

[206]  P D Duda,et al.  Tests of the psychological meaning of the power law. , 1975, Journal of experimental psychology. Human perception and performance.

[207]  Cornelius S. Ough,et al.  Determination of Odor Difference Thresholds , 1962 .

[208]  M H Birnbaum,et al.  Weight of evidence supports one operation for "ratios" and "differences" of heaviness. , 1984, Journal of experimental psychology. Human perception and performance.

[209]  H. Montgomery,et al.  Direct estimation: effect of methodological factors on scale type. , 1975, Scandinavian journal of psychology.

[210]  D. Dorfman,et al.  Maximum-likelihood estimation of parameters of signal-detection theory and determination of confidence intervals—Rating-method data , 1969 .

[211]  S. J. Rule Equal discriminability scale of number. , 1969, Journal of experimental psychology.

[212]  H STONE,et al.  Olfactory Discrimination and Weber's Law , 1965, Perceptual and motor skills.

[213]  H. Eisler HOW PROTHETIC IS THE CONTINUUM OF SMELL?: A further comment on the relation between magnitude and category scales , 1963 .

[214]  D. L. Tomko,et al.  The relation between category and magnitude estimates of tactile intensity , 1972 .

[215]  Scott Parker,et al.  The measurement of loudness using direct comparisons of sensory intervals. , 1974 .

[216]  L E Krueger,et al.  Perceived numerosity: A comparison of magnitude production, magnitude estimation, and discrimination judgments , 1984, Perception & psychophysics.

[217]  G. Ekman,et al.  Note on Subjective Scales of Number , 1965, Perceptual and motor skills.

[218]  S. S. Stevens,et al.  Scaling of saturation and hue , 1966 .

[219]  J. Zwislocki,et al.  On Some Factors Affecting the Estimation of Loudness , 1960 .

[220]  K. Norwich The magical number seven: Making a “bit” of “sense” , 1981, Perception & psychophysics.

[221]  R. M. Boynton,et al.  Visual Adaptation in Monkey Cones: Recordings of Late Receptor Potentials , 1970, Science.

[222]  D. W. Curtis,et al.  Judgment of duration relations: Simultaneous and sequential presentation , 1977 .

[223]  M TREISMAN,et al.  NOISE AND WEBER'S LAW: THE DISCRIMINATION OF BRIGHTNESS AND OTHER DIMENSIONS. , 1964, Psychological review.

[224]  E. Poulton Schooling and the new psychophysics , 1981, Behavioral and Brain Sciences.

[225]  B C Moore,et al.  Pure-tone intensity discrimination: some experiments relating to the "near-miss" to Weber's law. , 1974, The Journal of the Acoustical Society of America.

[226]  C. Auerbach Interdependence of Stevens' exponents and discriminability measures. , 1971 .

[227]  H. B. Barlow,et al.  The precision of numerosity discrimination in arrays of random dots , 1983, Vision Research.

[228]  Hannes Eisler,et al.  ON THE PROBLEM OF CATEGORY SCALES IN PSYCHOPHYSICS , 1962 .

[229]  H. Davis,et al.  Relations of the human vertex potential to acoustic input: loudness and masking. , 1968, The Journal of the Acoustical Society of America.

[230]  C. Auerbach A Note on Cross-Modality Matching , 1973, The Quarterly journal of experimental psychology.

[231]  David H. Raab,et al.  Magnitude Estimation of the Brightness of Brief Foveal Stimuli , 1962, Science.

[232]  M. Florentine,et al.  Level discrimination as a function of level for tones from 0.25 to 16 kHz. , 1987, The Journal of the Acoustical Society of America.

[233]  R. Teghtsoonian,et al.  Range effects in psychophysical scaling and a revision of Stevens' law. , 1973, The American journal of psychology.

[234]  L. M. Ward,et al.  Repeated magnitude estimations with a variable standard: Sequential effects and other properties , 1973 .

[235]  S. S. Stevens The Measurement of Loudness , 1955 .

[236]  T. Cornsweet,et al.  Luminance discrimination of brief flashes under various conditions of adaptation , 1965, The Journal of physiology.

[237]  R. Mansfield Visual adaptation: Retinal transduction, brightness and sensitivity , 1976, Vision Research.

[238]  Hannes Eisler,et al.  On theoretical and realizable ideal conditions in psychophysics: Magnitude and category scales and their relation , 1974 .

[239]  M. Treisman,et al.  Laws of Sensory Magnitude , 1963, Nature.

[240]  R. Teghtsoonian,et al.  On the exponents in Stevens' law and the constant in Ekman's law. , 1971, Psychological review.

[241]  H. Eisler On the nature of subjective scales , 1982 .

[242]  S. S. Stevens,et al.  Critical Band Width in Loudness Summation , 1957 .

[243]  J. Falmagne The generalized Fechner problem and discrimination , 1971 .

[244]  S. S. Stevens On the brightness of lights and loudness of sounds , 1953 .

[245]  H. Geissler Towards a new reconciliation of Stevens' and Helson's approaches to psychophysics: A tentative solution of the Stevens-Greenbaum puzzle , 1975 .

[246]  F. Attneave,et al.  Pitch as a medium: a new approach to psychophysical scaling. , 1971, The American journal of psychology.

[247]  M. Birnbaum,et al.  A harmonious note on pitch: Scales of pitch derived from subtractive model of comparison agree with the musical scale , 1984, Perception & psychophysics.

[248]  E. Scheerer,et al.  The unknown Fechner , 1987, Psychological research.

[249]  K. W. Oberlin Variation in intensive sensitivity to lifted weights. , 1936 .

[250]  D. Algom,et al.  Visual velocity input-output functions: the integration of distance and duration onto subjective velocity. , 1984, Journal of experimental psychology. Human perception and performance.

[251]  C. Pfaffmann,et al.  Gustatory adaptation to saliva and sodium chloride , 1963 .

[252]  B. Bridgeman,et al.  Relations between the physiology of attention and the physiology of consciousness , 1986, Psychological research.

[253]  R. Luce,et al.  What sort of measurement is psychophysical measurement? , 1972, The American psychologist.

[254]  J. Nachmias,et al.  Brightness and discriminability of light flashes. , 1965, Vision research.

[255]  W. R. Garner A Technique and a Scale for Loudness Measurement , 1954 .

[256]  R. M. Warren A basis for judgments of sensory intensity. , 1958, The American journal of psychology.

[257]  R D Luce,et al.  Measurement Scales on the Continuum , 1987, Science.

[258]  J. Zwislocki Absolute and other scales: Question of validity , 1983, Perception & psychophysics.

[259]  M. A. Bouman,et al.  Spatial Modulation Transfer in the Human Eye , 1967 .

[260]  E. Osman,et al.  Weber’s law, the “near miss,” and binaural detection , 1980, Perception & psychophysics.

[261]  Michel Treisman,et al.  What do Sensory Scales Measure? , 1964 .

[262]  Allen Parducci,et al.  Range-frequency compromise in judgment. , 1963 .

[263]  D. Jameson,et al.  Complexities of perceived brightness. , 1961, Science.

[264]  Hannes Eisler,et al.  Experiments on subjective duration 1868-1975: A collection of power function exponents. , 1976 .

[265]  Gerald S. Wasserman,et al.  Absolute timing of mental activities , 1979, Behavioral and Brain Sciences.

[266]  W. J. McGill,et al.  A study of the near-miss involving Weber’s law and pure-tone intensity discrimination , 1968 .

[267]  D M Green,et al.  Detection and intensity discrimination of a sinusoid. , 1984, The Journal of the Acoustical Society of America.

[268]  Leon M. Solomons,et al.  A new explanation of Weber's Law. , 1900 .

[269]  A. K. Myers Psychophysical scaling and scales of physical stimulus measurement. , 1982 .

[270]  Frank P. McKenna,et al.  Another look at the ‘new psychophysics’ , 1985 .

[271]  S. J. Rule Discriminability scales of number for multiple and fractional estimates , 1971 .

[272]  James C. Craig,et al.  Vibrotactile difference thresholds for intensity and the effect of a masking stimulus , 1974 .

[273]  W. Cain Odor magnitude: Coarse vs. fine grain , 1977 .

[274]  William P. Banks,et al.  The apparent magnitude of number scaled by random production , 1974 .

[275]  R. F. Fagot On the psychophysical law and estimation procedures in psychophysical scaling , 1963 .

[276]  L M Ward,et al.  Category judgments of loudnesses in the absence of an experimenter-induced identification function: sequential effects and power-function fit. , 1972, Journal of experimental psychology.

[277]  W. J. McGill Neural counting mechanisms and energy detection in audition , 1967 .

[278]  D. M. MacKay,et al.  Psychophysics of Perceived Intensity: A Theoretical Basis for Fechner's and Stevens' Laws , 1963, Science.

[279]  S. S. Stevens On the psychophysical law. , 1957, Psychological review.

[280]  Richard M. Warren,et al.  Measurement of sensory intensity , 1981, Behavioral and Brain Sciences.

[281]  J. Zwislocki,et al.  Absolute scaling of sensory magnitudes: A validation , 1980, Perception & psychophysics.

[282]  R M Nosofsky,et al.  Shifts of attention in the identification and discrimination of intensity , 1983, Perception & psychophysics.

[283]  G. S. Wasserman,et al.  Visual masking: mechanisms and theories. , 1980, Psychological bulletin.

[284]  R. Hellman,et al.  Prediction of individual loudness exponents from cross-modality matching. , 1988, Journal of speech and hearing research.

[285]  B C Moore,et al.  Continuous versus gated pedestals and the "severe departure" from Weber's law. , 1986, The Journal of the Acoustical Society of America.

[286]  Hannes Eisler,et al.  ON PSYCHOPHYSICS IN GENERAL AND THE GENERAL PSYCHOPHYSICAL DIFFERENTIAL EQUATION IN PARTICULAR , 1965 .

[287]  Gösta Ekman,et al.  Discriminal sensitivity on the subjective continuum , 1956 .

[288]  Neil A. Macmillan,et al.  Resolution for speech sounds: basic sensitivity and context memory on vowel and consonant continua , 1988 .

[289]  D. M. Green,et al.  Attention bands in absolute identification , 1976 .

[290]  W. J. McGill,et al.  Pure-tone intensity discrimination and energy detection. , 1968, The Journal of the Acoustical Society of America.

[291]  D. W. Curtis,et al.  Subject differences in input and output transformations from magnitude estimation of differences. , 1977, Acta psychologica.

[292]  R. Shepard,et al.  Toward a universal law of generalization for psychological science. , 1987, Science.

[293]  H S Colburn,et al.  Model for auditory localization. , 1976, The Journal of the Acoustical Society of America.

[294]  Clairice T. Veit,et al.  Scale-flee tests of an additive model for the size-weight illusion , 1974 .

[295]  R. R. Riesz A Relationship between Loudness and the Minimum Perceptible Increment of Intensity , 1932 .

[296]  Michael H. Birnbaum,et al.  Judgments of differences and ratios of numerals , 1975 .

[297]  S. S. Stevens The direct estimation of sensory magnitudes-loudness. , 1956, The American journal of psychology.

[298]  M. Birnbaum,et al.  Loudness “ratios” and “differences” involve the same psychophysical operation , 1977 .

[299]  C. H. Graham Psychophysics and Behavior , 1934 .

[300]  R T Verrillo,et al.  Vibrotacile masking of Pacinian and non-Pacinian channels. , 1983, The Journal of the Acoustical Society of America.

[301]  Michael H. Birnbaum,et al.  Loci of contextual effects in judgment. , 1982 .

[302]  D. W. Curtis,et al.  Judgments of average magnitude: Analyses in terms of the functional measurement and two-stage models , 1975 .

[303]  R. M. Warren,et al.  Basis for judgments of relative brightness. , 1958, Journal of the Optical Society of America.

[304]  S. S. Stevens Concerning the Psychophysical Power Law , 1964 .

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

[306]  S. S. Stevens Sensory scales of taste intensity , 1969 .

[307]  Michael H. Birnbaum,et al.  Using contextual effects to derive psychophysical scales , 1974 .

[308]  D. W. Curtis,et al.  Input and output transformations from magnitude estimation. , 1970, Journal of experimental psychology.

[309]  S. D. Nihm Polynomial law of sensation. , 1976, The American psychologist.

[310]  G. Ekman Weber's Law and Related Functions , 1959 .

[311]  M. Teghtsoonian,et al.  On the relation between the growth of loudness and the discrimination of intensity for pure tones. , 1987, The Journal of the Acoustical Society of America.

[312]  H Eisler,et al.  The connection between magnitude and discrimination scales and direct and indirect scaling methods , 1965, Psychometrika.

[313]  Michel Treisman,et al.  Sensory Scaling and the Psychophysical Law , 1964 .

[314]  D. M. Green,et al.  Variability and sequential effects in magnitude production and estimation of auditory intensity , 1977 .

[315]  H STONE,et al.  DETERMINATION OF ODOR DIFFERENCE LIMENS FOR THREE COMPOUNDS. , 1963, Journal of experimental psychology.

[316]  John C. Baird,et al.  Psychophysical study of numbers , 1975 .

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

[318]  J C Baird,et al.  An empirical test of two psychophysical models. , 1974, Acta psychologica.

[319]  P. Cobb The effect on foveal vision of bright surroundings - IV , 1916 .