Electrocutaneous psychophysical input-output functions and temporal integration

Electrocutaneous magnitude estimation functions were generated by stimuli ranging from 1.0 to 5.0 mA and from 100 to 6,400 msec in duration. The results indicate that when these functions are fitted by a two-parameter power function (ME = aI^b), the values of the constant, a, and the exponent, b, are altered by increases in stimulus duration, with a increasing and b decreasing. The exponent decreases from around 1.4 to 0.93 as duration increases from 100 to 6,400 sec. Equal magnitude estimation contours drawn for estimates ranging from “2“ to “50“ can be fitted by an equation representing partial integration, I × t^a = K. The exponent a decreases as a function of the level of the magnitude estimation, indicating less partial integration at higher than at lower levels of estimated magnitude. The electrocutaneous data are compared to data in other sensory modalities.     

On the consistency of intramodal intensity matching in olfaction

Magnitude matchings of odor intensity were obtained for three chemical compounds (hydrogen sulfide, pyridine, and dimethyl disulfide) in four experiments. An equal-sensation function in the form of a power function described the data well. This equation can be written neglecting the multiplicative constant, Ф_i = Ф_k ^b _ik, where i and k represent two different odorants. The exponent b_ik, where the first index stands for matching continuum and the second index for reference continuum, was fairly well predicted according to the formulae, (ie, 264, 2) where i, j, and k are three different odorants. The results validate the equal-sensation function and indicate implicitly that intensity matchings between different intramodal continua are approximately transitive and symmetric with respect to odor.     

Identification variability as a measure of loudness: an application to gender differences.

It is well known that discrimination response variability increases with stimulus intensity, closely related to Weber's Law. It is also an axiom that sensation magnitude increases with stimulus intensity. Following earlier researchers such as Thurstone, Garner, and Durlach and Braida, we explored a new method of exploiting these relationships to estimate the power function exponent relating sound pressure level to loudness, using the accuracy with which listeners could identify the intensity of pure tones. The log standard deviation of the normally distributed identification errors increases linearly with stimulus range in decibels, and the slope, a, of the regression is proportional to the loudness exponent, n. Interestingly, in a demonstration experiment, the loudness exponent estimated in this way is greater for females than for males.     

The Piéron function in the threshold region

The Piéron function (Piéron, 1914, 1920, 1952) describes the decay of reaction time (RT) when the intensity of the stimulus is increased. It is generally demonstrated within a suprathreshold range of intensities. However, in some studies, for the lowest range of intensities, the exponent of the function is clearly greater than that for the upper ranges of intensities. Such an increase in the exponent for the lowest intensities is assumed to result from a combined effect of stimulus intensity and of stimulis uncertainty in detection. Our first experiment used luminance levels that covered all the scotopic range and a spatial two-alternative forced-choice task in which both accuracy and RT were measured. It demonstrated a drastic increase in the exponent in the Piéron function when the intensities reached the threshold region. Since the estimates of the threshold region may have been biased by the use of a much larger range of luminances, a second experiment was conducted using luminances that covered only the threshold region. This experiment confirmed the previous estimates for the threshold region.     

Changes in absolute detection threshold and in subjective intensity of suprathreshold stimuli during olfactory adaptation and recovery

Olfactory adaptation and recovery to methyl isobutyl ketone at a concentration 10 times the absolute detection threshold (I_{t o}) was intensively studied in two human Ss. A combined psychophysical procedure was used that allowed comparisons of changes in threshold (I_t) with changes in the subjective intensity of suprathreshold stimuli. Information was also obtained on the effect of the adapting stimulus on the psychophysical power function for this odorant. A threshold detection procedure was used to estimate changes in I_t; an unstructured magnitude-estimation procedure was used to monitor changes in the subjective intensity of suprathreshold stimuli and the psychophysical power function. The data provided additional information on the behavioral course of olfactory adaptation and recovery and suggested that this combined method can be used profitably for further investigations of this kind. Complementary to the work of Cain and Engen (1969), the results suggested an increase in the exponent of the power function with increasing adaptation.     

The parameters in the near-miss-to-Weber's law

Many empirical data support the hypothesis that the sensitivity function grows as a power function of the stimulus intensity. This is usually referred to as the near-miss-to-Weber's law. The aim of the paper is to examine the near-miss-to-Weber's law in the context of psychometric models of discrimination. We study two types of psychometric functions, characterized by the representations P_a(x)=F(ρ(a)x^γ(a)) (type A), and P_a(x)=F(γ(a)+ρ(a)x) (type B). A central result shows that both types of psychometric functions are compatible with the near-miss-to-Weber's law. If a representation of type B exists, then the exponent in the near-miss is necessarily a constant function, that is, does not depend on the criterion value used to define “just noticeably different”. If, on the other hand, a representation of type A exists, then the exponent in the near-miss-to-Weber's law can vary with the criterion value. In that case, the parameters in the near-miss co-vary systematically.     

THE INFLUENCE OF INTENSITY AND DURATION OF ELECTRICAL STIMULATION ON SUBJECTIVE VARIABLES

The unpleasantness and subjective duration of an A.C. current of 50 c/sec applied to two fingers was scaled by subjects using the method of magnitude estimation. Stimulation was varied with regard to both intensity and duration. It was found that (1) unpleasantness increased logarithmically with stimulus duration, (2) unpleasantness was a power function, with the exponent 1.5, of stimulus intensity, (3) subjective duration was essentially linearly related to stimulus duration, and (4) subjective duration increased logarithmically with intensity of stimulation.     

The standard model for perceived magnitude: a framework for (almost) everything known about it

The psychophysics of perceived magnitude entails three aspects of sensory systems: range of sensitivity (dynamic range [DR]), resolving power (the capacity to resolve small changes in stimulus intensity), and the form of the function relating perceived magnitude to signal strength throughout the DR. A simple model is proposed that integrates what is known about all three aspects into a single framework. According to the model, perceived magnitude is a power function of stimulus strength (S. S. Stevens, 1956), and both the exponent of that function and a measure of resolving power are inversely related to the log of DR (R. Teghtsoonian, 1971). The DR is thought to have a characteristic value for each sensory system and may be estimated directly by measurement of upper and lower limits, or indirectly by estimating the exponent of the power function under optimal conditions. A central feature of the model is that all DRs are assumed to be subjectively equal. It is also suggested that the impression of perceived magnitude may be mediated by a single mechanism, regardless of the sensory system that is activated. It remains to be seen whether brain science is able to identify a neural basis for such a mechanism.     

Brightness and loudness as functions of stimulus duration

The brightness of white light and the loudness of white noise were measured by magnitude estimation for sets of stimuli that varied in intensity and duration. Brightness and loudness both grow as power functions of duration up to a critical duration, beyond which apparent magnitude is essentially independent of duration. For brightness, the critical duration decreases with increasing intensity, but for loudness the critical duration is nearly constant at about 150 msec. Loudness and brightness also grow as power functions of intensity. The loudness exponent is the same for all durations, but the brightness exponent is about half again as large for short durations as for long. The psychophysical power functions were used to generate equal-loudness and equal-brightness functions, which specify the combinations of intensity E and duration T that produce the same apparent magnitude. Below the critical duration ET equals k for equal brightness, and ET^a equa Is k for equal loudness. The value a is about 0.7 for threshold and about 1.25 for supraliminal loudness.     

Brightness and loudness as functions of stimulus duration

The brightness of white light and the loudness of white noise were measured by magnitude estimation for sets of stimuli that varied in intensity and duration. Brightness and loudness both grow as power functions of duration up to a critical duration, beyond which apparent magnitude is essentially independent of duration. For brightness, the critical duration decreases with increasing intensity, but for loudness the critical duration is nearly constant at about 150 msec. Loudness and brightness also grow as power functions of intensity. The loudness exponent is the same for all durations, but the brightness exponent is about half again as large for short durations as for long. The psychophysical power functions were used to generate equal-loudness and equal-brightness functions, which specify the combinations of intensity E and duration T that produce the same apparent magnitude. Below the critical duration ET equals k for equal brightness, and ET^a equals k for equal loudness. The value a is about 0.7 for threshold and about 1.25 for supraliminal loudness.     

METHODOLOGICAL NOTE ON SCALES OF GUSTATORY INTENSITY

E kman , G. Methodological note on scales of gustatory intensity. Scand. J. Psychol ., 1961, 2, 185–100.—The subjective salt intensity of seven concentrations of sodium chloride in water was measured by the method of ratio estimation and by three variants of the method of magnitude estimation. The four scales thus constructed were not in agreement. The magnitude scales varied systematically with the stimulus used as standard. The average magnitude scale was in good agreement with the scale constructed by the method of ratio estimation. A combined scale was constructed from all the data. This scale is a power function of stimulus concentration. The exponent of the function is 1.59. The function includes an additive constant, which may indicate either the lack of an absolute zero point of the scale, or the presence of a basic sensation without external stimulation.     

On the relation between similarity and ratio estimates

Summary Data obtained in four sets of experiments involving pitch, heaviness, greyness, and circular area were re-analyzed. It was found (1) that similarity estimates S _ijare a power function of stimulus ratios S _ijwith the exponent n _s,(2) that ratio estimates q _ijare also a power function of stimulus ratios S _ijwith the exponent n _q(i.e., Stevens' power law), (3) that the exponent n of similarity estimates as power function of ratio estimates is equal to the ratio n _s/n _q,and (4) that, inversely, the exponent m of ratio estimates as power function of similarities is equal to the ratio n _q/n _s.The investigation was supported by a grant from the Swedish Council for Social Science Research.     

Odor intensity and pleasantness for a diverse set of odorants

Data Analysis Office, U.S. Army Natick Laboratories, Natick, Massachusetts 01760 Observers compared the odor of butanol to the odors of various concentrations of 32 chemicals, and also rated the odor pleasantness and unpleasantness of these 32 odorants by a line matching procedure. All stimuli were presented to the observers by air dilution olfactometers. Odor intensity matches between each odorant and butanol were often describable by power functions. A derived magnitude estimate of odor intensity was obtained through a calibration of the butanol concentration scale. Most odorants grew less rapidly in intensity than butanol, and all odorants grew in intensity as decelerating functions of concentration. A more general function of the form P =: k₁ + k₂C^k3 was needed to account for the pleasantness-unpleasantness judgments. In this study, most odorants were rated either neutral or unpleasant. Observers showed far more variability in hedonic judgments than in intensity judgments.     

THE DEPENDENCE OF VIBROTACTILE THRESHOLD AND MAGNITUDE FUNCTIONS ON STIMULATION FREQUENCY AND SIGNAL LEVEL: A perceptual and neural comparison

F ranzén , O. The dependence of vibrotactile threshold and magnitude functions on stimulation frequency and signal level. A perceptual and neural comparison. Scand. J. Psychol ., 1969, 10 , 289–298.—Apparent intensity of vibrotactile signals was examined as a function of stimulation frequency and displacement. Two sorts of power transformations were observed. (1) The exponent decreased as frequency was increased. (2) At low signal levels perceived intensity was linearly related to the physical input. At a certain point on the intensity continuum an abrupt shift to a power function with a slope of 0.58 occurred. The successive change of the exponent of the magnitude functions is tentatively interpreted as a kind of successively increasing demultiplication in the rate of firing frequency in the sensory pathway. A dual mechanism of mechanoreception is discussed.     

PSYCHOPHYSICAL SCALES OF THE ODOR INTENSITY OF AMYL ACETATE

The paper presents psychophysical scales of amyl acetate in benzyl benzoate sniffed from cotton. Four scales obtained by direct scaling procedures, ratio estimation and magnitude estimation, yield functions of the form R = kSⁿ , with n ranging from 0.39 to 0.57. These data support earlier findings that the intensity of smell is a negatively accelerated function of stimulus intensity. In addition, comparison of magnitude and category scales indicate that the subjective intensity of smell is a prothetic continuum. Finally, further analysis of subjective ratios as a function of stimulus ratios again shows that ( a ) the magnitude scale is a ratio scale and ( b ) the function obtained conforms to the power law.     

Conditioned suppression of drl responding: Effect of ucs intensity, schedule parameter, and schedule context

In Experiment I, groups of rats were trained to press a lever for food reinforcement on differential reinforcement of low rate (DRL) schedules which differed in parameter value. A stimulus which terminated with either a 0.5-mA or 2.0-mA electric shock was then superimposed upon each DRL baseline. In general, the magnitude of conditioned suppression was an inverse function of DRL schedule parameter and a direct function of shock intensity. Experiment II demonstrated that the rate of responding maintained by the DRL component of a multiple DRL-extinction schedule decreased during a stimulus preceding a 0.5-mA shock, whereas the rate of responding maintained by the DRL component of a multiple DRL-variable interval schedule showed little change or increased slightly during a stimulus preceding a 0.5-mA shock.     

Intensity discrilnination: Performance in three paradigms

Performance in the following auditory intensity-discrimination paradigms was compared: (1) 2IFC, (2) single-interval rating with an intensity cue preceding each observation interval, and (3) single-interval rating with no cue. ROCs obtained in the single-interval conditions could be well approximated by assuming that the underlying distributions were both normal and had equal variance. No large difference was observed between performance in the cue and the no-cue conditions. The normalized separation of the means for 2IFC was approximately twice the corresponding estimate for the single-interval conditions. i.e., d₂ = 1.91 d₁. This is consistent with the hypothesis that the O in intensity-discrimination tasks bases his decisions on the difference between the observed input and that of a noisy stored reference. The familiar result that d₂ = (2)^1/2 d₁ can be predicted for simple detection.     

Variability and sequential effects in cross-modality matching of area and loudness

Individual subjects' performance was examined for cross-modality matching (CMM) of loudness to visual area, as well as for magnitude estimation (ME) of the component continua. Average exponents of power functions relating response magnitude to stimulus intensity were .73 for area, .20 for loudness, and 2.44 for CMM. Predictions of the CMM exponent based on ME were higher than the empirical values, whereas more accurate predictions were made from magnitude production exponents obtained in a previous study. Sequential dependencies were assessed by comparing the response on trial n to the response on trial n--1. The coefficient of variation of the response ratio Rn/Rn-1 was systematically related to the stimulus ratio Sn/Sn-1 for both area and loudness. The coefficient was lowest for ratios near 1 and increased for larger or smaller values. For CMM, the coefficient of variation appeared to be independent of stimulus ratios. The correlation between log Rn and log Rn-1 was also related to Sn/Sn-1 for both ME and CMM. The correlation was highest when Sn/Sn-1 was 1 and dropped to 0 with increasing stimulus separation, but CMM yielded a shallower function than ME.     

Excitation of a chain of neurones

When the first of a uniform chain of neurones is excited with a stimulus intensityS ₁, it is found that, according to the nature of the chain,either the excitation is always transmitted with decreasing intensity,or else the intensity for succeeding neurones of the chain approaches a fixed finite value, characteristic of the chain and independent ofS ₁, wheneverS ₁ exceeds a certain threshold value.     

Effect of presentation procedure on taste intensity functions

Magnitude estimations were made for the taste intensity of sodium chloride (NaCl) and quinine sulfate (QSO₄) presented by three different methods: sip, anterior dorsal tongue flow, and whole-mouth flow. Power functions fitted to the data indicate that, for the anterior tongue stimulus (NaCl), the two flowing procedures produced lower exponents than did the sip procedure. For the posterior tongue stimulus (QSO₄), the exponent obtained with dorsal tongue flow was lower than the exponents obtained with either of the whole-mouth procedures, sip or flow. The results are compared to previous experiments on ratio scaling of taste intensity to elucidate the effects of several procedural variables.