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.     

Emotional reaction to past and future events as a function of temporal distance

In three experiments with 30 Ss, imagined past and future events were used as stimuli. Scales were constructed by the ratio estimation method for (a) subjective temporal distance and (b) emotional reaction to the events. It was found (1) that subjective temporal distance was a power function of chronological distance, (2) that emotional reaction to past events could be described as an exponential function of subjective temporal distance; a simple relation thus exists between the two psychological variables, whereas emotional reaction is related in a more complicated way to the objective variable, and (3) that emotional reaction to future events could be described about as well by a power function as by an exponential function of both subjective and objective temporal distance.     

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.     

An Elementary Syllabus of Psychological Tests

The purpose of this study was to examine the universality of the “inverse square root law” insofar as it purports to show a constant relationship between emotional involvement and subjectively perceived geographical distance. It was argued that the square root exponent in the “law” was derived from experiments that used a limited range of stimuli (place names). With students as subjects, two experiments were conducted in order to discover the relationship between emotional involvement and subjective distance when both very close and very distant places were considered. It was shown that the inverse square root function was not constant but rather varied with the range of stimuli.     

Shift in stimulus range and the exponent of the power function for loudness

The exponent of the power function for loudness was tracked over the course of 60 trials with one stimulus range and compared to the exponent over the course of 60 subsequent trials with a different stimulus range. Three stimulus sets were used: (1) weak, a short range of relatively soft tones (45-55 dBA); (2) strong, a short range of relatively loud tones (64-74 dBA); and (3) complete, a longer range of soft to loud tones (40-90 dBA). All pairs of stimulus sets were tested, together with three control conditions in which no shift in range occurred. Ten subjects were run in each of the nine groups. For preshift trials, the mean exponent was lowest for the strong stimulus series, highest for the weak series, and at an intermediate value for the complete series. These differences were all significant. Following a shift in stimulus range, the weak series still yielded the highest exponent, but the exponents were not reliably different for the complete and strong series. Postshift exponents also depended significantly on the preshift range experienced by the subjects. These effects were not confined to the period immediately following the shift in range, but persisted for up to 60 trials.     

Psychophysical parameters of the perception of orally-retained liquid bulk

Bulk of liquid held in the mouth may be judged on its subjective volume. Over the range I ml-31 ml, scaling by the constant method and by ratio estimation yielded a Weber fraction which was not constant and decreased with stimulus magnitudes and a psychophysical power function with an exponent of 0.96. A “negative threshold” effect is reported.     

The relation between subjective distance and emotional involvement: Further experiment

The purpose of this experiment has been to test the value of an exponent of the power function describing the relation between emotional involvement and subjective distance, called the inverse square root law (Ekman and Bratfisch 1965). A group of 113 subjects were instructed to estimate 65 inter-city distances with Opole, Poland, as the center, and, next, to estimate the importance attributed to the cities, their own personal interest in them and involvement to them. The experiment partly confirmed the results obtained in original investigations, that is the inverse square root law holds true for cities of a range of distance not exceeding about 5000 km. For more distant cities a different trend has been observed, namely an increase of emotional involvement with increase of subjective distance to these cities. This might lead to the supposition that the relation between emotional involvement and subjective distance could be described by a parabolic relation.     

BRIGHTNESS SCALES FOR MONOCHROMATIC LIGHT

By means of amethod of ratio estimation, scale values were obtained for the subjective brightness of various physical intensities of monochromatic light of various wave lengths. In a second experiment the scale was constructed by a method of magnitude estimation. The brightness functions were studied by plotting the scale values against stimulus intensity for each wave length. The two experiments gave essentially the same results. It was shown: (1) Brightness of monochromatic light is a power function of stimulus intensity. The exponent of the function is approximately one-third for all wave lengths. (2) Properties of the brightness functions can explain certain empirical relations between brightness, hue and saturation.     

SCALES OF UNPLEASANTNESS OF ELECTRICAL STIMULATION

The subjective unpleasantness elicited by an A.C. current of 50 c/sec. applied to two fingers was scaled by 14 subjects using the methods of magnitude and of category estimation. Nine current intensities, ranging between 2 and 10 times the individual sensation thresholds, were used as stimuli. A power function yielded a good fit to the magnitude-estimation data; the exponent was 1.81. The difference between this value and a considerably higher exponent reported by previous investigators was interpreted in terms of the wider stimulus range used in the present study. The relation between the category scale and the magnitude scale had the same general form as that found in several previous investigations.     

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.     

Power laws for the perception of rotation and the oculogyral illusion

Magnitude estimation was used to measure subjective motion for two indicators of vestibular function. Twelve as made estimates of 5-sec pulses of angular acceleration across the range of angular acceleration × time (at) =10-150 deg/sec. Results were: (1) the power law describes subjective motion for all individual as, (2) the power function exponent (1.41) for the perception of rotation is slightly greater than the exponent (1.25) for the oculogyral illusion, (3) a significant number of as gave higher exponents for the perception of rotation, and (4) the magnitude estimates of the oculogyral illusion and perception of rotation were highly correlated within and across as.     

Visual expectations change subjective experience without changing performance

It is widely believed that visual expectations can change the subjective experiences of humans. We investigated how visual expectations in a recognition task affected objective performance and subjective perception. Using a 2-alternative-forced-choice task based on digit recognition of briefly presented and visually masked digits, we found over two experiments that expectations changed the quality of the experiences without changing the performance capabilities associated with the quality of experience. Expectations were manipulated by providing a cue indicating the set of possible digits that might appear on each trial.The results also inform the debate about whether subjective experiences can be categorized in a dichotomous manner or in a graded manner. We found that subjective experiences were graded near the objective threshold and more dichotomous away from the threshold. Furthermore, distinct expectations resulted in a more dichotomous distribution of subjective experience.We also provide evidence of an interesting relationship between stimulus duration, objective performance and subjective ratings. Only experiences that were rated as evoking some degree of perception showed systematic improvements in objective performance as a function of stimulus duration.These findings suggest that subjective experience cannot be understood without considering the broader cognitive context, namely that the quality of subjective experiences is dependent on a multitude of factors such as attention, task requirements and cognitive expectations.     

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.     

Fechnerian metrics in unidimensional and multidimensional stimulus spaces

A new theory is proposed for subjective (Fechnerian) distances among stimuli in a continuous stimulus space of arbitrary dimensionality. Each stimulus in such a space is associated with a psychometric function that determines probabilities with which it is discriminated from other stimuli, and a certain measure of its discriminability from its infinitesimally close neighboring stimuli is computed from the shape of this psychometric function in the vicinity of its minimum. This measure of discriminability can be integrated along any path connecting any two points in the stimulus space, yielding the psychometric length of this path. The Fechnerian distance between two stimuli is defined as the infimum of the psychometric lengths of all paths connecting the two stimuli. For a broad class of models defining the dichotomy of response bias versus discriminability, the Fechnerian distances are invariant under response bias changes. In the case in which physically multidimensional stimuli are discriminated along some unidimensional subjective attribute, a systematic construction of the Fechnerian metric leads to a resolution of the long-standing controversy related to the numbers of just-noticeable differences between isosensitivity curves. It is argued that for unidimensional stimulus continua, the proposed theory is close to the intended meaning of Fechner's original theory.     

Stimulus range,number of categories,and the “virtual” exponent

Three different stimulus modalities (line length, number, and sound pressure) were judged by magnitude scaling techniques and by 7-, 15-, 31-, and 75-point category scales. All of the 40 subjects were given the same number stimuli, but two different sound-pressure ranges were presented (each to 20 subjects) and four different line-length ranges were presented (each to 10 subjects). Analyses of lack of fit for various simple functions were performed to determine bestfitting functions. The simple power function was often found to be an adequate fit to the data for all the response modalities used, although all of the response modalities were sensitive to changes in stimulus range. For simple power functions, the category-scale exponent was a function of both the range of stimuli and the number of categories provided. Category scales did not always produce exponents smaller than those obtained with magnitude estimation, which calls into question the concept of a virtual exponent for category scales.     

Range and regression effects in magnitude scaling

The relation between power law exponents obtained by magnitude estimation and magnitude production was studied for both loudness and perceived distance. While the results confirm the usual finding of higher values for production for relatively large stimulus ranges, just the opposite occurs when the stimulus range is short, necessitating a revision of the Stevens-Greenbaum regression principle. The relation between range and exponent was explored, both for the case in which several intensities are presented for judgment and for the simpler case of only two intensities. In both cases, a power relation was described relating stimulus ratios to judgmental ratios, with exponents containing both range-dependent and range-independent components.     

Individual functions of subjective time distance and emotional reaction

Lundberg, U. & Ekman, G. Individual functions of subjective time distance and emotional reaction. Scand. J. Psychol., 1973, 14, 29–33.-Data from a previous study ere analysed on an individual level. It was found that a simple power function could describe the relation between subjective and objective time, while an exponential function fitted the data for the relation between emotional reaction and subjective time distance. The same simple alternative functions also described the group data in the previous study.     

Scales for perceived egocentric distance in a large open field: comparison of three psychophysical methods

Scales for perceived egocentric distance produced by three psychophysical methods in four ranges of distances were compared. It was found that (a) the exponents produced by ratio and fractionation methods are in good agreement; (b) the exponents of both these methods were larger than those produced by magnitude estimation; (c) an increase in range of distance was associated with a decrease in exponent, but this diminution seems to interact with the method used; (d) for all the psychophysical methods used, there was large variability in the individual exponent; (e) the exponent was smaller than 1.0 for approximately 78% of the pooled sample, with all adult observers (N = 612) considered; and (f) an arithmetic mean exponent equal to 0.90 represents fairly all the results obtained.     

Quantitative functions for size and distance judgments

A psychophysical approach was used to obtain judgments of visual extent under three conditions. In tuvo conditions a comparison stimulus at each of two distances was matched in size to a standard which varied in distance. Stimuli were presented on a well-lighted table and were judged by two observers under Objective instructions. Both the standard and comparison were located in either a frontal or longitudinal plane. In a third condition relative distance estimates were given of two stimuli which varied in their relative positions along the table. The mean results for all conditions were described as a power function of physical stimulus measures. The exponent was greater than 1.0 for frontal size and usually less than 1.0 for flat size and distance. The position of the comparison affected the magnitude of the exponents to a lesser degree. These findings have relevance for interpretations of size and distance judgments.     

Multidimensional Fechnerian Scaling: Probability-Distance Hypothesis

The probability-distance hypothesis states that the probability with which one stimulus is discriminated from another is a function of some subjective distance between these stimuli. The analysis of this hypothesis within the framework of multidimensional Fechnerian scaling yields the following results. If the hypothetical subjective metric is internal (which means, roughly, that the distance between two stimuli equals the infimum of the lengths of all paths connecting them), then the underlying assumptions of Fechnerian scaling are satisfied and the metric in question coincides with the Fechnerian metric. Under the probability-distance hypothesis, the Fechnerian metric exists (i.e., the underlying assumptions of Fechnerian scaling are satisfied) if and only if the hypothetical subjective metric is internalizable, which means, roughly, that by a certain transformation it can be made to coincide in the small with an internal metric; and then this internal metric is the Fechnerian metric. The specialization of these results to unidimensional stimulus continua is closely related to the so-called Fechner problem proposed in 1960's as a substitute for Fechner's original theory.