Effect of auditory masking on lingual vibrotactile thresholds and magnitude estimation scaling responses

Auditory masking has become a frequently employed part of the procedure used in vibrotactile research. Research investigating the effect of auditory masking on lingual vibrotactile thresholds of sensitivity has shown that there is little difference between lingual vibrotactile thresholds under masking and no masking conditions. The purpose of the present study was to extend the investigation of the effect of auditory masking to include lingual vibrotactile suprathreshold scaling responses. 20 young adult subjects of mean age 19 yr. completed lingual vibrotactile-threshold and magnitude-estimation scaling tasks under conditions of bilateral auditory masking and no masking. Similar lingual vibrotactile-threshold values and magnitude-estimation power-function exponents for the conditions of masking and no masking were noted.     

Unmasking the magnitude estimation response

The fuzzy judgement model of Ward (1979) predicts an inverse relation between the amount of stimulus information available to subjects and the magnitude of sequential dependencies on previous stimuli and responses in psychophysical scaling tasks. Ward confirmed this prediction for magnitude estimations of interdot distance for previous responses but not for previous stimuli, although the inverse relation has been repeatedly reported for both the previous stimuli and responses in absolute identification (e.g., Mori, 1989). This paper further explores this seemingly puzzling contradiction. A magnitude estimation of loudness experiment was conducted in which the amount of stimulus information available to subjects was manipulated by a modified version of informational masking (Watson, 1987). An absolute-identification-with-feedback experiment was also conducted to check the effectiveness of the informational masking in reducing the amount of stimulus information. The results of the magnitude estimation experiment show a striking similarity with those of Ward and generalize the failure of sequential dependencies on previous stimuli to vary inversely with stimulus information. An additional assumption that judgement strategies are altered under low-information conditions is necessary to explain this result.     

Effects of exposure to psychophysical scaling on lingual vibrotactile magnitude estimation and magnitude production

The purpose of the present study was to determine if the results obtained by the scaling methods of magnitude estimation and magnitude production could be influenced by providing subjects with prior exposure to psychophysical scaling in the form of magnitude estimation or magnitude production. Group 1 (n = 10, Mage = 21.1 yr.) performed lingual vibrotactile-magnitude estimation followed by lingual vibrotactile magnitude production. Group 2 (n = 10, Mage = 19.7 yr.) performed lingual vibrotactile-magnitude production (using the magnitude-estimation responses provided by Group 1), followed by lingual vibrotactile-magnitude estimation. For the magnitude estimations there was no over-all statistically significant difference between the two groups, but there was for the magnitude-production values. Magnitude-estimation scaling was apparently not influenced by prior exposure to magnitude production, while magnitude-production scaling was influenced by prior exposure to magnitude estimation. The results are discussed in terms of how subjective scaling behavior in psychophysical experimentation may be influenced by the interaction between an absolute internal scaling mechanism and parameters set by the experimenter, such as scaling method and range of stimulus intensity.     

Sensori-motor spatial training of number magnitude representation

An adequately developed spatial representation of number magnitude is associated with children's general arithmetic achievement. Therefore, a new spatial-numerical training program for kindergarten children was developed in which presentation and response were associated with a congruent spatial numerical representation. In particular, children responded by a full-body spatial movement on a digital dance mat in a magnitude comparison task. This spatial-numerical training was more effective than a non-spatial control training in enhancing children's performance on a number line estimation task and a subtest of a standardized mathematical achievement battery (TEDI-MATH). A mediation analysis suggested that these improvements were driven by an improvement of children's mental number line representation and not only by unspecific factors such as attention or motivation. These results suggest a benefit of spatial numerical associations. Rather than being a merely associated covariate, they work as an independently manipulated variable which is functional for numerical development.     

Individual differences in magnitude estimation of loudness

Twenty-two male and female subjects, aged 15 to 31 years, participated in two sessions, 11 weeks apart, of magnitude estimations of loudness. Stable individual differences in the exponent of the psychophysical power law, ψ=k?ⁿ, were shown. The correlation between subjects’ exponents of the first and second sessions was +.59. The generality of these findings and the origin of the individual differences were discussed.     

Hierarchical number estimation

We investigated number estimation using dot patterns grouped by proximity into larger clusters. Participants estimated the number of dots and clusters in separate trials. Estimation was most accurate when the numbers of elements on both scales were the same. When the number of elements on the unattended scale was higher, overestimation occurred. Conversely, when the number of elements on the unattended scale was lower, underestimation occurred. In Experiment 2, response cues were blocked to reduce any tendency toward attending the irrelevant level. The results were essentially unchanged, indicating response confusion alone cannot account for the effect. The data support the existence of an opposite scale effect in which the number of elements at the unattended level influence the processing of number.The preliminary results of the two experiments were presented at the Annual Meeting of The Association for Research in Vision and Ophthalmology, April 29–May 4, 2001, in Fort Lauderdale, Florida, USA     

Two classes of models for magnitude estimation

One class of models assumes that presentation of a signal results in an internal representation as a random variable. Depending on whether the signal is close to or far from the preceding signal, the variance of the representation is smaller or larger. Responses are determined largely by this random variable; however, when the signal is close to the preceding one, the response is generated by modifying the representation multiplicatively by some function of the ratio of the previous response to its representation. Power and linear functions are explored. The form of the random variable is assumed to be that arising from either the timing or the counting model operating on a Poisson process. Detailed analyses are carried out successfully only for the timing model with neural sample sizes independent of intensity; however, the data require the sample to increase with intensity. The linear response function coupled with the constant sample size counting model appears somewhat viable, but detailed calculations are very difficult to carry out. The second class of models postulates a power function relation between magnitude estimates and signals intensity for which the exponent is a Gaussian distributed random variable and the unit is the product of two log normal random variables. Again we assume an attention band such that succesive stimuli that are widely separated in intensity lead to independent samples of the random variables while a variety of assumptions is explored for successive stimuli that are near each other in intensity. Although they each give rise to the qualitative features of the data, estimates of parameters are sufficiently inconsistent that we are led to reject all of the submodels studied.     

Polarity correspondence in comparative number magnitude judgments

When asked which of two digits is greater, participants respond more quickly if physical size corresponds to number magnitude, such as in 3 7, than when the two attributes contradict each other, such as in 3 7. This size congruence effect in comparative number judgments is a well-documented phenomenon. We extended existing findings by showing that this effect does not depend on physical size of the number alone but can be observed with number symmetry. In addition, we observed that symmetric numbers are judged as being smaller than asymmetric numbers, which renders an interpretation of the number symmetry congruence effect in terms of physical size implausible. We refer to the polarity correspondence principle (Proctor & Cho, 2006) to explain the present findings.     

The development of automaticity in accessing number magnitude

This study traces developmental changes in automatic and intentional processing of Arabic numerals using a numerical-Stroop paradigm. In Study 1, university students compared the numerical or physical size of Arabic numerals varying along both dimensions. In Study 2, first graders (mean age = 6 years 6 months), third graders (mean age = 8 years 4 months), and fifth graders (mean age = 10 years 3 months) were tested to examine developmental changes in numerical and physical comparisons. In the numerical comparison task, a size congruity effect was found at all ages (i.e., relative to a neutral control, congruent physical sizes facilitated, and incongruent sizes interfered with, the numerical comparison). The pattern of facilitation and interference, however, was modulated by age. In the physical comparison task, the incongruity between physical and numerical size affected only older children and adults. These findings strongly suggest that the automatization in number processing is achieved gradually as numerical skills progress.     

A scale for the psychological magnitude of number

A scale of the “psychological magnitude” of number was constructed from similarity ratings of the 45 number pairs that can be obtained from a set of 10 integers. A nonmetric analysis of these similarity ratings showed that “psychological number” was a power function of number.     

Cognitive reference points in judgments of symbolic magnitude

Research on speeded symbolic magnitude comparisons indicates that decisions are made more quickly when the magnitudes of the stimuli being compared are relatively close to an explicit or implicit reference point. Alternative explanations of this phenomenon are tested by seeking similar effects in nonspeeded rating tasks. In accord with the predictions of discriminability models, rated magnitude differences between stimuli in the vicinity of a reference point are expanded relative to differences between stimuli far from it. The inferred locations of cities along a west-east axis varies systematically depending on which coast, Pacific or Atlantic, is specified as the reference point. Scales derived from the rating data are correlated with the pattern of reaction times obtained in a comparable speeded comparison task. In addition, the distance between the cities nearest the locale of our subjects is subjectively stretched. Reference point effects are also observed when the form of the comparative specifies an implicit reference point at either end of a continuum of subjective size; however, these effects are very small and do not clearly support a discriminability interpretation. Stronger evidence for discriminability effects is obtained when an explicit reference point is established at an arbitrary size value. An implicit scaling model, related to range-frequency theory, is proposed to account for the influence of reference points on relative discriminability of stimulus magnitudes. The implicit scaling model is used to develop an account of how symbolic magnitudes may be learned and of how habitual reference points can produce asymmetries in distance judgments.     

The response ratio hypothesis for magnitude estimation

Assume that each presentation of a signal produces two independent random variable representations and that the ratio of responses on successive trials of a magnitude estimation experiment are proportional to the ratio of a representation from the present trial, which representation is then lost, to the remaining one from the previous trial. The mean response to a particular signal depends on the mean of the representation used, but in general exhibits drift over trials and sequential effects due to the preceeding trial; the mean response ratio does not exhibit drift, but it has a simple form only when there are no sequential effects; however, a modified mean ratio function has a simple form. A model suggested by D. V. Cross is a special case of this one. Simple timing and counting models for the representations fail to exhibit sequential effects, contrary to considerable data. However, data of the authors have suggested a version of the timing model in which the sample size of the representation varies by an order of magnitude depending on how close the signal is to the preceding one; this hypothesis accounts for the observed sequential effects and other aspects of the data.     

Cross-modality matching functions generated by magnitude estimation

It is possible to generate cross-modality matching functions by having subjects make magnitude estimates of sets of stimuli appropriate to different modalities. The sets are interspersed among each other in the same test session and judged on a common absolute scale of sensory magnitude. An appropriate statistical device locates stimulus levels that appear, on the average, to match. The method is fast, efficient, circumvents the need for continuous stimulus adjustment, and holds promise for the study of the individual as well as the average psychophysical function. To illustrate its potential uses, advantages, and limitations, we used the method to generate cross-modality matching functions relating loudness and brightness. Compared to the scales of loudness and brightness generated by the magnitude estimations of the same stimuli, the matching functions (1) conform better to power functions, (2) may show less variation in slope (exponent), and (3) show far less variation in absolute magnitude (position).     

Extensions of Narens' theory of ratio magnitude estimation

Stevens postulated that the responses of a participant in a ratio scaling experiment can be used directly to construct a psychophysical function. Today, it is generally accepted that the axioms of commutativity and multiplicativity are crucial for the interpretation of the subjects' ratio scaling behaviour. Empirical findings provide evidence that commutativity holds, whereas multiplicativity fails to hold across different sensory modalities. This shows that, in principle, Stevens' direct scaling methods yield measurements on a ratio scale level, but that the numerals occurring in a ratio scaling experiment cannot be taken at face value. Thus, Narens and others introduced a transformation function f, which converts the numerals used in an experiment into the latent mathematical numbers. The aim of the present paper is to specify the (unknown) shape of the transformation function f, by analysing different extensions of the multiplicative property. The results provide evidence that f is either a power function or a logarithmic function.     

A behavioristic analysis of Stevens magnitude estimation method

A procedure independently proposed by Oyama and Lewis for treating the data of magnitude estimation is discussed in relation to the Graham-Stevens controversy on the psychophysical methods. In this procedure, the critical value of the stimulus needed to make the subject report numbers equal to or greater than each integral number is sought, instead of the median or geometrical mean of numbers reported for each level of stimulus intensity. Stevens’ magnitude estimation method has no special advantage over the other cross-modality matching methods, and the subjective magnitude of number should be estimated if one wants to know real relations between stimulus intensities and sensory magnitudes in various modalities.     

Magnitude production and magnitude estimation of taste intensity

Magnitude productions of sodium chloride (salty), quinine hydrochloride (bitter), and sucrose (sweet) yielded steeper psychophysical functions than those obtained with magnitude estimation. Hydrochloric acid (sour) produced the opposite effect. The results are discussed with respect to previous findings in taste intensity scaling and to general psychophysical considerations.     

Bias effects on magnitude and ratio estimation power function exponents

A bias model of relative judgment was used to derive a ratio estimation (RE) power function, and its effectiveness in providing estimates of exponents free of the effects of standards was evaluated. The RE bias model was compared with the simple RE power function that ignores bias. Results showed that when bias was not taken into account, estimates of exponents exhibited the usual effects of standards observed in previous research. However, the introduction of bias parameters into the RE power function virtually eliminated these effects. Exponents calculated from "equal-range segments" (e.g., low stimulus range vs. high stimulus range) judged by magnitude estimation (ME) were examined: the effects of equal-range segments on exponents were much stronger for ME than standards were for RE, using the bias model.