Hannes Eisler

On theoretical and realizable ideal conditions in psychophysics: Magnitude and category scales and their relation

By spacing 10 stimuli (white noise) between 40 and 110 dB according to two criteria [equal response ambiguity (ERA) and equal discriminability (ED)], an attempt was made to construct an “ideal” case for magnitude estimation and category rating. The “ideal” case is defined by linear and constant Weber functions (SDs as a function of scale values) for the two scales, respectively. Altogether, three group and two individual magnitude and category rating experiments were run with these two spacings. It was found that the ERA spacing approximated the ideal case well for both Weber functions and the ED spacing only for the Weber function of the category scale. The general psychophysical differential equation that relates scale values and Weber functions for the two scales allowed good prediction of the category scales from the magnitude scales and the Weber functions. The data suggested a distinction between phenotypic (empirical) and genotypic Weber functions, analogous to “real” and “ideal” cases in physics.

Perception of human ecology: cross-cultural and gender comparisons

This study examined cultural and gender influences on attitudes, beliefs, opinions, and perceived risk factors in human ecology; further, on the level of knowledge about nature and the environment, and finally, on behavior affecting the environment. Subjects from Japan, Germany, Sweden, and the United States completed a survey scale consisting of seven components: (1) image of the sea, (2) image of the mountain, (3) image of the river, (4) sea affairs score, (5) environmental attitudes scale, (6) environmental knowledge scale, and (7) environmental behavior scale. Cultural differences revealed by the analyses included the following: (1) the Japanese group rated the sea, the mountain, and the river as less pleasant than did the other three groups, (2) the Japanese had the highest scores in environmental knowledge and the Americans the lowest, (3) the German group had the lowest sea affairs scores, and (4) both the German and the Swedish participants described and evaluated their behavior as most protective and the Japanese as least protective of the environment. Gender differences were also obtained, between as well as within cultures. Compared with male subjects, female subjects across countries perceived the risk factors as more serious as regards ecological and environmental problems, the global instability caused by economic nationalism, and the growing gap between rich and poor nations. Male subjects showed higher environmental knowledge, whereas females showed higher motivation for ecological thinking and behavior. These findings are discussed in terms of culture, gender, and cognition.

A mechanism of subjective similarity

SUMMARYThe mechanism of perception of similarity in the dimension of pitch was investigated. Similarity estimates were obtained and a pitch scale was constructed. It was shown that subjective similarity between two tones of equal loudness is equal to the ratio between the lower pitch and the average of the two pitch values. This relation is in a general agreement with Helsons concept of adaption level.

The connection between magnitude and discrimination scales and direct and indirect scaling methods.

Abstract(1) An analysis of the method of paired comparisons shows that Case V and Case VI, the latter characterized by log-normal distributions and Webers law for subjective continua, are fundamentally indistinguishable. Case VI produces a log-arithmetic interval scale of subjective magnitude. (2) It is demonstrated that the difference between discrimination scales according to Case V and from category rating is due to the difference between intra- and interindividual variability yielding different Weber functions.

Multidimensional similarity: an experimental and theoretical comparison of vector, distance, and set theoretical models: I. Models and internal consistency of data

Abstract In an experiment (conducted by the senior author) subjects were instructed to give three kinds of quantitative judgment on pairs of simple geometrical stimuli: similarity, commonality ratio and magnitude ratio. It was assumed that the different kinds of judgments could be interpreted in terms of one cognitive structure, and that formal models for each of these judgments should be validated by predicting one kind of judgment from knowledge of another kind of judgment. The present report proposes two different, though related, systems of formal models for similarity, commonality and magnitude ratio judgments. One, called E-model, interprets the judgments in terms of set- and vector-representations, and connections between them; the other, called R-model, interprets the judgments in terms of set- and distance-representations and their connections. The results are slightly in favor of the E-model. In a subsequent paper, the authors will report the results of multidimensional analyses for the same data, which slightly favor the R-model.

Relative attention in judgments of heterogeneous similarity

Shepard’s (1964) study on similarity of stimuli with clearly discernible dimensions was repeated with some modifications, the most important being that the Os had to make numerical similarity estimates of the stimulus pairs. The overall outcome did not deviate much from Shepard’s findings. By using quantitative estimates and choosing stimulus series so that the two dimensions were negatively correlated, data for each 0 could be analyzed separately with a partial correlation technique. It was found that the more an 0 attended to one dimension the less he attended to the other. The shifts in attention seemed to be random rather than regular. Consequently, the meaningfulness of a contention like Shepard’s as to the nonexistence of a metric is questioned.

Psychophysical similarities between rats and humans

Church and Deluty (1977) found that rats bisected pairs of durations at their geometric mean and concluded that the psychophysical function for duration in rats is logarithmic. From the same experimental finding and the assumption that the similarity between the short duration and the bisection point equals the similarity between the bisection point and the long duration, together with the unidimensional similarity function proposed by Eisler and Ekman (1959), Stevens’ psychophysical power function is derived instead. Since the similarity function thus seems to hold for animals as well as for humans, dealing with similarities appears to make more perceptual than cognitive demands.

Applicability of the parallel-clock model to duration discrimination.

The parallel-clock model assumes that when an observer is presented with two durations in succession, the total subjective duration (corresponding to the sum of first and second durations) and the second duration are each accumulated in a separate sensory register. In dealing with some relation between the two durations, the observer compares the difference between the contents of the two registers with the contents of the second register. With the further assumption that the psychophysical power law is valid for the continuum of time, the model has previously been shown to account well for duration scaling data. After adapting the model in the vein of Thurstone for duration discrimination data, it was tried out on such data gathered by Allan (1977) from 13 observers. With chi-square as the examined statistic, (1) five distributions were compared and the normal one chosen, (2) one categorization model, three choice models, and two linear regression models were compared with the 3-parameter version of the parallel-lock model, which proved superior, and (3) a 4–5-parameter version of the parallel-clock model, assuming a discontinuity in the psychophysical function, was shown to yield an excellent fit in terms of the Kolmogorov-Smirnov statistic.

On the ability to estimate differences: A note on Birnbaum’s subtractive model

ConclusionThe discussion about the appropriateness of the subtractive or the ratio model is highly reminiscent of the corresponding argumentation regarding the two equivalent representations of Thurstone’s Case V (Eisler, 1965a). Bock and Jones (1968, pp. 65–66, p. 273) provided evidence in favor of the ratio representation. For direct scaling, Eisler (1965b) argued, likewise, for the ratio representation. Further evidence in favor of the ratio representation can be found in Eisler (1975), where magnitude estimation of durations yields roughly the same power function exponent as the one obtained from duration reproduction. Also, the attempt to quantitatively relate different ratio-level estimates of the same stimuli proved successful (Eisler & Roskam, 1977a, 1977b), thereby supporting the ratio model.From the above it may be tentatively concluded that there is an alternative to Birnbaum’s model, according to which combinations of “difference” and “ratio” instructions in psychophysical experiments can be represented by a single scale, the sensation scale, and a single operation, ratio formation. Whether this representation is preferable to Birnbaum’s (1978) or to one with two operations on two scales is a question that requires further investigation.

The parallel-clock model: replies to critics and criticisms.

ConclusionThe parallel-clock model accounts for both scaling and discrimination data. This is an appealing property, since it unites two different theoretical approaches and experimental paradigms.The four different formulations of the model in the original paper (Eisler, 1975) obviously failed to convey my ideas fully, since the objections raised against the model seem mostly to be based on misunderstandings. The present paper is an attempt to remedy these shortcomings.