Magnitude estimation of apparent sums and differences

Subjects were required to indicate the magnitudes of subjective sums of areas of regular 20-sided polygons by three methods-generation of a polygon of matching area, estimation of the ratio of the subjective sum to a fixed area, and magnitude estimation. Power law exponents were estimated for each subject by maximum likelihood estimation. A very large amount of interindividual exponent variation was observed. Exponents resulting from magnitude estimation were consistent on the average with previous results, but exponents from area matching and ratio estimation were much larger and close to unity. When subjects were given feedback on the discrepancy between their responses and physical area summation, they readily shifted their exponents toward unity.

Section: Resultsmentioning

confidence: 47%

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Intra- and interindividual variation in the power law exponent for area summation

Ramsay

1979

“…Stevens (1971, Figure 4) discusses work of Beck and Shaw (1967) and of Dawson (1971), who obtained magnitude estimations of difference in loudness for pairs of tones. Both studies showed that these judgments were not linearly related to Stevens' sone scale.…”

Section: Related Workon Loudness Differencingmentioning

confidence: 99%

Bisection of loudness

Carterette

Anderson

1979

In a loudness bisection task, subjects varied one sound to lie halfway between two given sounds in terms of loudness. The two given sounds were varied from 30 to 90 dB in a 4 by 9 factorial design. Functional measurement methods based on monotone analysis provided good support for the bisection model, and yielded a loudness scale with an exponent of about .3, except for a falloff at lower intensities. Two other tasks, judging average loudness and difference in loudness of the two given sounds, yielded mixed results. In Experiment 2, in particular, the differencing judgments were not additive, even under monotone transformation. These analyses also indicated that previous applications of monotone analysis have typically lacked adequate power to allow any conclusion about the operative model. Overall, the present bisection scale agrees with Garner's lambda scale, and the present theoretical approach agrees with that of Garner in its emphasis on algebraic models as a foundation for psychological measurement.The quality of loudness has good reasons for being a primary focus of psychophysical measurement. It has enormous dynamic range, in contrast to skin temperature or pressure. It is an energetic, sensory dimension, in contrast to length. It has nearly the ecological importance of brightness, but not nearly the complications from adaptation. And it is experimentally flexible and easy to control. For these and other reasons, loudness has become a primary test case for theories of psychophysical measurement.The method of bisection is attractive because it rests on sensory comparison and avoids artificial response language. If the subject's bisection response was indeed at the sensory midpoint, then a simple procedure of successive bisection would yield a linear (equal-interval) scale of sensation. Two arbitrary initial stimuli would be called 0 and 100. Their bisector would then have the value 50, two further bisections would yield the 25 and 75 points, four further bisections would yield the 12.5, 37.5, 62.5, This work was supported by National Institute of Mental Health Grant MH-07809 to the first author, and by National Science Foundation Grant BMS 74-19124 to the second author. A preliminary report of this work was presented at the XXI International Congress of Psychology, Paris, July 1976. We wish to thank Alan Barnebey for help with apparatus and computing, Cheryl Smart for programming and managing the experiments, Clifford Butzin and Anthony Harris for advice and assistance in data analysis, and Edward Alf for developing the HP-67 program used for fitting power functions. Requests for reprints may be sent to Edward Carterette, Psychology, University of California. Los Angeles, Los Angeles, California 90024, or to Norman Anderson, Psychology C-009, University of California, San Diego, La Jolla, California 92093. and 87.5 points, and so on, to as fine a division as desired. Granted that the bisection response is at the sensory midpoint, these numbers would constitute a linear scale of loudness.But the method of ...

“…Most of the evidence gathered thus far does not appear to be conclusive and shows merely that, under some circumstances, the additivity is consistent with direct proportionality between sensation magnitudes and the numbers assigned to them (e.g., Cain, 1976;Dawson, 1971;Hellman & Zwislocki, 1963;Marks, 1978aMarks, , 1978bMarks & Bartoshuk, 1979;Murphy, Cain, & Bartoshuk, 1977). A stronger case was made by Levelt, Riemersma, and Bunt (1972) for binaural summation of loudness and by Marks (1978b) for loudness summation in simultaneous heterofrequency tone pairs by using nonmetric conjoint measurement (Luce & Tukey, 1964).…”

mentioning

confidence: 99%

Group and individual relations between sensation magnitudes and their numerical estimates

Zwislocki

1983

The study deals mainly with absolute magnitude estimation (AME) of the component loudnesses and the total loudness of pairs of heterofrequency, sequential tone bursts. Two kinds of relations are derived from the obtained group and individual data on the assumption of loudness additivity and a two-stage scaling model. They refer to numerical loudness estimates versus derived loudness magnitudes and to the loudness magnitudes versus tone sensation levels. The relations are validated by means of indirect and direct loudness matches. In an auxiliary experiment, the same subjects performed AMEs of subjective line lengths. The resulting group and individual relations between the numerical estimates and the underlying physical line lengths were found to be nearly the same as those between the numerical loudness estimates and the derived loudness magnitudes. The mutual consistency among the several sets of empirical and derived data strongly supports the assumptions of loudness additivity and the two-stage model.