Test of a response bias model of bisection

Fagot, Robert F.; Stewart, Manard R.

doi:10.3758/bf03210160

Cited by 15 publications

(21 citation statements)

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“…Because of the dissimilarity in training and testing procedures between the human bisection task and the animal bisection task, it is legitimate to question whether the bisection points obtained in each procedure measure the same thing. Fortunately, this question has been addressed in experiments by Fagot and Stewart (1970) for human bisection and by Raslear (1983) for animal bisection. Both procedures have been found to be consistent with the Pfanzagl (1968) bisection model.…”

Section: Notementioning

confidence: 99%

“…For example, changes in stimulus context, such as stimulus spacing, stimulus frequency, or stimulus order in time and space, have been shown to affect psychophysical tasks in humans (Helson, 1964). Fagot and Stewart (1970) demonstrated that the BP shifts with changes in stimulus spatial order in a human brightness bisection task, and Raslear has demonstrated that changes in stimulus spacing produce shifts in the BP for rats in auditory bisection (Raslear, 1975) and in temporal bisection (Raslear, 1983) tasks.…”

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confidence: 99%

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Perceptual bias and response bias in temporal bisection

Raslear

1985

Perception & Psychophysics

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Section: Notementioning

confidence: 99%

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confidence: 99%

Perceptual bias and response bias in temporal bisection

Raslear

1985

Perception & Psychophysics

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“…The empirical verification of all equalities in Equation 12 is believed to support the possibility that M C M A M B M C (w .5), making actual measurement possible (Adams & Fagot, 1975;Coombs, Dawes, & Tversky, 1970;Cross, 1964;Fagot & Stewart, 1970;Irtel, 2005;Pfanzagl, 1971;Raslear, Shurtleff, & Simmons, 1992). …”

Section: Bisymmetry Conditionmentioning

confidence: 92%

On the bisection operation

Masin

Toffalini

2009

Attention, Perception & Psychophysics

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Given two perceived magnitudes of a single kind of sensory attribute, A and B, the operation of bisection is the selection of the perceived magnitude of this attribute, C, that differs from A as much as it differs from B (Plateau, 1872). With M A , M B , and M C denoting the measures of A, B, and C, respectively, Pfanzagl (1959) proposed thatwith w constant in the interval [0, 1], and showed that the bisection operation is compatible with this weighted arithmetic mean when it satisfies the following condition. Bisymmetry ConditionFor a given sensory attribute, let M 1 , M 2 , M 3 , and M 4 denote any measures of perceived magnitude sufficiently different from one another. Throughout this article, subscript numerals are used as labels. Bisections yield the measuresWith w unknown, Equations 2-5, 8, and 9 implyEquation 11 expresses the bisymmetry condition (Aczél, 1948). When w .5, Equations 2-10 implyThe empirical verification of all equalities in Equation 12 is believed to support the possibility that M C M A M B M C (w .5), making actual measurement possible (Adams & Fagot, 1975;Coombs, Dawes, & Tversky, 1970;Cross, 1964;Fagot & Stewart, 1970;Irtel, 2005;Pfanzagl, 1971;Raslear, Shurtleff, & Simmons, 1992). Gage's ConditionWhen the effects of the orders of presentation of A, B, and C are counterbalanced, Cross (1964, p. 5) showed that the bisymmetry condition is equivalent to the following condition proposed by Gage (1934a). Let M 1 and M 2 denote measures of two perceived magnitudes delimiting a sufficiently large sensory interval. Bisections yield the measuresEquations 13-16 imply On the bisection operation SERGIO CESARE MASIN AND ENRICO TOFFALINI University of Padua, Padua, ItalyFor two perceived sensory magnitudes, A and B, the bisection operation yields a perceived sensory magnitude, C, equally different from A and B. Available data do not resolve whether this operation is equivalent to a linear or a nonlinear mean. We tested these alternatives, using the evidence of functional measurement research that ratings are linear sensory measures. With A and B varied factorially, linear means predict that the curves relating rated C to rated A for each B are parallel straight lines, and nonlinear means predict that these curves are nonlinear and nonparallel. Using brightness and perceived size as sensory attributes, the present experiments confirm the first of these predictions, indicating that the bisection operation is equivalent to a linear mean.

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“…The bisection model implies that these bisection points are a function of both d and the parameters of the psychophysical function for brightness. Using an iterative least squares procedure, they were able to estimate a mean d of .41 or .45 (Fagot & Stewart, 1970, Table I), dependent on the assumed form of the psychophysical power function. A d less than 1/2 was interpreted as due to a response bias.…”

Section: Resultsmentioning

confidence: 99%

“…Fagot and Stewart (1970) obtained bisection points for a number of intervals on the brightness continuum. The bisection model implies that these bisection points are a function of both d and the parameters of the psychophysical function for brightness.…”

Section: Resultsmentioning

confidence: 99%

An experimental check on Stevens’s explanation of the partition paradox by successive doubling and bisecting

Masin

1983

Perception & Psychophysics

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Scaling methods based on direct estimation of sensory ratios and intervals give discrepant results (the partition paradox). Stevens's explanation of this discrepancy was tested here. Given a psychological magnitude, 1jJ, observers were required to select a magnitude 21jJ, and subsequently to bisect the interval between IjJ and 21jJ. Stevens's hypothesis predicts that the bisected psychological magnitude falls between 1.411jJ and 1.501p. The hypothesis is not substantiated, since a bisected magnitude of 1.551jJ was obtained. Furthermore, observers had to bisect the interval between IjJ and an imagined magnitude of 21jJ. The results show that observers are able to producereliably both a visual and a representational double.Ratio scaling is based on the assumption that the human observer is capable of directly reporting sensory ratios between two values of a perceptual variable. The method of fractionation or multiplication requires the observer to estimate, or produce, fractions or multiples (ratios) of given values of a perceptual variable. Interval scaling is based on the assumption that the observer is capable of directly reporting sensory intervals. The method of bisection requires the observer to set the value of a perceptual variable until it is midway between two fixed values of the same perceptual variable, thus producing two equal-appearing intervals.Typically, the exponent of a power function obtained by the method of bisection is smaller than the exponent obtained by a method based on ratio scaling (Stevens, 1955). Thus, methods based on direct estimation of sensory intervals and ratios do not give consistent results (the partition paradox). According to Stevens (Stevens, 1971, 1975Stevens & Davis, 1938), this discrepancy originates in the method of bisection. In bisecting a sensory interval, the observer can adopt two different strategies: He can set the middle value midway between the two end values to obtain two equal-appearing intervals, or he can set the middle value so that the ratio of the middle value to the lower value equals the ratio of the higher value to the middle value. The actual performance, Stevens argued, represents a compromise between these two possibilities.In an experiment by Garner (1954), a group of observers set a variable stimulus so that the corresponding perceptual value, lIIv' stood in the middle of the I wish to thank Martha Teghtsoonian for a careful reading of the first draft of this manuscript. 294two perceptual values lIIi and lpj' The setting was carried out under two conditions. In one condition, the observers were instructed to set the variable stimulus to produce equal distances, that is, lpv-lpi =lpj -lIIv'In the other condition, they had to set the variable stimulus to produce equal ratios, that is, lpv/lpi = lpj!lpv' For most observers, the selected value for the variable stimulus was the same under the two conditions. If an estimate of the values lpi and lpj were at our disposal, we would be in a position to know whether the observer under the bisection task ap...

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Test of a response bias model of bisection

Cited by 15 publications

References 10 publications

Perceptual bias and response bias in temporal bisection

Perceptual bias and response bias in temporal bisection

On the bisection operation

An experimental check on Stevens’s explanation of the partition paradox by successive doubling and bisecting

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