Stevens’ power law and the problem of meaningfulness

Augustin, Thomas

doi:10.1016/j.actpsy.2007.12.005

Cited by 18 publications

(23 citation statements)

References 24 publications

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“…Equations 4-7 predict the multiplicativity condition that Π z 0 Π ab . It turned out that Π z < Π ab for a and b larger than 1 (Ellermeier & Faulhammer, 2000) and Π z > Π ab for a and b smaller than 1 (Zimmer, 2005), confirmed by Augustin (2008) and Augustin and Maier (2008). These results indicate that ratio evaluation is inconsistent with multiplication.…”

Section: Consistency Testssupporting

confidence: 45%

On the ability to directly evaluate sensory ratios

Masin

2012

Atten Percept Psychophys

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The study explored whether participants could directly evaluate sensory ratios. The results indicate that they did not exhibit this ability for the extensive continuum of length and the intensive continua of brightness and brightness difference. Functional measurement analysis, combined with a chronometric analysis of responses, indicated that participants used mental counting for length and used difference evaluation for brightness and brightness difference. The finding that participants evaluated brightness differences under instructions to evaluate brightness ratios suggests that difference judgments may be a general human capability. It resolves questions raised by prior tests of Torgerson's conjecture and by prior consistency tests of ratio evaluation.

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Section: Consistency Testssupporting

confidence: 45%

On the ability to directly evaluate sensory ratios

Masin

2012

Atten Percept Psychophys

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“…In statistics, this property is the power function will vary across variables of different intensities, such as brightness or loudness. As pointed out by Augustin (2008), however, it is critical that the exponent be constant for a given-intensity variable. Exponents should not, for instance, depend on the specific levels chosen in an experiment.…”

Section: Critiques Of Inference By Significance Testsmentioning

confidence: 99%

Bayesian t tests for accepting and rejecting the null hypothesis

Rouder

Speckman

Sun

et al. 2009

Psychonomic Bulletin & Review

3,440

3,401

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“…Steingrimsson and Luce (2007) replicated both results in a loudness production experiment by using a different methodology. The experimental data of Peißner (1999) on brightness production as well as Augustin (2008) and Augustin and Maier (2008) on area production provide evidence for the generality of these results across different sensory modalities.…”

Section: Introductionmentioning

confidence: 79%

“…It is important to note here that this result cannot be generalized to other sensory modalities such as area or brightness perception, where the stimuli can be presented simultaneously. To give a concrete example, Augustin (2008) presented two white circular curves on a dark blue screen, the left one being the standard stimulus, the right one adjustable by the participant. The participants' task was to adjust the area of the variable circle in such a way that it appeared to be p times ( p =1/3, 1/2, 1, 2, 3) as large as the area of the standard stimulus.…”

Section: 3 Extensionmentioning

confidence: 99%

“…Additionally, Narens (1996) showed that the axiom of multiplicativity determines the shape of the transformation function f: if multiplicativity and commutativity hold along with some technical side conditions, then the transformation function f is a power function of the form f ð pÞ ¼ p a . The multiplicative property was tested empirically by Augustin (2008), Augustin and Maier (2008), Ellermeier and Faulhammer (2000), Peißner (1999), Steingrimsson and Luce (2007), and Zimmer (2005). The results clearly indicate that multiplicativity is violated for ratio production experiments.…”

Section: Introductionmentioning

confidence: 99%

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Extensions of Narens' theory of ratio magnitude estimation

Augustin

2010

Brit J Math & Statis

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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.

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Stevens’ power law and the problem of meaningfulness

Cited by 18 publications

References 24 publications

On the ability to directly evaluate sensory ratios

On the ability to directly evaluate sensory ratios

Bayesian t tests for accepting and rejecting the null hypothesis

Extensions of Narens' theory of ratio magnitude estimation

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