What are we estimating when we fit Stevens’ power law?

Bernasconi, Michele; Seri, Raffaello

doi:10.1016/j.jmp.2016.04.007

Cited by 6 publications

(5 citation statements)

References 101 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A limitation of this study is that the findings tell us little about preference heterogeneity. The power function predicts the preferences of the general population; this evidence, however, does not imply that the power function predicts preferences at the individual level (i.e., utility) [34,35]. Functions that perform well in aggregate data may perform poorly when predicting the preferences of a specific individual, and vice versa.…”

Section: Study Limitationsmentioning

confidence: 99%

Quality-Adjusted Life-Years without Constant Proportionality

et al. 2018

View full text Add to dashboard Cite

show abstract

Section: Study Limitationsmentioning

confidence: 99%

Quality-Adjusted Life-Years without Constant Proportionality

et al. 2018

View full text Add to dashboard Cite

show abstract

“…For example, Freides and Phillips (1966) and Steingrimsson and Luce (2006) revealed a lack of fit of the power function when applied to individual data. Generally, differences between psychophysical functions seem to emerge when these are fitted on the individual level rather than on the group level (Bernasconi & Seri, 2016). Other studies, however, also reported a good fit of the power function when fitted to individual as well as to aggregated data (Algom & Marks, 1984Marks & Stevens, 1966).…”

Section: Criticism Of the New Psychophysicsmentioning

confidence: 93%

On the difficulty to think in ratios: a methodological bias in Stevens’ magnitude estimation procedure

Mertens

Lerche

2021

Atten Percept Psychophys

View full text Add to dashboard Cite

In the field of new psychophysics, the magnitude estimation procedure is one of the most frequently used methods. It requires participants to assess the intensity of a stimulus in relation to a reference. In three studies, we examined whether difficulties of thinking in ratios influence participants’ intensity perceptions. In Study 1, a standard magnitude estimation procedure was compared to an adapted procedure in which the numerical response dimension was reversed so that smaller (larger) numbers indicated brighter (darker) stimuli. In Study 2, participants first had to indicate whether a stimulus was brighter or darker compared to the reference, and only afterwards they estimated the magnitude of this difference, always using ratings above the reference to indicate their perception. In Study 3, we applied the same procedure as in Study 2 to a different physical dimension (red saturation). Results from Study 1 (N = 20) showed that participants in the reversal condition used more (less) extreme ratings for brighter (darker) stimuli compared to the standard condition. Data from the unidirectional method applied in Study 2 (N = 34) suggested a linear psychophysical function for brightness perception. Similar results were found for red saturation in Study 3 (N = 36) with a less curved power function describing the association between objective red saturation and perceived redness perception. We conclude that the typical power functions that emerge when using a standard magnitude estimation procedure might be biased due to difficulties experienced by participants to think in ratios.

show abstract

“…One of the most well-known models in mathematical psychology is Stevens' model, in which (see Stevens 1975, Kornbrot 2014, Bernasconi & Seri 2016:…”

Section: The Statistical Modelmentioning

confidence: 99%

“…In this situation, the convergence rates presented in this paper constitute a worst-case scenario. 6 In psychology, the risks of averaging across individuals when they are characterized by different functions has been stressed, e.g., in Skinner (1958, p. 99), Yost (1981, p. 212) and Bernasconi & Seri (2016).…”

Section: Introductionmentioning

confidence: 99%

Nonparametric Estimation and Inference in Economic and Psychological Experiments

Seri,

Centorrino,

Bernasconi

2019

Preprint

Self Cite

View full text Add to dashboard Cite

The goal of this paper is to provide some tools for nonparametric estimation and inference in psychological and economic experiments. We consider an experimental framework in which each of nsubjects provides T responses to a vector of T stimuli. We propose to estimate the unknown function f linking stimuli to responses through a nonparametric sieve estimator. We give conditions for consistency when either n or T or both diverge. The rate of convergence depends upon the error covariance structure, that is allowed to differ across subjects. With these results we derive the optimal divergence rate of the dimension of the sieve basis with both n and T . We provide guidance about the optimal balance between the number of subjects and questions in a laboratory experiment and argue that a large n is often better than a large T . We derive conditions for asymptotic normality of functionals of the estimator of T and apply them to obtain the asymptotic distribution of the Wald test when the number of constraints under the null is finite and when it diverges along with other asymptotic parameters. Lastly, we investigate the previous properties when the conditional covariance matrix is replaced by an estimator.

show abstract

What are we estimating when we fit Stevens’ power law?

Cited by 6 publications

References 101 publications

Quality-Adjusted Life-Years without Constant Proportionality

Quality-Adjusted Life-Years without Constant Proportionality

On the difficulty to think in ratios: a methodological bias in Stevens’ magnitude estimation procedure

Nonparametric Estimation and Inference in Economic and Psychological Experiments

Contact Info

Product

Resources

About