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Modeling Psychophysical Data in R pp 107–139Cite as

The Psychometric Function: Introduction

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Part of the book series: Use R! ((USE R,volume 32))

Abstract

The psychometric function is a summary of the relation between performance in a classification task (such as the ability to detect or discriminate between stimuli) and stimulus level [59, 176]. Stimulus level is typically a measure of magnitude of a physical stimulus along a single physical dimension such as size, distance, light or sound intensity, concentration, or frequency. We will use the terms “stimulus level and “stimulus intensity interchangeably. We gave an example of a psychometric function in Chaps. 1 and Chaps. 2, we discussed the close relationship between the psychometric function and the generalized linear model. While there is no need to use the GLM in fitting psychometric functions we will see that doing so makes it very convenient to apply advanced statistical methods to psychophysical data.

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Notes

  1. 1.

    Also, I is the name of a function in R, and it is best to avoid variables with the same names as functions.

  2. 2.

    This is the default behavior of optim. It can be made to maximize by including the argument control = list(fnscale = -1).

  3. 3.

    However, see the mle function in the recommended package stats4 [146].

  4. 4.

    They state, “No special statistical methods are necessary to determine which curve fits the data, since smaller and larger values of n are easily excluded by visual comparison.” Such graphical short-cuts to fitting were common (and unavoidable) before availability of the enormous computational resources of the current era.

  5. 5.

    The use of a Gaussian to describe these data is less heretical than one might think. For example, Crozier [42, 43] argued against a Poisson model and in favor of a Gaussian model to describe detection psychometric functions.

  6. 6.

    H. Sun, personal communication.

  7. 7.

    Lower-order terms are marginal to higher-order terms. For example, main effects are marginal to interactions and simpler interactions are marginal to more complex ones. It is advised to test higher-order interactions without removing marginal effects that include the same terms as the higher-order effects. Conversely, one should not test marginal effects in the presence of significant non-marginal effects.

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  1. Department of Integrative Neurosciences, Stem-cell and Brain Research Institute INSERM U846, 18 avenue du Doyen Lépine, Bron, France

    Kenneth Knoblauch

  2. Department of Psychology Center for Neural Science, New York University, 6 Washington Place, 2nd Floor, New York, USA

    Laurence T. Maloney

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Knoblauch, K., Maloney, L.T. (2012). The Psychometric Function: Introduction. In: Modeling Psychophysical Data in R. Use R!, vol 32. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4475-6_4

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