Testing hypotheses about psychometric functions

モンテカルロ法(ブートストラップ法)による精神測定関数の検討。
下記プロジェクトサイトから、計算を実行するためのMATLAB用のmex file (toolbox)や文献のpdf file の入手が可能。
cf.
Wichmann & Hill: The psychometric function
Percept Psychophys. 2001 Nov;63(8):1293-313.

References
bootstrap-software.org
Testing hypotheses about psychometric functions: psignifit toolbox for Matlab 5 and up
http://bootstrap-software.org/psignifit/

Wichmann & Hill: The psychometric function

Percept Psychophys. 2001 Nov;63(8):1293-313.

The psychometric function: I. Fitting, sampling, and goodness of fit.

Wichmann FA, Hill NJ.

University of Oxford, England.

The psychometric function relates an observer's performance to an independent variable, usually some physical quantity of a stimulus in a psychophysical task. This paper, together with its companion paper (Wichmann & Hill, 2001), describes an integrated approach to (1) fitting psychometric functions, (2) assessing the goodness of fit, and (3) providing confidence intervals for the function's parameters and other estimates derived from them, for the purposes of hypothesis testing. The present paper deals with the first two topics, describing a constrained maximum-likelihood method of parameter estimation and developing several goodness-of-fit tests. Using Monte Carlo simulations, we deal with two specific difficulties that arise when fitting functions to psychophysical data. First, we note that human observers are prone to stimulus-independent errors (or lapses). We show that failure to account for this can lead to serious biases in estimates of the psychometric function's parameters and illustrate how the problem may be overcome. Second, we note that psychophysical data sets are usually rather small by the standards required by most of the commonly applied statistical tests. We demonstrate the potential errors of applying traditional chi2 methods to psychophysical data and advocate use of Monte Carlo resampling techniques that do not rely on asymptotic theory. We have made available the software to implement our methods.

Klein, A. Psychometric function

Percept Psychophys. 2001 Nov;63(8):1421-55.

Measuring, estimating, and understanding the psychometric function: a commentary.

Klein SA.

School of Optometry, University of California, Berkeley 94720-2020, USA.

The psychometric function, relating the subject's response to the physical stimulus, is fundamental to psychophysics. This paper examines various psychometric function topics, many inspired by this special symposium issue of Perception & Psychophysics: What are the relative merits of objective yes/no versus forced choice tasks (including threshold variance)? What are the relative merits of adaptive versus constant stimuli methods? What are the relative merits of likelihood versus up-down staircase adaptive methods? Is 2AFC free of substantial bias? Is there no efficient adaptive method for objective yes/no tasks? Should adaptive methods aim for 90% correct? Can adding more responses to forced choice and objective yes/no tasks reduce the threshold variance? What is the best way to deal with lapses? How is the Weibull function intimately related to the d' function? What causes bias in the likelihood goodness-of-fit? What causes bias in slope estimates from adaptive methods? How good are nonparametric methods for estimating psychometric function parameters? Of what value is the psychometric function slope? How are various psychometric functions related to each other? The resolution of many of these issues is surprising.