#### Keywords

Signal detection theory, Sensitivity, Response bias

#### Abstract

Signal detection theory has been well accepted in vision science to measure human sensitivity to stimuli in a Psychophysical experiment. The theory is formulated so that the measured sensitivity is independent from a response bias (criterion). The formulation is based on an assumption that number of trials in the experiment is infinite but this assumption cannot be satisfied in practice. The assumption came from two normal distributions used in the formulation. The distributions respectively represent a set of signal trial and that of noise trials in the experiment. In this study, I will show how the violation of the assumption affects results in a signal detection experiment testing some sensitivity and a way to derive a likelihood function of the sensitivity based on measured sensitivity and criterion. The likelihood function allows us to use results of the signal detection experiment efficiently for Bayesian inference. I will also discuss how the criterion affects the results of the experiment under the violation of the assumption.

#### Start Date

14-5-2015 5:15 PM

#### End Date

14-5-2015 5:40 PM

#### Session Number

04

#### Session Title

Theory

#### Included in

Cognition and Perception Commons, Cognitive Psychology Commons, Experimental Analysis of Behavior Commons, Quantitative Psychology Commons

A signal detection experiment with limited number of trials

Signal detection theory has been well accepted in vision science to measure human sensitivity to stimuli in a Psychophysical experiment. The theory is formulated so that the measured sensitivity is independent from a response bias (criterion). The formulation is based on an assumption that number of trials in the experiment is infinite but this assumption cannot be satisfied in practice. The assumption came from two normal distributions used in the formulation. The distributions respectively represent a set of signal trial and that of noise trials in the experiment. In this study, I will show how the violation of the assumption affects results in a signal detection experiment testing some sensitivity and a way to derive a likelihood function of the sensitivity based on measured sensitivity and criterion. The likelihood function allows us to use results of the signal detection experiment efficiently for Bayesian inference. I will also discuss how the criterion affects the results of the experiment under the violation of the assumption.