# A generalized Gaussian SPRT model for two alternative forced -choice tasks

#### Abstract

Signal detection theory (SDT) is a “static” model and perhaps for this reason has difficulty with the results of recent work by Balakrishnan (1998). Random walk models are “dynamic” and more powerful in many respects than signal detection theory. However, while SDT's prediction that the decision rule will be biased under the unequal base rate situation has been shown to be fundamentally wrong, this model can easily predict the findings that observers will adopt a suboptimal decision rule when the base rate of two signals are unequal. The question is whether the dynamic models can predict unbiased and suboptimal decision rules, while maintaining their ability to account for other known properties of human discrimination. However, since this issue has never been explicitly addressed by theorists, it is not clear what properties of these models needed to be adjusted. An even more serious disadvantage of previous studies of random walk models is their dependence on the ‘small steps’ assumption. This thesis developed and investigated a random walk model, called a generalized Gaussian SPRT model that made the correct predictions about the decision rules without introducing the small step assumption. ^ The work involves three types of analyses: mathematical proof, experimental tests and simulations. The mathematical proofs include four theorems. ^ The first theorem shows that when a bound moves toward zero direction with the other bound unchanged, the choice probabilities associated with the bound will increase while the choice probabilities associated with the other bound will decrease. Theorem 2 shows that the generalized Gaussian SPRT model predicts an unbiased decision rule. A direct result from theorem 2 is that when the base rates are unequal, the model predicts observers do not use an optimal decision rule. Theorem 3 shows that the model predicts that percentage of correct response is increasing with confidence level. The last theorem discusses how the drift rate influences the difference between the two cumulative distribution functions F(R_{k}:S_{A}) and F(R_{k}:S_{ B}), where F(R_{k}:S_{A}) and F(R_{k}:S_{ B}) are cumulative distribution functions of response given stimulus S_{A} and stimulus S_{B}, respectively. ^ An experiment and a simulation study were conducted to test the theories. The data from both the experiment and simulation support the predictions made by the theorems. ^

#### Degree

Ph.D.

#### Advisors

Major Professor: J. D. Balakrishnan, Purdue University.

#### Subject Area

Psychology, Psychometrics|Psychology, Cognitive

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