Variations of the triangular method and the relationship of its unidimensional probabilistic models to three‐alternative forced‐choice signal detection theory models

Frijters, J.E.R.

doi:10.1111/j.2044-8317.1979.tb00595.x

Cited by 67 publications

(41 citation statements)

References 8 publications

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“…It can be shown that Equation 30 is identical to the one obtained by Bradley (1963) and Frijters (1979b).…”

Section: Highly Correlated Observations; £2 =0supporting

confidence: 62%

“…Thus, it is argued that a good decision procedure is to select the vertex most distant from the other two. Bradley (1963) and Frijters (1979b) have presented an analysis of this task based on that decision rule. Frijters, Kooistra, and Vereijken (1980) have published tables on d' as a function of the percentage of correct responses for the three-alternative oddity task.…”

Section: Three-interval Oddity Paradigmmentioning

confidence: 99%

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The optimum decision rules for the oddity task

Versfeld¹,

Dai

Green

1996

Perception & Psychophysics

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This paper presents the optimum decision rule for an m-interval oddity task in which m -1 intervals contain the same signal and one is different or odd. The optimum decision rule depends on the degree of correlation among observations. The present approach unifies the different strategies that occur with "roved" or "fixed" experiments (Macmillan & Creelman, 1991, p. 147). It is shown that the commonly used decision rule for an m-interval oddity task corresponds to the special case of highly correlated observations. However, as is also true for the same-different paradigm, there exists a different optimum decision rule when the observations are independent. The relation between the probability of a correct response and d' is derived for the three-interval oddity task. Tables are presented of this relation for the three-, four-, and five-interval oddity task. Finally, an experimental method is proposed that allows one to determine the decision rule used by the observer in an oddity experiment.The oddity task provides a means of measuring the observer's ability to discriminate between different stimuli.In the most general form, m stimuli are presented on each trial and there are m response alternatives. Despite the number ofresponse alternatives, there are actually only two stimuli. On any single trial, m -1 ofthe stimuli are the same; only one stimulus is different, the odd stimulus. The observer's task is to select the alternative with the odd stimulus. A frequent argument given for the use of this procedure is that it does not force the observer to distinguish between the two stimuli on some predetermined sensory dimension; rather, it offers the observer the freedom to make the distinction on whatever basis is most convenient. Therefore, when the stimuli are complex-as is often the case in, for example, food research-the oddity task is frequently used to assess the subject's ability to discriminate between different food alternatives.Forced-choice paradigms differ in the degree and extent to which the specific stimulus alternatives must be labeled or categorized. Without prior knowledge of the stimulus alternatives, it is often difficult to label the stimuli without considerable practice and training. It may even be impossible if the stimuli are not fixed, but vary over trials. To take a concrete example, suppose the task is to select from a pair of sinusoids the one with the higher pitch. One sound has frequency I: S], whereas the other sound has frequency j+ Sf. Let us calljthe standard frequency. In a one-interval, forced-choice paradigm, a single sinusoid isThe authors gratefully acknowledge Todd Maddox, Sandy MacRae, and an anonymous reviewer for their valuable comments, and for their suggestions for improving the readability of the manuscript. Correspondence should be addressed to N. 1. Versfeld, TNO

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“…It can be shown that Equation 30 is identical to the one obtained by Bradley (1963) and Frijters (1979b).…”

Section: Highly Correlated Observations; £2 =0supporting

confidence: 62%

Section: Three-interval Oddity Paradigmmentioning

confidence: 99%

The optimum decision rules for the oddity task

Versfeld¹,

Dai

Green

1996

Perception & Psychophysics

View full text Add to dashboard Cite

show abstract

“…The present experiment deals with these four models, and since they were extensively described in Frijters (1979), only a brief summary of their theory is given here, after which the aims of the experiment are described.…”

mentioning

confidence: 99%

“…In a recent paper (Frijters, 1979), one of these triangular method models was called the Thurstone-Ura model, and it was compared theoretically to a similar distance model for the 3-AFC procedure, called the normal 3-AFC SOT model. In the same paper, the logistic variants of these models were developed and compared with each other.…”

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confidence: 99%

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Three-stimulus procedures in olfactory psychophysics: An experimental comparison of Thurstone-Ura and three-alternative forced-choice models of signal detection theory

Frijters

1980

Perception & Psychophysics

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The experimental differences between the triangular method and three-alternative forcedchoice(3-AFC) signal detection theory procedure are briefly reviewed, and the conditions to be met for a valid application of the respective procedures under the Thurstone-Ura and 3-AFC models are described. The assumptions of both of these unidimensional probabilistic models are given, and the functions relating the probability of a correct response to 0, a parameter of sensory stimulus distance, are specified. Since the two models both contain 0, the hypothesis of invariability of this parameter with the triangular method and the 3·AFC procedure was tested using olfactory stimuli. This hypothesis was strongly confirmed, since the functions relating 0 to the logarithm of the ratio of the physical stimulus values were virtually identical for the two methods and their concomitant models. The results are important not only for the field of olfactory psychophysics; they also have Wider methodological and psychophysical interest. The bias against the middle stimulus of a triangle in the triangular method observed when olfactory stimuli are used can be explained as the resultant of sensory adaptation. Finally, some practical implications of the present results for application of the triangular method are discussed.

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Statistical Power Analysis for Standard Discrimination Tesst

Bi¹

2005

Sensory Discrimination Tests and Measurements

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Variations of the triangular method and the relationship of its unidimensional probabilistic models to three‐alternative forced‐choice signal detection theory models

Cited by 67 publications

References 8 publications

The optimum decision rules for the oddity task

The optimum decision rules for the oddity task

Three-stimulus procedures in olfactory psychophysics: An experimental comparison of Thurstone-Ura and three-alternative forced-choice models of signal detection theory

Statistical Power Analysis for Standard Discrimination Tesst

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