The difference model with guessing explains interval bias in two-alternative forced- chocice detection procedures

The standard difference model of two-alternative forced-choice (2AFC) tasks implies that performance should be the same when the target is presented in the first or the second interval. Empirical data often show “interval bias” in that percentage correct differs significantly when the signal is presented in the first or the second interval. We present an extension of the standard difference model that accounts for interval bias by incorporating an indifference zone around the null value of the decision variable. Analytical predictions are derived which reveal how interval bias may occur when data generated by the guessing model are analyzed as prescribed by the standard difference model. Parameter estimation methods and goodness-of-fit testing approaches for the guessing model are also developed and presented. A simulation study is included whose results show that the parameters of the guessing model can be estimated accurately. Finally, the guessing model is tested empirically in a 2AFC detection procedure in which guesses were explicitly recorded. The results support the guessing model and indicate that interval bias is not observed when guesses are separated out.

Interval bias in 2AFC detection tasks: sorting out the artifacts

Proportion correct in two-alternative forcedchoice (2AFC) detection tasks often varies when the stimulus is presented in the first or in the second interval.Reanalysis of published data reveals that these order effects (or interval bias) are strong and prevalent, refuting the standard difference model of signal detection theory. Order effects are commonly regarded as evidence that observers use an off-center criterion under the difference model with bias. We consider an alternative difference model with indecision whereby observers are occasionally undecided and guess with some bias toward one of the response options. Whether or not the data show order effects, the two models fit 2AFC data indistinguishably, but they yield meaningfully different estimates of sensory parameters. Under indeterminacy as to which model governs 2AFC performance, parameter estimates are suspect and potentially misleading. The indeterminacy can be circumvented by modifying the response format so that observers can express indecision when needed. Reanalysis of published data collected in this way lends support to the indecision model. We illustrate alternative approaches to fitting psychometric functions under the indecision model and discuss designs for 2AFC experiments that improve the accuracy of parameter estimates, whether or not order effects are apparent in the data.

A model for the time-order error in contrast discrimination.

Trials in a temporal two-interval forced-choice discrimination experiment consist of two sequential intervals presenting stimuli that differ from one another as to magnitude along some continuum. The observer must report in which interval the stimulus had a larger magnitude. The standard difference model from signal detection theory analyses poses that order of presentation should not affect the results of the comparison, something known as the balance condition (J.-C. Falmagne, 1985, in Elements of Psychophysical Theory). But empirical data prove otherwise and consistently reveal what Fechner (1860/1966, in Elements of Psychophysics) called time-order errors, whereby the magnitude of the stimulus presented in one of the intervals is systematically underestimated relative to the other. Here we discuss sensory factors (temporary desensitization) and procedural glitches (short interstimulus or intertrial intervals and response bias) that might explain the time-order error, and we derive a formal model indicating how these factors make observed performance vary with presentation order despite a single underlying mechanism. Experimental results are also presented illustrating the conventional failure of the balance condition and testing the hypothesis that time-order errors result from contamination by the factors included in the model.