Staircase 2AFC

A stimulus is presented one of two randomly selected intervals. The intervals may be different places in space and presented simultaneously (spatial forced choice) or in the same place in space but at two different times. After both intervals have been presented, the observer must indicate whether the stimulus was present in the first interval or the second interval. The magnitude of the stimulus may or may not be modified for the next presentation.


Certain criteria or rules can be used to estimate different probabilities of a correct response. The desired probability of a correct response may be defined as the variable level at which an observer responds correctly 50%, 79% or any other level. If the stimulus level is decreased after every 3 correct responses in a row and the stimulus level is increased after every 1 incorrect response, then stimulus level will approach the point at which the observer is 79% correct.

Some common rules and threshold definitions are listed below.

Common Rules and Thresholds
Number of
Correct Responses
Number of
Incorrect responses
Estimated probability
of correct response

The estimated threshold probability can be calculated in the following way. If the probability of the observer being correct, p(T), is 50%, then the probability of being correct three times is p(T)*p(T)*p(T). At 50% threshold, an observer produces response patterns which result in a decrease as often as he/she produces responses patterns which result in an increase. As a result p(T)*p(T)*p(T) = .5 = p(F). So p(T) = (.5)^(1/3) = .79370053.

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© 1995 Lance Hahn (