27 Apr 2014

Levitt (1971) ‘Transformed up‐down methods in psychoacoustics’, notes

Corry Shores
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H. Levitt

Transformed up‐down methods in psychoacoustics

Brief summary:

The authors discuss methods for doing psychoacoustic experiments in which the subject’s responses determine the course of the experiment. For our purposes, we focused on the step-procedure. Here, a positive response means reducing the stimuli by a step, and a negative response means stepping the stimuli up. Then, it seems a middle point can be determined mathematically. [In the case of Weichselgartner & Sperling (1985), the subject needs to indicate when the brightness of a steady stimuli matches with a stimuli whose brightness is varying. If the subject just pushes a button, there is the problem of response times and variations they might introduce (one time being quicker, another especially slow). So instead, after the stimuli finish, the subject says whether the click comes before or after the perceived match in visual stimuli. If says comes after, then move the click back a step. If before, then move forward. Then, with all this data, it is then calculated when in fact they do perceive it as matching, the X50 value of the psychometric curve.]




A. Adaptive Procedures in Psychophysics

An adaptive procedure is one in which the stimulus level on any one trial is determined by the preceding stimuli and response. [467]

Up-down methods are a type of sequential experiment, which is one where the course of the experiment is determined by experimental data. There are two types: (a) ones where the number of observations is determined by the data and (b) ones where the choice of stimulus levels is determined by the data. [467A]

B. The Psychometric Function


Look at fig 1a. The abscissa is the stimulus level. The ordinate is the proportion of ‘positive’ responses. A positive response might for example be the report from the subject that ‘the signal is present’.

[Please see the article to obtain a correct interpretation of its contents. For our purposes, I think we can derive what we need from figure 4 below. It seems if the response is positive, then the next trial takes the stimulus down a step. If the response is negative, then it steps up. Perhaps over time this approximates where the match would be. In the case of the Weichselgartner & Sperling (1985) experiment, this would mean that they use this step procedure to estimate when the subject senses the match between the steady reference stimuli and the varying test stimuli. The problem with having the subject just press the button when they sense the match could be the response time and the inaccuracies and variances it can introduce. But in this step method, the subjects chose the option (‘before,’ ‘after’) after the stimuli are all done. So there is not a response delay involved. ]


Levitt, H. "Transformed Up‐Down Methods in Psychoacoustics." The Journal of the Acoustical Society of America 49 (1971): 467-477.



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