One of the great contributions of psychophysics to psychology is the
notion of measuring threshold, i.e. the signal strength required for a
criterion level of response by the observer (Pelli & Farell, 1994;
Farell & Pelli, 1999). Watson and Pelli (1983) described a maximum
likelihood procedure, which they called QUEST, for estimating threshold.
The Quest toolbox in the Psychtoolbox is a set of MATLAB functions
that implement all the original QUEST functions, plus several others.
You can think of it as a Bayesian toolbox for testing observers and
estimating their thresholds. This QUEST toolbox is self-contained,
and runs on any computer with MATLAB 5 or better.
By commenting and uncommenting five lines below, you can use this file
to implement three QUEST-related procedures for measuring threshold.
QuestMode: In the original algorithm of Watson & Pelli (1983), each
trial is at the MODE of the posterior pdf. Their final estimate is
maximum likelihood, which is the MODE of the posterior pdf after
dividing out the prior pdf. (Subsequent experience has shown that it’s
better not to divide out the prior, simply using MODE of posterior pdf
QuestMean: In the improved algorithm of King-Smith et al. (1994), each
trial and the final estimate are at the MEAN of the posterior pdf.
You begin by calling QuestCreate, telling Quest what is your prior
knowledge, i.e. a guess and associated sd for threshold. Then you run
some number of trials, typically 40. For each trial you ask Quest to
recommend a test intensity. Then you actually test the observer at some
intensity, not necessarily what Quest recommended, and then you call
QuestUpdate to report to Quest the actual intensity used and whether the
observer got it right. Quest saves this information in your Quest struct,
which we usually call “q”. This cycle is repeated for each trial. Finally,
at the end, when you’re done, you ask Quest to provide a final threshold
estimate, usually the mean and sd (of the posterior pdf).
It is important to realize that Quest is merely a friendly adviser,
cataloging your data in your q structure, and making statistical
analyses of it, but never giving you orders. You’re still in charge. On
each trial, you ask Quest (by calling QuestMode, or QuestMean, or
QuestQuantile)) to suggest the best intensity for the next trial. Taking
that as advice, in your experiment you should then select the intensity
yourself for the next trial, taking into account the limitations of your
equipment and experiment. Typically you’ll impose a maximum and a
minimum, but your equipment may also restrict you to particular discrete
values, and you might have some reason for not repeating a value.
Typically you’ll choose the available intensity closest to what Quest
recommended. In some cases the process of producing the stimulus is so
involved that the exact stimulus intensity is known only after it’s been
shown. Having run the trial, you then report the new datum,
the actual intensity tested and the observer’s response, asking Quest to
add it to the database in q.
To use Quest you must provide an estimated value for beta. Beta
controls the steepness of the Weibull function. Many vision studies use
Michelson contrast to control the visibility of the stimulus. It turns
out that psychometric functions for 2afc detection as a function of
contrast have a beta of roughly 3 for a remarkably wide range of targets
and conditions (Nachmias, 1981). However, you may want to estimate beta
for the particular conditions of your experiment. QuestBetaAnalysis is
provided for that purpose, but please think of it as a limited optional
feature. It allows only two free parameters, threshold and beta. You may
prefer to use a general-purpose maximum likelihood fitting program to
allow more degrees of freedom in fitting a Weibull function to your
psychometric data. However, once you’ve done that it’s likely that
you’ll settle on fixed values for all but threshold and use Quest to
Note that data collected to estimate threshold usually are not
good for estimating beta. The psychometric function is sigmoidal, with a
flat floor, a rise, and a flat ceiling. To estimate threshold you want
all your trials near the steepest (roughly speaking) part of the rise.
To estimate beta, the steepness of the rise, you want to have most of
your trials at the corners, where the rise begins and where it ends. The
usual way to achieve this is to first estimate threshold and then to
collect a large number of trials (e.g. 100) at each of several
intensities chosen to span the domain of the rise. These data can
be plotted, making a nice graph of the psychometric function and
they can be fed to QuestBetaAnalysis, to estimate threshold and beta.
Farell, B., & Pelli, D. G. (1999). Psychophysical methods, or how to
measure threshold, and why. In J. G. Robson & R. H. S. Carpenter (Eds.),
A Practical Guide to Vision Research (pp. 129-136). New York: Oxford
King-Smith, P. E., Grigsby, S. S., Vingrys, A. J., Benes, S. C., and
Supowit, A. (1994) Efficient and unbiased modifications of the QUEST
threshold method: theory, simulations, experimental evaluation and
practical implementation. Vision Res, 34 (7), 885-912.
Nachmias, J. (1981). On the psychometric function for contrast detection.
Vision Res, 21(2), 215-223.
Pelli, D. G. (1987) The ideal psychometric procedure. Investigative
Ophthalmology & Visual Science, 28 (Suppl), 366.
Pelli, D. G., & Farell, B. (1994). Psychophysical methods. In M. Bass,
E. W. Van Stryland, D. R. Williams & W. L. Wolfe (Eds.), Handbook of
Optics, 2nd ed. (Vol. I, pp. 29.21-29.13). New York: McGraw-Hill.
Watson, A. B. and Pelli, D. G. (1983) QUEST: a Bayesian adaptive
psychometric method. Percept Psychophys, 33 (2), 113-20.
All the papers of which I’m an author can be downloaded as PDF files
from my web site:
Try “help Quest”.