Perception demos

Let your answers choose: adaptive methods on the Müller-Lyer illusion

The three classical methods fix the plan before the first trial: constant stimuli spent 70 displays on seven lengths, many of them far from where your judgment tips over. Adaptive methods let your answers choose the next display, so most trials land where they are informative. Measure your Müller-Lyer illusion again with three of them, and look at the track each one leaves behind.

Levitt, H. (1971). Transformed up-down methods in psychoacoustics. Journal of the Acoustical Society of America, 49, 467–477. · Watson, A. B., & Pelli, D. G. (1983). QUEST: A Bayesian adaptive psychometric method. Perception & Psychophysics, 33, 113–120.

Or watch a simulated observer. You set the truth, then see whether each method finds it.

The simulated observer answers "longer" with the probability given by a logistic psychometric function; on a lapse it answers at random. Run a method several times: the estimate changes from run to run, although the observer does not. Then set the lapse rate to 20 % and watch the tracks, the gap between the two transformed tracks, and the slope of the fitted function. Switching this box clears the results.

How it works. The display and the question are the same as in the classical-methods demo; only the rule that picks the next length differs. "Down" means the plain line gets shorter.
  • Simple staircase (1-up/1-down): after "longer" the plain line gets shorter, after "shorter" it gets longer. The track walks to the length where both answers are equally likely and oscillates there. A change of direction is a reversal; the estimate is the mean of the last six of eight reversals. Steps are 4 % until the second reversal, then 2 %. Two tracks, one starting too long and one too short, are interleaved at random.
  • Transformed staircase (Levitt, 1971): the 1-up/2-down track steps down only after two "longer" answers in a row, so it settles where "longer" is given on 70.7 % of displays (p² = .5). Its mirror image, 2-up/1-down, settles at 29.3 %. In a task with right and wrong answers, such as detection in 2AFC, 1-up/2-down is the standard rule, because the 50 % point there is pure guessing.
  • QUEST (Watson & Pelli, 1983): no steps at all. It assumes the shape of your psychometric function (a fixed slope and lapse rate), keeps a probability distribution over the one unknown, the PSE, and updates it with Bayes' rule after every answer. Each display is placed at the current best guess.
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