# The object-oriented approach to staircases in Matlab

When I was first learning to program it took me a long time to appreciate why object-oriented approaches would be useful. I found a great example recently though, when I decided to write a generic "staircase" method to use in my psychophysical experiments. I find staircases to be the most efficient data collection method to use for most experiments (they are even as good as the* considerably more complex* entropy-minimising Bayesian methods such as qCRF, a topic which I will address in the near future). The code is at the bottom of this post, so skip the next two paragraphs if you already know what a staircase is etc.

The staircase method was first used by Dixon and Mood (1948) to study the volatility of explosives. Since then it has found a wide use within many fields, including psychophysics. Staircase methods involve determining the next stimulus level to be tested by reacting to the results of previous trials. In the simplest case of a one-up one-down staircase, a correct response on the previous trial results in the next trial being tested with a lower stimulus magnitude (i.e. making the task more difficult) while an incorrect response results in the next trial being tested with a higher stimulus magnitude. As the staircase then overshoots the point at which the behaviour changes it will reverse direction again, eventually oscillating around a value of interest. For example, a one-up one-down staircase will tend to sample at stimulus magnitudes where the probability of a positive response is approximately 0.5 (staircases of this type are typically used for matching experiments where the point of subjective equality is the value to be determined). It possible therefore to use the average of the staircase reversals to calculate an estimate of the stimulus magnitude that gives that response probability. Personally though I prefer to fit the data with a psychometric function.

For a two-alternative forced choice study (where you have a 50% guess rate, and so want to sample around 75%) a good choice is a three-down one-up staircases, which aims to converge at P (correct) = 0.794 (Wetherill, 1963; Wetherill & Levitt, 1965). Simulations have shown that the staircase may fail to reach this value (García-Pérez, 1998), however as I always end up fitting psychometric functions anyway the actual value that the staircases converge at is not critical.

You can push the button below to show the staircase class code I have (so far). The advantage of using a class to manage your staircases is that they look after themselves. You set them up with the rules you want them to follow (number of right or wrong answers for a reversal, etc.) and then they will tell you what stimulus to use on each trial, and you can tell them how the observer responded. At the end you query the staircase object to find out how many times each level was tested and how many of those the observer got right. *Particularly* useful is that you can define an array of staircase objects in Matlab, so you would be able to have SC(1), SC(2), SC(3)* etc. all with their own private rules. At the moment I am experimenting with interleaving staircases that have different up/down rules to sample different points on the psychometric function (and so better constrain the measured psychometric slope).

The code is perfectly functional at the moment, though I do not doubt it could do with improvements. For example, I don't think it's actually necessary for me to use a Matlab "handle" class here. Have fun with it and let me know what you think in the comments.

References:

Dixon, W. J., Mood, A. M., 1948. A Method for Obtaining and Analyzing Sensitivity Data. Journal of the American Statistical Association 43 (241), 109–126.

García-Pérez, M. A., 1998. Forced-choice staircases with fixed step sizes: asymptotic and small-sample properties. Vision Research 38, 1861–1881.

Wetherill, G. B., 1963. Sequential Estimation of Quantal Response Curves. Journal of the Royal Statistical Society. Series B (Methodological) 25 (1), 1–48.

Wetherill, G. B., Levitt, H., 1965. Sequential estimation of points on a psychometric function. The British Journal of Mathematical and Statistical Psychology 18 (1), 1–10.

* You can collapse across multiple objects in Matlab by using the square bracket notation, for example the statement below will return 1 only if all the SC(1) to SC(n) staircases are finished.

all([SC.isFinished])