Consider a psychophysics procedure using a standard staircase method to adaptively find the threshold, using a 2AFC paradigm and a 1-up, 3-down method to determine the 75% threshold. Now suppose the use of steps that are unequal in size. I am not referring to decreasing the step size after a certain amount of reversals as described by Levitt (1971), but to the use of unequal step sizes. So for example suppose that the available steps are 0.5 - 0.5 - 0.5 - 1 - 1.5 - 0.5 - 2.5 - 2. So this would translate to a discrete set of available stimulus levels of: 0 - 0.5 - 1 - 1.5 - 2.5 - 4 - 4.5 - 7 - 9. Since step size can be used to alter the correct rate at which the staircase procedure converges (e.g., 50%, 75% etc.) Kaernbach (1991), I was wondering what my proposed stimulus-level distribution would mean for the threshold definition of a 1-up 3-down procedure intended to converge onto a 75% threshold?
It is going to mean bad things. If you can only create stimuli with a predefined non uniformly sampled set of "levels" then the the corresponding percent correct that the staircase will track will depend on the threshold of an individual observer. For example, if you can create stimuli with levels of 0, 1, 2, 3, ..., 100, 110, 130, 170, 250, 410, where for small levels the up and down step sizes are equal, but for large levels the up step size is twice the down step size. This means the percent correct point is going to be different depending on the threshold of the subject. You wouldn't have to worry about it if you use something like the method of constant stimuli.