What is the difference between .x and .xStaircase?

[Matt J Dunn]

In PAL_AMUD (staircase procedure), there is a field .x and another .xStaircase. What is the difference between these two fields? They seem to be identical most (if not all) of the time, so is it safe to use the values from either when constructing a psychometric function?

[Nick Prins]

With default settings, .x and .xStaircase will be the same. However, when the possible values to be used for stimulus values are limited using 'xMin' and/or 'xMax' options and the 'truncate' option is set to 'no', the up/down procedure will act in accordance with a suggestion made in: Garcia-Perez, M.A. (1998). Vision Research, 38, 1861-1881. It gets a little tricky, perhaps best explained by example. Let's say you set 'xMin' to 0 and 'truncate' to 'no'. In that case .x and .xStaircase will be identical unless and until the up/down rules would suggest a negative value (say -1). At that point .x and .xCurrent will be set to 0 (as limited by 'xMin') but .xStaircase is not truncated by 'xMin' and will be set to -1. The stimulus should be presented at .xCurrent (i.e., at 0) but the next step (be it up or down) will be made relative to the value in .xStaircase (i.e., -1). But when 'truncate' is set to 'yes' (and 'xMin' is still set to 0), .x, .xCurrent, and .xStaircase will all be truncated at 0. Next step will again be made relative to value in .xStaircase.

When fitting data after the fact with a psychometric function, you should always use the stimulus intensities that were actually used (i.e., .x), not those in .xStaircase.