What is the best way of testing the differences between two psychometric functions?
One way is to use a bootstrap method, as implemented in psignifit, to get error bars on the threshold and slope for each of the two conditions, and then to make an informal judgment based on whether the error-bars overlap. Perhaps a more satisfying way would be to do Monte Carlo simulation of the distribution of threshold and slope differences, and to test simultaneously the observed differences in threshold and in slope, based on a null-hypothesis that the two data sets in fact came from the same underlying psychometric function. I have put together, in a provisional sort of way, the Matlab m-files that I use for this process, an released it under the name pfcmp. The pfcmp release runs (in theory) on Matlab 5.2 and up, and requires the psignifit toolbox to be installed already. It can be downloaded from the download page. This approach circumvents many of the problems associated with bootstrap methods (it is not actually a bootstrap, but rather a direct Monte Carlo test of a given nul
