Mathematical tools for the design and accurate reporting of transformed up-and-down staircases (L)

A surprising number of citations of studies on psychophysical methods come from journals in which the topics do not include psychophysics. Powerful tools have been developed by statisticians to support experimental methods originally borrowed from psychophysics, some of which predate the simplistic and misleading analyses that are commonly cited. This Letter adapts selected results from the mathematical foundations of transformed staircases. Two key results are presented, a more accurate definition of the targeted probability of response and a method to calculate the distribution of signal levels presented-sequentially and asymptotically-that will support advancements in data collection, analysis, and interpretation.