I wish to apply SDT for an experiment whereby, while listening to a piece of music, subjects were asked to press a key when detecting a certain cue in the music. Based on the parts of the piece where the cue was actually present, it was simple enough to define each keypress as either a hit (filled dot) or as a false alarm (empty dot):
However, less clear is how to get to the hit- and false-alarm rates (HR, FAR) of each subject, since these imply dividing the total number of hits/false alarms by the total number of "signal present" and "signal absent" trials respectively.
The problem would be easier if the music (or: the time series of the keypresses) were discretised in time, but since it is continuous, my questions are:
1) For the FAR, since the number of "signal absent" trials is difficult to define (it's all the moments where a cue is NOT present in the music!), does it make sense to - as an approximation/compromise - divide instead by the total number of keypresses employed by the subject?
2) For the HR, is it correct to divide by the total number of cues that exist in the piece, since these are indeed all of the "signal present" moments in the timeseries?
3) As an even more non-orthodox SDT adaptation, does it make any sense to define both HR and FAR by diving by the same quantity, namely total number of keypresses?