Closed ricardoV94 closed 4 years ago
Hey @ricardoV94,
yes, this is an issue I've been investigating since some time, as I've seen and had conflicting feedback about that formula. Unfortunately, Hautus' paper isn't crystal clear regarding it. But indeed I agree with your conclusion (thanks for the thorough investigation!), I'll update that formula soon :)
This has been fixed in the latest version ☺️
https://github.com/neuropsychology/psycho.R/blob/611e984742890e698c4e94b6965d917432e98348/R/dprime.R#L77-L79
This potential issue has been raised before here: https://github.com/neuropsychology/neuropsychology.R/issues/10
I think the correct formula is:
The confusion, I think, comes from the wording of the referenced paper (Hautus, 1995, link):
What I think the author meant is that if you are using the row or column totals in your formula, then 1 should be add to those (and not in addition to the 0.5 to each cell)
hit_rate_adjusted <- (n_hit + 0.5)/(n_signal_trials + 1)
This I think would be the formula implied by (Stanislaw & Todorov, 1999, link):
I tracked down the first reference by Hautus, (Fienberg, 1980, p.64):
Note that they don't mention an extra 1 should be added (this is a mere consequence of adding .5 + .5 to the two cells in a row or column.
I am not totally confident of my interpretation, but I could not find a convincing source for the formula used in the library either...