when your h = 0 and f = 1

Interesting and useful fact of the week:

If you’re using d′ as a measure of discrimination sensitivity, and if you have small numbers of trials from which to calculate proportions of hits and false alarms, you are likely to end up trying to get z-transformations of 0 or 1, which means that d‘ is undefined.

There is however a range of conventions for how to deal with this.

Wickens (2001) says a value can arbitrarily be assigned to the otherwise empty category, eg, for f, a value corresponding to 1/(N+1), or 1/(2N+1), or 1/(10N+1) can be assigned, where N = number of noise trials.

This chap says, for proportions of 0 use instead 1/N and for proportions of 1 use (N-1)/N, where N is the number of trials used in calculating the proportions.

Macmillan and Creelman make two suggestions. One is to convert proportions of 0 to 1/(2N), and proportions of 1 to 1-1/(2N), where N is the number of proportions used in the calculation. The other is to add 0.5 to all data cells regardless of whether there are zeroes present.

Most usefully of all, this information can all be found online, in Google Books in the case of Wickens and Macmillan and Creelman. Although thanks to the prodigious – the triumphant – efficiency of the note-taking skills of one of my officemates, we didn’t even need to resort to googling in order to have the information at our fingertips. It’s very satisfying when that happens.