Mj. Hautus, CORRECTIONS FOR EXTREME PROPORTIONS AND THEIR BIASING EFFECTS ON ESTIMATED VALUES OF D', Behavior research methods, instruments, & computers, 27(1), 1995, pp. 46-51
Estimating d' from extreme false-alarm or hit proportions (p = 0 or p
= 1) requires the use of a correction, because the z score of such pro
portions takes on infinite values. Two commonly used corrections are c
ompared by using Monte-Carlo simulations. The first is the 1/(2N) rule
for which an extreme proportion is corrected by this factor before d'
is calculated. The second is the log-linear rule for which each cell
frequency in the contingency table is increased by 0.5 irrespective of
the contents of each cell. Results showed that the log-linear rule re
sulted in less biased estimates of d' that always underestimated popul
ation d'. The 1/(2N) rule, apart from being more biased, could either
over- or underestimate population d'.