I am trying to compute the non parametric measure of sensitivity A' according to the following formula reported by Stanislav & Todorov (1999):

$$ A'= .5+sign(H-F)*((H-F)^2+abs(H-F))/(4*max(H,F)-4*H*F) $$

where H is Hit Rate and F is False Alarm Rate. A' is an index thought to approximate the area under the ROC curve in task with no confidence intervals. Among the perks of this index is that, differently from $d'$, it does not jump to infinite when Hit rate (or False Alarm) is 1 (or to -Infinite when 0). Nevertheless, in a scenario of a really confused observer providing positive answer to all trials, you will end up having 100% of Hit Rate AND 100% False Alarm Rate. In this case, $A'=.5+0/0$, hence indeterminate. Same happening for 0% Hit Rate and False Alarm Rate.

Is there any correction to be applied in this really extreme cases?



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