[visionlist] How to compute d' when hit rate or false alarm rate is 0 or 1?

vitdrga at psychophysics.org vitdrga at psychophysics.org
Thu Aug 16 18:03:53 GMT 2007

[following up a thread from June 3rd....]

There is no single best solution.

The expected dprime and standard error are affected by:
the observer's underlying sensitivity,
the observer's criterion, 
the sample size (number of trials run),
the adjustment rule used by the experimenter.
As it happens, there are complicated interactions among these factors.

Below is a list of some adjustment rules that have been used 
and papers on the topic. Many of these paper used Monte Carlo 
simulations to help get a handle on what's going on. 
You might be able to match some of the Monte Carlo parameters 
to your own situation to see what tradeoffs there many be 
with the other factors involved.

Good luck,


Some rules that have been used are:

-- Adjust only cumulative tallies of 0 and N in the contingency table 
by some arbitrary adjustment value, k < 1.0, 
to obtain 0+k and N-k instead of 0 and N,
then divide by N as usual to get cumulative proportions.
This approach is equivalent to setting a maximum absolute dprime value. 
Adjustment values that people have tried have include 0.5,  1/(2N),  and 0.0001.

-- Pool adjacent rating categories (if using an ordinal rating scale 
with m>2 categories)

-- Ignore data when the extremes occur, 
i.e. analyse only data that produce finite dprime values

-- Adjust all contingency table tallies by adding 0.5 to the tallies 
and divide all cumulative tallies by N+1  ( = a log-linear adjustment).
The first rule given above only adjusts at the ends of a rating scale.
This rule adjusts all entries.


Hautus (1995)
"Corrections for extreme proportions and their
biasing effects on estimated values of d' "
Behavior Research Methods, Instruments, & Computers, 
vol 27 (1), pp. 46-51.

Miller (1996)
"The sampling distribution of d' "
Perception & Psychophysics, vol 58 (1), pp. 65-72.

Simpson et al. (1997)
"Equivalent background speed in recovery
from motion adaptation"
JOSA A, vol 14 (1), pp. 13-22.
(Appendix A follows MacMillan and Creelman's discussion).

Kadlec (1999)
"Statistical Properties of d' and beta Estimates of
Signal Detection Theory"
Psychlological Methods, vol. 4 (1), pp. 22-43.

Brown and White (2005)
"The optimal correction for estimating extreme discriminability"
Behavior Research Methods
vol 37 (3), pp. 436-449.

Hautus and Lee (2006),
"Estimating sensitivity and bias in a yes/no task"
British Journal of Mathematical and Statistical Psychology, 
vol 59, pp. 257-273.


At 10:03 PM +0800 6/3/07, Hang Zhang wrote:
>In signal detection theory, sensitivity d' is computed as the 
>z-score difference between false alarm rate and hit rate. I am 
>puzzled about what is the z-score for a 0 or 1 rate, because 
>theorically the value is indefinite. But an indefinite d' for an 
>observer in a psychological experiment seems unreasonable... Could 
>someone tell me how to compute d' when hit rate or false alarm rate 
>is 0 or 1? Many Thanks.
>Hang ZHANG, PhD Candidate
>State Key Laboratory of Brain and Cognitive Science
>Institute of Psychology, Chinese Academy of Sciences
>4A, Datun Road, Chaoyang District
>Beijing 100101, China
>Tel: 8610 6483 7209
>Fax: 8610 6487 2070
>Email: zhangh at psych.ac.cn

"If you think education is expensive, try ignorance" --Derek Bok

Vit Drga * School of Psychology * University of St Andrews
         St. Mary's College * South Street
      St. Andrews * Fife KY16 9JP * Scotland

Ph. (00)44 (0)1334 462097
email: vitdrga att psychophysics dott org

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