[visionlist] signal detection query

Daniel Oberfeld oberfeld at uni-mainz.de
Wed Jul 21 08:26:54 GMT 2010

Hi Joseph,

Re (1) : If you use the correct formula for calculating d', then it will 
automatically correct for unequal numbers of old and new pictures.

Re (2): I think this is no problem for calculating the SDT statistics, 
but rather for the interpretation of your results - does it make sense 
to compare responses to old stimuli+TMS and responses to new stimuli 
without TMS...?

There is one very serious issue with calculating d' for your data, 
however. In case you collected binary responses ("Is the picture old or 
new?"), then for calculating d' you will have to assume that the 
internal distributions for "signal" and "noise" have identical standard 
deviations (cf. Macmillan & Creelman, 2005). It is known for a long time 
that this assumption is frequently incorrect for experimental data 
(e.g., Swets, 1986). And thus d' is not a valid measure of sensitivity 
because it is strongly influenced by response bias (Verde, MacMillan, & 
Rotello, 2006).

The simple solution (at least for future experiments) is to obtain 
rating responses rather than binary responses - with these responses, 
you can caculate for example the area under the ROC curve, which is a 
valid index of sensitivity even if the SDs of the internal distributions 
are unequal (Swets, 1986).  Again, Macmillan & Creelman (2005) explain 
in detail how to conduct such an experiment.

Macmillan, N. A., & Creelman, C. D. (2005). Detection theory: A user's 
guide (2. ed.). Mahwah, NJ [et al.]: Lawrence Erlbaum Associates.
Swets, J. A. (1986). Indices of discrimination or diagnostic accuracy: 
their ROCs and implied models. Psychological Bulletin, 99(1), 100-117.
Verde, M. F., MacMillan, N. A., & Rotello, C. M. (2006). Measures of 
sensitivity based on a single hit rate and false alarm rate: The 
accuracy, precision, and robustness of d ', A(z), and A '. Perception 
and Psychophysics, 68(4), 643-654.



Dr. Daniel Oberfeld-Twistel
Johannes Gutenberg - Universitaet Mainz
Department of Psychology
Experimental Psychology
Wallstrasse 3
55122 Mainz

Phone ++49 (0) 6131 39 39274
Fax   ++49 (0) 6131 39 39268

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