The process suggests a way of determining the best sample size for an experiment.

Firstly, determine the amount of error, in standard deviations, you are willing to tolerate in the measure of the area under the ROC curve.

If you know the theoretical performance then you can calculate the area under the ROC curve and use a graph or table of the standard deviation versus the number of samples for that particular area. You can then simply read off the number of samples.

If you don't know the theoretical performance then I suggest two approaches:

Firstly, I would suggest calculating the number of samples based on an area of 0.5 - chance performance. This is where the variability is the greatest. If you intend to use signal-to-noise ratio as an independent variable then this is probably the best thing to do.

Otherwise I would suggest running a pilot study to get a rough idea of where in the ROC space the observer is tending. This may reduce the number of samples needed but this needs to be traded-off with the time taken to do the pilot study.

One other approach is suggested in the literature by Pollak et al (1969). They suggested that the maximum standard deviation could be approximated by a binomial. Rearranging his formula gives a way of estimating the number of samples: simply mulitply the area with one minus the area and divide by the square of the standard deviation. This overestimates the true standard deviation especially for small sample sizes but it is quick and easy.