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Convert random sample values to observer rating on an R-point rating scale
Repeat for N samples per SN and N event
Calculate the area under the ROC curve
Repeat for M replications
Calculate mean and standard deviation of the area under the ROC curve
Repeat for different size N
Notes:
Next, I transformed these samples into ratings on a 100 point rating scale so that ROC analysis could be done. I repeated the sampling of size N 100 times so that the variability of the area could be calculated. And finally, I systematically varied the number of samples. Starting with 50 samples per event, I doubled the sample size until there were 819200 samples per event.