# Is there a common strategy to measure if a difference-significance of two areas under two ROC curves

I conduct sound detection experiments with mice. I have a stimulus sound and a "noise" sound that shoukd be ignored.

I want to measure how well the mouse ignors the noise (with respect to, say, ignoring 100% of the noise stimuli).

I have sessions with, say 200 trials of stimulus sound that sould be detected and 40 trials of noise sounds that should be ignored.

I created the confusion matrix and ROC curve (I use Matlab). Now I want to know how well my mouse is performing compared with "ignoring all noise stims".

Is there a way, or a common used formula, to get a evaluation or a confidence interval of "how good is my ROC AUC comparing to AUC(ROC) = 1"?

Thanks!

• What is your current AUC? – Bruno Lubascher Dec 3 '19 at 13:37
• @BrunoGL, its 0.93352. You are right.. I will add to my questions the confusion matrix and ROC curve. Thank you. – user135172 Dec 3 '19 at 14:08

The AUC is a summary statistic of your dataset. As such, if you did the same experiment again you would get a slightly different value - and if repeated several times, you'd get a distribution of values. You probably want to show that your distribution rarely or never includes 0.5 (indicating random classification). When you have an empirical distribution like this, or a histogram of repeated experiments, you can just count how many of your estimates are $$\approx 0.5$$. If none, you're golden.