Or do the statistics only work the other way around?
No, the stats work much the same way, with a little difference. If you are in a robbery you already know what the situation is, and thus can make an accurate assessment about what might happen. With "unknown noise" you have no idea. A comparison might be "unknown crime" info. Hard to figure out what to do if you don't know if it is a burglary, a robbery, rape, murder, etc. Obviously a burglary or a robbery gives a better chance of compliance being the right choice than a rape or murder.
Again, that is why there are noises and then there are NOISES! If the noise is such that you think you better grab a gun, odds are you're in a problem. If lights and noise from you don't make the BG go away, odds are you are in a problem. How do you minimize your loss of resources?