I'm at a midsize company that is trying to grow moderately aggressively, so we have a constant, high interview load.
There are many tools that are built around telling you your interviewing funnel, or the percentage of people who you reject after each round of interviewing. This number is useful for quantifying how much time you spend interviewing at each stage, however it doesn't give you much insight into how to fix your hiring process. For instance, if the first phone screen cuts 50 out of 100 candidates, is that a good thing or a bad thing?
When you think about it for a second, you'll see that there's no way to know. Let's call the percentage you cut simply the "negatives" -- you don't know how many of those were "true negatives" (people who truly were a bad match) versus "false negatives" (people you rejected but who would have succeeded in the role you're recruiting for). If 40 of the 50 you cut are false negatives, then that's really bad because you could have hired all those people and you didn't! False positives are bad too, but you can at least approximate that number for the last round of your interviews by looking at how many people quit / are fired.
It's basically impossible to know for certain what your exact false negative rate is given your limited exposure to candidates you reject, but in order to improve the quality and speed of our hiring I would like to approximate it. What information could I ask coworkers, recruiters, managers, candidates, former candidates, etc. for in order to make a good guess? (My only thought so far is to somehow use referrals or references, or maybe look at the places candidates actually went instead of my company.)