I see what you're saying. I was pointing out the dangers of false negatives, but he responded that he hires 10% of the people he invites for an onsite interview.
Even if you hire 10% of the candidates you on-site interview, that says nothing about your actual false positive or false negative rate. For all I know, he could be weeding out all the top candidates at the pre-interivew stage, and then hiring the best of a mediocre group of people.
It's easy to measure your false positive rate, people you are forced to fire (or wish you could fire if not for corporate bureaucracy).
It's harder to measure your false negative rate. The only way you could measure your false negative rate is to pick a random sample of people who fail your interview, AND HIRE THEM ANYWAY. (However, that could be a lawsuit risk. It would be unfair to the people who hire despite failing the interview. A small business couldn't afford to do it, only some huge corporation could do the experiment.)
Also, I doubt the ability of most businesses to identify the best performers AFTER THEY ARE HIRED and working there for a couple of years.
No, I did not say I hire 10% of candidates I interview :). What I said was that's a fair estimate in industry.
I feel you are truly confused about FP and FN. Whether there are 99% bad developers out there or if you hire 10% of candidates you interview - these both quantities are independent of FN and FP. FN says that you are turning away X good people and it's again independent of FP which ultimately decides how many bad developers you would eventually end up hiring regardless of other 3 quantities I mentioned. See here: http://en.wikipedia.org/wiki/Confusion_matrix
It's not easy to measure FN, FP, TN or TP. Even good people fail due to different reasons like bad manager and bad people may succeed despite of mediocre skills. Looking at who you had to fire or who got promoted doesn't give accurate measurements at all although they may serve as weak proxy. The scenario I described was hypothetical to point out that cost of FP is far more higher than additional cost in hiring due to FN.
May be I'm completely missing something here but my understanding is this: FP = (good hires you made) / (all hires you made). Your likelyhood of making bad hire is 1-FP. If you hired 100 people and your FP was 10% then on average you would have 10 bad hires on your team. So FP determines the number of bad hires you would eventually have. FN has nothing to do with it - it only determines how long before you make a good hire, it doesn't influence actual number of bad hires you will make.
I'm using standard terminologies here. There are plenty of textbooks and articles on confusion matrix, precision, recall, RoC etc. Not sure what definitions you are using to arrive at conclusion that FN increases the number of good hires (it only increases effort).
Sorry, I did mixed up precision in my reply. I just got time to think about this whole debate more carefully and I realize you are actually right if we fix up some of the terminology you have used. The mis-statements and confusion on my part has occurred due to this terminology differences.
First FP and FN are not probabilities. They are just unbounded numbers. This may feel pedantic but in a moment I'll show you why this is critical. Let me draw the confusion matrix first (G = Good candidates, H = Hired candidate etc):
\ H NH
\---------
G | TP FN
B | FP TN
What you are referring to as probabilities is actually False Positive Rate or FPR and TNR respectively which is defined as follows:
Now the quantity you are after is probability that given you did hiring and ended up with good guy which is, nothing but precision:
precision = P(G|H) = TP/H
So how do we get TP to calculate precision if we only knew FPR, FNR, G and B? I did little equation gymnastics using above and got below:
TP = G - GFNR
H = TP + FP = TP + FPRB
So now you can plug this in to above equation for precision and find that as you increase FNR, precision goes down while you keep FPR constant. So you are actually correct. Although it might look like unnecessary exercise vs following intuition I think above equation can actually help calculate exact drop in precision and multiply that with cost of FP vs FN to get the operating sweet spot. On my part I need to do some soul searching to figure out why this didn't triggered to me before :).
Even if you hire 10% of the candidates you on-site interview, that says nothing about your actual false positive or false negative rate. For all I know, he could be weeding out all the top candidates at the pre-interivew stage, and then hiring the best of a mediocre group of people.
It's easy to measure your false positive rate, people you are forced to fire (or wish you could fire if not for corporate bureaucracy).
It's harder to measure your false negative rate. The only way you could measure your false negative rate is to pick a random sample of people who fail your interview, AND HIRE THEM ANYWAY. (However, that could be a lawsuit risk. It would be unfair to the people who hire despite failing the interview. A small business couldn't afford to do it, only some huge corporation could do the experiment.)
Also, I doubt the ability of most businesses to identify the best performers AFTER THEY ARE HIRED and working there for a couple of years.