In preparing a recent talk on probability for physics grad students – it’s here if you’re interested – I thought up a rather nice example to bring out a key feature of frequentist probability. I decided not to include it, as the talk was already pretty heavy, but it seemed too good an illustration to throw away. So here it is.
Suppose you’ve applied for a job. You make the short list and are summoned for interview. You learn that you’re one of 5 candidates.
So you tell yourself – and perhaps your partner – not to get too hopeful. There’s only a 20% probability of your getting the job.
But that’s wrong.
That 20% number is a joint property of yourself and what statisticians call the collective, or the ensemble. Yes, you are one of a collective of 5 candidates, but those candidates are not all the same.
Let me tell you – from my experience of many job interviews, good and bad, on both sides of the table, about those 5 candidates .
One candidate will not turn up for the interview. Their car will break down, or their flight will be cancelled, or they will be put in Covid-19 quarantine. Whether their subconscious really doesn’t want them to take this job, or they have a guardian angel who knows it would destroy them, or another candidate is sabotaging them, or they’re just plain unlucky, they don’t show. There’s always one.
A second candidate will be hopeless. They will have submitted a very carefully prepared CV and application letter that perfectly match everything in the job specification, bouncing back all the buzz-words and ticking all the boxes so that HR says they can’t not be shortlisted. But at the interview they turn out to be unable to do anything except repeat how they satisfy all the requirements, they’ll show no signs of real interest in the work of the job apart from the fact that they desperately want it.
The third candidate will be grim. Appointable, but only just above threshold. The members of the panel who are actually going to work with them are thinking about how they’re going to have to simplify tasks and provide support and backup, and how they really were hoping for someone better than this.
Candidate four is OK. Someone who understands the real job, not just the job spec in the advert, and who has some original (though perhaps impractical) ideas. They will make a success of the job and though there will be occasional rough patches they won’t need continual support.
Candidate five is a star. Really impressive qualification and experience on paper, glowing references, and giving a superb interview performance, answering questions with ease and enthusiasm and using them to say more. They will certainly get offered the job – at which point they will ask for a delay, and it will become clear that they’re also applying for a much better job at a superior institution, and that they don’t really want this one which is only an insurance in case they don’t get their top choice.
So there are the five. (Incidentally, they are distributed evenly between genders, backgrounds and ethnicities). Don’t tell yourself your chance is 20%. That’s true only in the sense that your chance of being male (as opposed to female) is 50%. Which it is, as far as I’m concerned, but certainly not as far as you’re concerned.
Instead ask yourself – which of the five candidates are you?
(If you don’t know, then you’re candidate #3)