## Estimators for attendance.

For the discussion of math. Duh.

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the tree
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### Estimators for attendance.

So I'm organising an event and a lot of people aren't RSVPing very promptly but I do need to buy some refreshments etc so I am trying to make a guess for attendance based on who actually has gotten back to me. It's been a while since I did any maths and probability was never my forté but I got curious about this one for some reason so.

I figured that if I've invited S people, y people have said they are coming and n people have said they aren't then the expected attendance is one of

(y+S-n)/2

or
S * y/(y+n)

or possibly,
y + y/(y+n) * (S-y-n)

As best as I can tell they are all unbiassed so I was wondering how would you pick the best estimator out of those?

(oh and yeah and before you ask I am just going to order enough food for S-n people, I'm not crazy).

lightvector
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### Re: Estimators for attendance.

Your second and third options are actually the same. In general, you want something of the form y + (S-y-n) * p, where p is your best guess or estimate of the proportion of people who have not RSVPed who will end up deciding to come. Your first option is this with p = 1/2, and your second option is this with p = the empirical ratio of yes and no so far. The correct choice of p is not directly a question that math can solve, because it will depend heavily on context and what other information you have. What actually *is* your best guess, taking into account all the information you've seen?

If you have a strong belief (based on past experience, context, external knowledge, or any other such reason) that the remaining people who haven't responded are actually 50-50 to come despite the empirical ratio so far, you should choose the first option with p = 1/2.

If you are very unsure and believe that the empirical ratio of yes and no in responses so far is your best estimate for p, you should choose the second option with p = the empirical ratio so far.

If for various reasons (past experience, context, etc.) you believe that people who haven't responded up until now are very unlikely to come, you should choose p to be a very small value, matching your belief.

If you are unsure and believe that the empirical ratio is a good estimate, except that maybe people who haven't responded are slightly less likely to come because putting it off indicates that they aren't as interested, you should choose p = the empirical ratio minus a little bit.

Etc, etc.

Also, the choice of how much food to buy probably should depend not just on p and the expected number of people, but also on the relative costs of having too much and having too little food, which again depends on context. Between buying too much food and buying too little food, is one significantly worse than the other?

firechicago
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### Re: Estimators for attendance.

If this is a large event I would also be very surprised if everyone who RSVPs actually shows up. Depending on the nature of the event and your relationship with the attendees you might only see half of those people on the day.

So your estimate should be something like pY*y + pM*m where y is the number of RSVPs, pY is the probability of someone showing up given that they have RSVPed, m is the number of maybes or people who haven't responded, and pM is the probability of someone showing up given that they haven't responded.

Ultimately the hard part of this is not the math, it's the empirical questions of what pY and pM are. Answering those questions requires a lot of other information. (What is the event? Who are the guests? What sort of personal relationship do you have with the guests? Is this event being put on by an organization? What is the personal relationship between the guests and that the organization? Do these guests have a track record in either showing or not showing at events?)

the tree
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### Re: Estimators for attendance.

Thank you both.

If you're interested then here's some further context:

I've recently taken over someone else's job and don't have too many of their old records. I don't know how heavily previous events were promoted (these are, by the way, non compulsory training events for long term volunteers) and I really don't know if anyone was even asked for RSVPs before the previous events or if everyone was just expected to turn up on the day (if they weren't I guess that means that attendees are less likely to RSVP since they're not used to the practice).

A lot of this job appears to involve working with some very incomplete records: I have previous attendance lists but can only assume the invitee lists are nearly the same as mine - that's essentially what I'm going on to get a rough idea of scale and so far the estimators that I listed above seem to agree with that rough idea. In this case S is just over 50 so I know that informed guesswork is the more helpful option but it is nice to see when a bit of maths agrees with your own guesswork.

In terms of balancing costs, I know that volunteers dislike change and will be looking for areas to fault me so above all I want to look prepared - so over ordering on food will be the best choice in this case. I will also actually keep records of what I do for this event so that I have better data for next time.