Originally Posted by
muishkin
The sampling error (assume no biases) is a function of the sqrt of the sample size. From 2 to 4 or 20 to 40, the difference in both cases is a multiple of sqrt(2). I think we only disagree on the qualitative meaning of negligible here. For 20 people, the error is about 20% and for 40 it is about 15%. For me that is a small difference.
For your F cabin example, other errors such as rounding becomes dominant since you can't have 1.75 chicken, 3.5 pork and 0.75 fish..
For the CW cabin, if 35/40 pre-orders, then you can overload the remaining meals by 200% and still come out ahead of the expected 115% error mark for the entire cabin.
On the last point: but that's the whole point: they won't overcater more, their whole idea is to reduce costs as much as possible, and certainly not to use the exact prediction of part of the group to become more generous on the way to treat those who do not pre-assign. Moreover, it would create exactly the wrong incentive structure as BA's goal is to push as near 100% of pax as possible to pre-order, so if anything, overcatering rates will go down, not up. And yes, rounding error and more will add to sampling error.
On your first point, I certainly don't want to start what wounds like a professional argument or we'll bore everyone, but there are many different ways to measure sampling error. Most will (rightly) take into account the characteristics of the variable you are trying to estimate and not only the population and sample sizes which of course matter a lot. Again, for the benefit of our Ft crowd, it makes a lot of intuitive sense to do that: let's say that you have a population of 1000 and a sample of 31. If you are using that sample to estimate gender (two values with uniform distribution), chances are that your estimation will be pretty good. However, if you use that very same sample to estimate the day of the month people are born (31 values with uniform distribution) chances are that your estimates will be pretty poor.
As you say, we can disagree on what constitutes marginal or sizeable in theory, but I'm not making an abstract theoretical argument but rather a practical one: in the case we are talking about, we may well end up with 5 people and 5 options with skewed distribution: there will be error and some people simply won't get their first choice, and it will happen more often than before even though an increasing number of people will have been secured into a 'true' choice.
Now again, concretely and commercially, my suggestion is that the best answer, the 'win win scenario', is for BA to create a genuine incentive for pre-order by using pre-order to give people significant extra choice. You will never reach 100% of pre-orders but commercially, it makes it much easier to claim that whilst the 1 or 2 people left in the cabin will almost certainly not get their first choice, they will get what they deserve for not using that sublime book the cook facility with its 10 or 20 options!
