>I have been trying to explain to some co-workers
>that a sample can be too big. That is not very
>easy because it is contradictory to what intuition
>says.
>
>Can someone point me to some good arguments or
>literature? Or correct me if my assumption is
>wrong?
Suppose you are taking a random sample of bills sent to a large customer to
assess the total amount that your customer has overpaid (or that you have
overbilled). You don't want to review every single bill, since there are
thousands of them. So you and the customer agree that you will pay back the
upper confidence limit on the estimated total overpayment based on a sample.
It costs a certain amount to review each bill, and after you have audited a
certain number of bills, you will see diminishing returns. It might cost you
an extra dollar of sampling effort just to gain an additional fifty cents of
precision on your confidence interval.
That's an example of a sample size that is too large. The proper sample size
in this case is one where the cost of sampling equals the precision of the
confidence interval.
This works in more general contexts than just money. Each unit of
imprecision in your confidence interval "costs" you something. You might
have to make some difficult value judgements here. How much does it cost AC
Nielsen when they can only estimate the total number of Superbowl viewers to
within plus or minus 5 million? In practice that sort of question is
difficult to answer. But in theory it can be done.
Balance the cost of imprecision against the cost of sampling. When the cost
of sampling exceeds the cost of imprecision, your sample size is too big.
I hope this helps.
Steve Simon, [EMAIL PROTECTED], Standard Disclaimer.
STATS - Steve's Attempt to Teach Statistics: http://www.cmh.edu/stats
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