Re: Unusual formulae for confidence intervals

Stephen J. Herschkorn wrote:
Just to clarify, I wrote exactly what I meant.


Ray Koopman wrote:

---- snip ----
- For a population proportion, use as the standard error 0.5 /
sqrt(n), where n is the sample size. The justification was that
since we do not know the population proportion pi, use pi = 0.5 for a
conservative interval estimate. Most formulae I have seen substitute
the sample proportion Q (my notation) to get sqrt(Q (1-Q) / n) for
the standard error. If one is going to be a stickler, one can solve the
quadratic inequality
-z <= (Q - pi) / sqrt( pi (1- pi) / n) <= z for explicit bounds on
pi. So using 0.5 seems silly to me.

That's for choosing the sample size (before the data are collected)
so that the standard error is guaranteed to be small enough.



No, they explicity said to use 0.5 / sqrt(n) for all confidence intervals for the proportion. Actually, more precisely, they cicuitously said use sqrt(P_u (1-P_u) / n), where P_u is the population proportion, and set P_u = 0.5 for a conservative estimate. I am familiar with the standard techniques for determining sample size; the book was not discussing this issue.

---- snip ----



That can be read as giving the *usual* way of constructing the confidence interval, *and* the way to get a more conservative estimate, can it not?


--
Bruce Weaver
bweaver@xxxxxxxxxxxx
www.angelfire.com/wv/bwhomedir
.

Relevant Pages

  • Re: Unusual formulae for confidence intervals
    ... There is only one place in public policy applications I have seen something like this. ... In planning the sample size for a random sample study, 50% is used as the working population proportion if there is no other information about what it might be. ... For a population proportion, use as the standard error 0.5 / sqrt, where n is the sample size. ...
    (sci.stat.math)
  • Re: Unusual formulae for confidence intervals
    ... As we were discussing confidence intervals, ... For a population proportion, use as the standard error 0.5 / ... Personally, I always use S / sqrtwith the t distribution, since ...
    (sci.stat.math)