[R] Off-topic: (Simple?) Random Sampling when n is a random variable

[Andrew Robinson]

Hi everyone,

I'm involved in a discussion with a colleague.  He suggested a sample
design for a finite-sized process that (to all intents and purposes)
involves tossing a coin and examining the unit if the coin shows
Heads.

I should emphasize that we're both approaching the problem from a
design-based sampling theory point of view.  So I have no argument
about the appropriateness of the design as such.

Can this design be called 'Simple Random Sampling'?  My intuition
suggests that it can not, because the sample size is a random
variable, so the usual standard error equations for SRS will be
inaccurate.  But I can't find any citations to back me up.  So maybe
I'm wrong.  My questions are:

1) does this design have a name, and

2) are the usual SRS formula for e.g. the standard error of the mean
exactly accurate?  Or are they defensibly accurate approximations?

3) can anyone suggest some citations that provide guidance either way?

Thanks for any assistance!

Andrew

-- 
Andrew Robinson  
Program Manager, ACERA 
Department of Mathematics and Statistics            Tel: +61-3-8344-6410
University of Melbourne, VIC 3010 Australia               (prefer email)
http://www.ms.unimelb.edu.au/~andrewpr              Fax: +61-3-8344-4599
http://www.acera.unimelb.edu.au/

Forest Analytics with R (Springer, 2011) 
http://www.ms.unimelb.edu.au/FAwR/
Introduction to Scientific Programming and Simulation using R (CRC, 2009): 
http://www.ms.unimelb.edu.au/spuRs/