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

[Andrew Robinson]

On Tue, Jun 14, 2011 at 11:02:52AM +1000, Andrew Robinson wrote:
> 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

Bernoulli sampling.

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

Not exact.  Can be approximately ok.  See 'Estimation of a Population
Total Under a "Bernoulli Sampling" Procedure' Strand 1979 American
Statistician 33 (2) 81-84.

See also Sarndal et al 'Model Assisted Survey Sampling'.

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

As above!

Best wishes to all

Andrew

> 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/
> 
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-- 
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/