XPost: rec.arts.sf.written, rec.arts.sf.science   
   From: b.scott@csuohio.edu   
      
   On Fri, 24 Jan 2014 10:01:56 -0600, David DeLaney   
    wrote in   
    in   
   rec.arts.sf.written,rec.arts.sf.science,rec.arts.sf.misc:   
      
   > On 2014-01-24, Brian M. Scott  wrote:   
      
   >> Chrysi Cat  wrote in   
      
   >>> Statistics work. If you couldn't extrapolate from a proper   
   >>> sample (which would probably be closer to 500 or 5000 for   
   >>> that 50 mil), then we'd pretty much be up a creek for   
   >>> knowing what people do and think...   
      
   >> Actually, the margin of error depends almost entirely on the   
   >> absolute sample size; in real-life settings there is almost   
   >> no dependence on the ratio between population and and sample   
   >> sizes.  A sample of 50 out of 50 million is virtually as   
   >> good as a sample of 50 out of 50,000.  It *is* a bit too   
   >> small; I???d want a few hundred, and a sample of 1000 would be good.   
      
   > That's the basic "gets more accurate as the inverse square   
   > root of the sample size" rule in action, in part, isn't   
   > it? 50 good to one part in seven, 1000 good to 3%, 10,000   
   > good to 1%... derived from the law of large numbers and   
   > ... the shape of the bell curve, was it?   
      
   Yep.  Since the sample is taken without replacement, there   
   is a correction factor that depends on the ratio between   
   sample and population sizes, but in most real-life settings,   
   with samples that are a small fraction of the population,   
   the correction factor is over 0.95.  In fact it’s almost   
   0.99 already when the ratio is 0.025.   
      
   Brian   
      
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