72c8cad2   
   From: b.scott@csuohio.edu   
      
   On Sat, 27 Dec 2008 23:15:38 +0000, Catja Pafort   
    wrote in   
      
   in rec.arts.sf.misc:   
      
   > David Friedman  wrote:   
      
   [...]   
      
   >> I didn't actually say "statistically significant," but if I had then   
   >> your response would be entirely irrelevant   
      
   > Err, what other 'significant' do you mean when you're   
   > talking about statistics?   
      
   Intrinsic significance, i.e., real-world significance.   
      
   Suppose that you know that the mean height of a certain   
   population P is 178.0 cm.  You take a random sample from   
   another population, Q, and find that the mean height of this   
   Q-sample is 178.1 cm.  Does this mean that the Q population   
   really is on average very slightly taller than the P   
   population?  Suppose that it isn't.  Then our Q-sample is   
   just a bit unrepresentative, since it, unlike the Q   
   population as a whole, *does* have a greater mean height   
   than the P population.  The larger the sample is, the more   
   likely it is to be representative, and of course the less   
   likely it is to be unrepresentative.  These likelihoods can   
   be calculated.  If the sample is big enough so that this   
   degree of unrepresentativeness has at most a 5% chance of   
   occurring in a randomly chosen sample of that size, the   
   difference is said to be statistically significant.  This   
   just means that IF the Q population really is no taller than   
   the P population on average, THEN there's at most a 5%   
   chance of getting a Q-sample of this size whose mean height   
   is at least 178.1 cm.   
      
   Now 5% is fairly small: one chance in 20.  Thus, IF the   
   Q-population really is no taller than the P population on   
   average, it's rather surprising that we got the kind of   
   sample that we did get: 19 times out of 20 we'd get one with   
   a smaller mean height.  We conclude that there's a very good   
   chance that the Q population really is just a bit taller   
   than the P population.  (Why 5%?  It's traditional.  I   
   personally don't like making any particular level of   
   significance a magic boundary and prefer to say that   
   something is significant at the 5% level, or at the 2%   
   level, at the 0.01% level, etc.)   
      
   But does a one millimetre difference in mean height of two   
   human populations have any significance in the real world?   
   Obviously not.  (Hell, we typically shrink more than that in   
   the course of a day on our feet!)   
      
   [...]   
      
   Brian   
      
   --- SoupGate-Win32 v1.05   
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