A Thing That I Learned, Today

I've been reading about statistics.  I've read that it's a bad idea to compare 2 things, when all you know about the things is percentages.  I've been trying to understand why.
Example:
  • Ask 100 people if they own a pet.  50 say "Yes," and 50 say "No."
  • Ask 10 people the same question.  5 say "Yes," and 5 say "No."
Clearly, in each case, 50% of each group owns a pet.  But, imagine going one more step, and adding 1 more pet-owning person to each survey.  What happens?
  • 51/101 people --  50.5% -- report owning a pet.
  • 6/11 people -- 54.5%(!) -- report owning a pet.
Look at that!  One more vote, and the results diverge by quite a bit.  They aren't equally "stable."  The 10-person survey is heavily influenced by the addition of just one more vote.  The 100-person survey isn't.

I guess it's something like having 2 fuel tanks in my car, one with a gauge-needle that moves whenever I hit a bump.  They both read "¼" right now.  Maybe that's because I have a ¼-tank of gas.  And maybe it's because I just hit a pot-hole.  Which tank has more gas?  I dunno.  The unstable needle means I can't really compare the measurements.

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This page contains a single entry by Eofhan published on January 13, 2010 12:29 PM.

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