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April 7th, 2008, 11:53 AM  #1 
Newbie Joined: Apr 2008 Posts: 1 Thanks: 0  Comparing multiple data sets with different n values
I'm not sure if this is the correct place to toss this topic out there, so if this is the wrong place, I apologize. I'm having a wine tasting party in a few weeks. I have little cards that I hand out to everyone who tastes the wine, and they score it based on a 15 rank, 1 being the worst and 5 being the best. If everyone voted on every wine, it'd be easy to select a winner at the end of the night, but my problem is that based on past parties, not everyone ends up voting on each wine, and so the value of n varies from one set to another, and my ancient stat classes in college aren't of any help, though I'm pretty sure that's my fault and not the stat classes. How can I compare these sets in a statistically accurate way and determine a winner? As an example, let's say that the Merlot (sorry Sideways) gets the scores {1,3,3,4,5,5,5}, the Sauvignon Blanc gets {2,2,3,4,4,4,4,4,5,5,5,5}, and the Pinot Grigio gets {1,1,2,3,5,5,5,5,5}. Is there a way to weight them according to the number of responses to make the comparisons accurate, or is the data not directly comparable? 
April 7th, 2008, 01:43 PM  #2  
Global Moderator Joined: May 2007 Posts: 6,727 Thanks: 687  Re: Comparing multiple data sets with different n values Quote:
 
April 7th, 2008, 03:01 PM  #3 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 
It's a somewhat hard problem since people have different standards  one person might give out mostly 4s and 5s, and another rate wines 1, 2, 3, 4, and 5. But ignoring that point for a moment, in the interest of simplicity: I would recommend taking the median, then the average as a tiebreaker. That way there's less incentive, as it were, to rate a wine you didn't like artificially low. 

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