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Conference rusure::math

Title:Mathematics at DEC
Moderator:RUSURE::EDP
Created:Mon Feb 03 1986
Last Modified:Fri Jun 06 1997
Last Successful Update:Fri Jun 06 1997
Number of topics:2083
Total number of notes:14613

1147.0. "Simpson's paradox" by LEDS::HAMBLEN (skazhi kishmish!) Thu Nov 02 1989 12:49

	Gentle People, who can tell me about Simpson's paradox?  I have 
heard that it's in the general area of probability theory, or a closely
related field.  Just curious.
					Dave
T.RTitleUserPersonal
Name		DateLines
1147.1Also known as the Aggregation Paradox.CADSYS::COOPERTopher CooperFri Nov 03 1989 13:5037
    I tried to come up with a concrete example to illustrate it and
    couldn't come up with one on my own, so I got this one out of the
    Encyclopedia of Statistical Science (fleshing it out a bit):
    
    Imagine that a survey, involving a single yes/no question, is done.
    Two different NY and LA are used.  What is of interest is the
    difference between men and women in the proportion of "yes" answers.
    
    Here are the results:
    
             NY      LA
    	    ----    ----
    	    M  F    M  F
         -----------------
    	Y|  4  3 |  1  3 |
    	N|  6  3 |  9 18 |
    	 -----------------
    
    Notice that at both locations, a higher proportion of females than
    males answered "yes".  But if we condense the table by eliminating the
    "nuisance" variable of location, we get:
    
            M  F
    	 ---------
    	Y|  5  6 |
    	N| 15 21 |
    	 ---------
    
    and a higher proportion of males than females are seen to have answered
    "yes".  This results from the strong differences in the male/female
    ratio in the populations sampled at the two locations, making
    condensation inappropriate.  This is known as Simpson's paradox.  It
    is a paradox in the sense of being a counter-intuitive truth (the
    sum being proportioned the "other" way from all of its components)
    rather than in the sense of being a logical contradiction.
    
    					Topher
1147.2thanksLEDS::HAMBLENskazhi kishmish!Tue Nov 07 1989 10:405
              <<< Note 1147.1 by CADSYS::COOPER "Topher Cooper" >>>
                  -< Also known as the Aggregation Paradox. >-

	Thanks, Topher.  A most lucid exposition.
						Dave