This is an interesting paradox from statistics. It is not exactly a paradox because there is no logical contradiction. It can be stated as "Aggregate proportions can reverse the direction of the relationship seen in the individual pieces". (There may be a better, comprehensive way to state it.)
Let me explain it. Let's say Me and Anand throw stones at a spot for two hours and in the first and second hours both, he gets a better percentage of hits than me, still I might end up with a better agrregate percentage of hits. Sounds unbelievable. Take this example:
HITS
THROWS
% HITS
HITS
THROWS
% HITS
Me: First Hour
73
100
73%
Anand: First Hour
75
100
75%
Me: Second Hour
4
8
50%
Anand: Second Hour
30
50
60%
At this stage he has defeated me in both the hours of contest, isn't it?
But see the aggregate results:
HITS
THROWS
% HITS
My Total
77
108
71.3%
Anand's Total
105
150
70%
See Me is Better than Anand!
Well it's not as tough as it looks, it's just that the percentages in the second hour of throwing were generally low and I cleverly threw less times.
So looking at the data in two different ways gives two different pictures. So moral of the story is, I am the clever guy.(kidding, when will they introduce a tag for kidding in HTML?) Tuesday, May 28, 2002
