MY COMMENTS IN CAPS At 04:15 PM 8/26/2007, you wrote:
The Math-Fun list is a family list. We have several teenage subscribers.
Referring to the Prom Theorem, there are several things that could spoil it:
a) Averages must match, but medians don't need to. Nothing says that the distributions of the two groups are the same.
CORRECT. FOR EXAMPLE THERE COULD BE A SMALL GROUP OF GIRLS WITH A VERY LARGE NUMBER OF PARTNERS. (THEY COULD BE CALLED POPULAR OR PROMISCUOUS DEPENDING ON THE CONTEXT.)
b) There could be recall bias, especially at higher numbers.
THERE'S A WAY AROUND THIS I WILL DESCRIBE IN A LATER COMMUNICATION.
c) The Prom Theorem assumes a definite beginning and end to the dance. If it's a permanent on-going affair, snapshots don't have to add up. d) Interview subject selection bias. Some people have left the dance early and moved out of state. They don't get interviewed.
YES. IN THE REAL WORLD CASE, (WHERE THE ACTIVITY UNDER STUDY IS NOT DANCING), THERE'S A POSITIVE PROBABILITY THAT SOME OF THE RESPONDENTS' FORMER PARTNERS WILL HAVE DIED BY THE TIME THE CENSUS IS TAKEN. SINCE WOMEN OUTLIVE MEN BY AROUND 6 YEARS AN ACCURATE COUNT SHOULD SHOW MEASURABLY MORE PARTNERS FOR THE "GIRLS" THAN THE "BOYS".
e) Ambiguity about "What's a dance?". f) Assumption of a bipartite graph, with edges.
g) Possible confusion between number of dances, and number of different dance partners.
IT DOESN'T MATTER AS LONG AS YOU ARE CONSISTENT. THE NUMBER OF DANCES FOR BOYS AND GIRLS MUST ALSO BE EQUAL
I'm sure that Prof. Gale knows all of these, but perhaps Ms. Kolata has overlooked some of them.
Rich
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David Gale Professor Emeritus Department of Mathematics University of California, Berkeley