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Politics : View from the Center and Left -- Ignore unavailable to you. Want to Upgrade?

To: Alastair McIntosh who wrote (21074)	6/15/2006 11:48:23 AM
From: TimF	Respond to of 541877

The unexpected thing here is that the size of the population does not matter! Yes I've heard that before. But I think it might just be an approximation. If 1000 people is a reasonable sample size for American voters (say 120 million people), it might also be a reasonable sample size for the population of India (about ten times as many people), in fact the difference in confidence may be negligible. But I don't think it could be considered a reasonable sample size for a hypothetical inter-galactic civilization with 10^26 people. And even if it is, saying "the population does not matter" would mean not just that it was a reasonable samples size but that there was no decrease in confidence, and that there still would not be if the population was higher than the number of sub-atomic particles in the universe multiplied by 10^100^100^100^100. Even if the theory says there would be no degradation of confidence at even impossibly high populations I don't buy it. The equations may work out that way but if so I believe the equations only approximate reality. Granted there is no reality with impossibly high numbers to compare the equations to but I would still have reduced confidence in the numbers with merely incredibly higher numbers like the earlier mentioned inter-galactic civilization, mainly because my confidence that even a survey with impeccable methodology is truly getting a representative sample is reduced as the numbers get bigger. This might be considered more an aspect of non sampling error, a claim that the sample isn't truly random. Maybe you want to consider it that, but I'm not talking about any correctable weaknesses in the methodology. When the sample size is such an insignificant fraction of the population sampled (say surveying 1000 people out of 10^26, or trying to estimated the salinity of the ocean based on a small drop of ocean water, even if that drop was assembled from tiny droplets taken at numerous random locations) I think the traditional margin of error calculations are less than enough to give a reasonable approximation of the true chance of error. The relatively simple equations become less adequate in dealing with an increasingly complex reality. Tim