本帖最後由 dye 於 2010/10/9 01:02 編輯
STATISTICS OF SMALL NUMBERS
How will it look like? (As I understand it)
Suppose a person randomly select 3 person in the world and they all happened to be male. He concluded that there is no female in the world.
Why is it wrong?
Suppose the share of male-female is 50-50. What is the chance the above scenario happening? 50%^3 = 12.5%. Not very unlikely.
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Now suppose you randomly select 100 person in the world and they all happened to be male. You concluded that there is no female in the world.
Suppose the share of male-female is 50-50. What is the chance the above scenario happening? 50%^100 = 0%. Very unlikely.
Suppose the share of male-female is 95-5. What is the chance the above scenario happening? 95%^100 = 0.5%. Very unlikely.
Suppose the share of male-female is 99-1. What is the chance the above scenario happening? 99%^100 = 36.6%. Not very unlikely.
You can see that the conclusion have some force in this case. That, is the difference.
If he wish to give the conclusion a "full force", try randomly select 500 person in the world, see if they are all male.
Suppose the share of male-female is 99-1. What is the chance they are all male? 99%^500 = 0.6%. Very unlikely.
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THe validity depends on the size sample as much as the conclusion to be made, as much as the sampling method, as much as the error allowed, etc.. |