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Statistics... is all based on... the steady augmentation of the confidence level... or an n times increase in sample size, we increase our knowledge by the square root on n. ...Where statistics ...fails us, is when we have distributions that are not symmetric... If there is a very small probability of finding a red ball in an urn dominated by black ones, then our knowledge about the absence of red balls will increase slowly. ...On the other hand, our knowledge of the presence of red balls will dramatically improve once one of them is found. This asymmetry in knowledge... is the central philosophical problem for... David Hume and Karl Popper. (en) |
