Friday, March 07, 2014

On sample sizes

Freeman Dyson "In 1866, the year Mendel’s paper was published, but without any knowledge of Mendel, Darwin did exactly the same experiment. Darwin used snapdragons instead of sweet peas, and tested the inheritance of flower shape instead of pod color. Like Mendel, he bred three generations of plants and observed the ratio of normal-shaped to star-shaped flowers in the third generation. Unlike Mendel, he had no understanding of statistical fluctuations. He used a total of only 125 third-generation plants and obtained a value of 2.4 for the crucial ratio. This value is within the expected statistical uncertainty, either for a true value of 2 or for a true value of 3, with such a small sample of plants. Darwin did not understand that he would need a much larger sample to obtain a meaningful result." in The case for blunders   Professor Karandikar talks about sample sizes here which is not clear to me "This held good even if the sample size was as small as 4,000 irrespective of whether a constituency had one lakh voters or 20 lakh voters, he said.
“This is something which is counterintuitive but it is not a matter of faith but of calculation…the point is that it is only the percentages and not the absolute numbers that determine the accuracy,” Prof. Karandikar said." The two parts seem to point to different things; may be the clue is in 'the percentages'.

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