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Unformatted text preview: Key questions revisited 673 the true value in the universe. That is because the devia- tions from the sample mean are not all independent of one another. In fact, by definition, the sum of all the de- viations of the observations from the mean is 0! (Try to prove it as an exercise.) Therefore, if we are told N 2 1 of the deviations from the mean in a sample of N obser- vations, we can calculate the missing deviation, because all the deviations must add up to zero. It is simple to correct for this bias in our estimate of variance. Whenever we are interested in the variance of a set of measurementsnot as a characteristic of the particular sample but as an estimate of a universe that the sample representsthen the appropriate quantity to use, rather than s 2 itself, is [ N /( N 2 1)] s 2 . Note that this new quantity is equivalent to dividing the sum of squared deviations by N 2 1 instead of N in the first place, so All these considerations about bias also apply to the sample covariance. In the preceding formula for the cor- relation coefficient, however, the factor N /( N 2 1) would appear in both the numerator and the denomina- tor and therefore cancel out, and so we can ignore it for the purposes of computation.the purposes of computation....
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This note was uploaded on 01/10/2011 for the course BIOL BIOL taught by Professor Johnson during the Spring '08 term at Aberystwyth University.
- Spring '08