Correction For Correlation in The Sample
If values of the measured quantity A are not statistically independent but have been obtained from known locations in parameter space x, an unbiased estimate of the true standard error of the mean (actually a correction on the standard deviation part) may be obtained by multiplying the calculated standard error of the sample by the factor f:
where the sample bias coefficient ρ is the widely used Prais-Winsten estimate of the autocorrelation-coefficient (a quantity between -1 and 1) for all sample point pairs. This approximate formula is for moderate to large sample sizes; the reference gives the exact formulas for any sample size, and can be applied to heavily autocorrelated time series like Wall Street stock quotes. Moreover this formula works for positive and negative ρ alike. See also unbiased estimation of standard deviation for more discussion.
Read more about this topic: Standard Error
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