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Statistics, computations

For computational purposes one usually splits up the estimate of err2X, given by Eq. (15), into two parts

err2X=1nvar(x)+1n(cov(x)var(x)),

which equals

1n2nk=1(xkˉxn)2+2n2k<l(xkˉxn)(xlˉxn)

The first term is the same as the error in the uncorrelated case, Eq. (16). This means that the second term accounts for the error correction due to correlation between the measurements. For uncorrelated measurements this second term is zero.