The covariance matrix of the corrected results is given by the transformation

(6.25) |

where . The elements of are given by

(6.26) |

In this case we get

(6.27) | |||

Cov | (6.28) | ||

(6.29) | |||

(6.30) |

reobtaining the results of Section . The total uncertainty on the single measurement is given by the combination in quadrature of the individual and the common standard uncertainties, and all the covariances are equal to . To verify, in a simple case, that the result is reasonable, let us consider only two independent quantities and , and a calibration constant , having an expected value equal to zero. From these we can calculate the correlated quantities and and finally their sum ( ) and difference ( ). The results are

(6.31) | |||

(6.32) |

It follows that

(6.33) | |||

(6.34) |

as intuitively expected.