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

(14.14) |

where . The elements of are given by

(14.15) |

In this case we get

(14.16) | |||

Cov | (14.17) | ||

(14.18) | |||

(14.19) |

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

(14.20) | |||

(14.21) |

It follows that

(14.22) | |||

(14.23) |

as intuitively expected.