  The Guide to the Expression of Uncertainty in Measurement advocates the use
of an 'effective number of degrees of freedom' for the calculation of an
interval of measurement uncertainty. However, it does not describe how this
number is to be calculated when (i) the measurand is a vector quantity or (ii)
when the errors in the estimates of the quantities defining the measurand (the
'input quantities') are not incurred independently. An appropriate analysis for
a vector-valued measurand has been described (Metrologia 39 (2002) 361-9), and
a method for a one-dimensional measurand with dependent errors has also been
given (Metrologia 44 (2007) 340-9). This paper builds on those analyses to
present a method for the situation where the problem is multidimensional and
involves correlated errors. The result is an explicit general procedure that
reduces to simpler procedures where appropriate. The example studied is from
the field of radio-frequency metrology, where measured quantities are often
complex-valued and can be regarded as vectors of two elements.
