**B.1** This appendix summarizes a conventional procedure, given by the
*Guide* [2] and
Dietrich [10], intended for use in calculating
a coverage factor *k* when the conditions of the Central Limit Theorem
are met (see subsection 5.4) and (1) a value
other than *k* = 2 is required for a specific application
dictated by an established and documented requirement; and (2) that value of
*k* must provide an interval having a level of confidence close to a
specified value. More specifically, it is intended to yield a coverage factor
*k _{p}* that produces an expanded uncertainty

The four-step procedure is included in these guidelines because it is expected
to find broad acceptance internationally, due in part to its computational
convenience, in much the same way that *k* = 2 has become the
conventional coverage factor. However, although the procedure is based on a
proven approximation, it should not be interpreted as being rigourous because
the approximation is extrapolated to situations where its applicability has
yet to be fully investigated.

**B.2** To estimate the value of such a coverage factor requires taking
into account the uncertainty of *u*_{c}(*y*), that is, how
well *u*_{c}(*y*) estimates the standard deviation
associated with the measurement result. For an estimate of the standard
deviation of a normal distribution, the degrees of freedom of the estimate,
which depends on the size of the sample on which the estimate is based, is a
measure of its uncertainty. For a combined standard uncertainty
*u*_{c}(*y*), the "effective degrees of freedom"
ν_{eff} of
*u*_{c}(*y*), which is approximated by appropriately
combining the degrees of freedom of its components, is a measure of its
uncertainty. Hence ν_{eff}
is a key factor in determining *k _{p}*. For example, if
ν

**B.3** The four-step procedure for calculating *k _{p}* is as
follows:

1) Obtain *y* and *u*_{c}(*y*) as indicated in
Appendix A.

2) Estimate the effective degrees of freedom
ν_{eff}
of *u*_{c}(*y*) from the Welch-Satterthwaite formula

(B-1) |

where *c _{i}* ≡ ∂

(B-2) |

The degrees of freedom of a standard uncertainty
*u*(*x _{i}*) obtained from a Type A evaluation is
determined by appropriate statistical methods
[7]. In the common case discussed in
subsection A.4 where

The degrees of freedom to associate with a standard uncertainty
*u*(*x _{i}*) obtained from a Type B evaluation is more
problematic. However, it is common practice to carry out such evaluations in a
manner that ensures that an underestimation is avoided. For example, when
lower and upper limits

NOTE - See the Guide [2] for a possible way to estimate ν_{i}when this assumption is not justified.

3) Obtain the *t*-factor *t _{p}*(ν

4) Take
*k _{p}* =