##
Guidelines for Evaluating and Expressing the
Uncertainty of NIST Measurement Results

# Appendix D

**D.1 Terminology**
**D.2 Identification of uncertainty
components**
**D.3 Equation (A-2)**
**D.4 Measurand defined by the measurement
method; characterization of test methods; simple calibration**
**D.5 ***t*_{p} and the quantile
*t*_{1-α}
**D.6 Uncertainty and units of the SI; proper
use of the SI and quantity and unit symbols**
**D.7 References**

**D.5 ***t*_{p} and the quantile *t*_{1-α}
**D.5.1** As pointed out in the *Guide*, the *t*-distribution
is often tabulated in quantiles. That is, values of the quantile
*t*_{1-α} are given, where 1 - α denotes
the cumulative probability and the relation

defines the quantile, where *f* is the probability density function of
*t*. Thus *t*_{p} of this Technical Note and of the
*Guide* and *t*_{1-α} are related by
*p* = 1 - 2α. For example, the value of the
quantile *t*_{0.975}, for which
1 - α = 0.975 and α = 0.025, is the
same as *t*_{p}(ν) for *p* = 0.95, It should
be noted, however, that in reference [D.2] the
symbol *p* is used for the cumulative probability
1 - α, and the resulting *t*_{p}(ν) is called
the "quantile of order *p* of the *t* variable with ν
degrees of freedom." Clearly, the values of *t*_{p}(ν)
defined in this way differ from the values of *t*_{p}(ν)
defined as in this Technical Note and in the *Guide*, and given in
Table B.1 (which is of the same form as that
given in reference [10]). Thus, one must
use tables of tabulated values of *t*_{p}(ν) with some
care.