Measurement Uncertainty
The Guide to the Expression of Uncertainty in Measurement (GUM) treads a fine line between two mainstream ways of statistical thinking and pragmatic measurement science. On the pragmatic side, the GUM assumes that a Gaussian distribution will adequately describe the uncertainty associated with a result. The standard uncertainty of x, written u(x), is the standard deviation of the Gaussian distribution describing values that could reasonably be assigned to the result x. The calculation of standard uncertainty described in the GUM, and implemented in GUM Tree designs, assumes that the measurement equation is nearly linear over the range of uncertainty associated with the input quantities. If not, the technique should not be used. This rules out equations such as
xm=x12
if the best estimate of x1 is close to the origin on the scale of u(x1),
for example.