ABSTRACT
Experience shows that it is practically impossible to measure exactly the true
value of a physical quantity. This is because various imperfections occur at
various stages involved in a measurement, including uncontrollable experimen-
tal errors, inaccurate standards, and other uncertainties arising in the data
measurement and interpretation (reduction) process. Around any reported
experimental value, therefore, there always exists a certain range of similar,
more or less plausible, values that may also be true. In turn, this means that
all inferences, predictions, engineering computations, and other applications of
measured data are necessarily founded on weighted averages over all the possi-
bly true values, with weights indicating the degree of plausibility of each value.
These weights and weighted averages are what we call probabilities and ex-
pectation values. Consequently, the evaluation of scientific data is intrinsically
intertwined with probability theory. The basic types of errors and probability
distributions usually associated with them will be presented in Section 1.1.