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.