Some Statistical Aspects of the Calibration and Use of Linear Measuring Systems

Some statistical aspects of results obtained from a measuring system where the measurement might or might not be directly of the property of interest, but is at least linearly related to it, are described. The systems are restricted to those subject to calibration with known standards. It is shown that, because the system must be examined for two types of bias, neither a valid estimate of a sample property nor of its variance can be made if only a single standard is used. It is shown that, when more than one standard is used, the obvious estimate of the sample property is biased; an unbiased estimate is derived, as well as its variance. Testing the null hypotheses of no bias is described and equations to be used if these are accepted are given. The effect of accepting a null hypothesis which is not true has not been discussed.