Errors of Measurement, Precision, Accuracy and the Statistical Comparison of Measuring Instruments

A very important and yet widely misunderstood concept or problem in science and technology is that of precision and accuracy of measurement. It is therefore necessary to define the terms precision and accuracy (or imprecision and inaccuracy) clearly and analytically if possible. Also, we need to establish and develop appropriate statistical tests of significance for these measures, since generally a relatively small number of measurements will be made or taken in most investigations. In this paper a discussion is given of some of the pertinent literature for estimating variances in errors of measurement, or the “imprecisions” of measurement, when two or three instruments are used to take the same observations on a series of items or characteristics. Also, present techniques for comparing the imprecision of measurement of one instrument with that of a second instrument through the use of statistical tests of significance are reviewed, as well as procedures for detecting the significance of the difference in biases or levels of measurement of two instruments. Finally, we indicate methods of extending present theory to the case of three measuring instruments, for which rather sensitive statistical test of significance are developed for dealing with the precision and accuracy problem. An example for the three instrument case is given to illustrate the suggested methodology of analysis.