A Problem in the Statistical Comparison of Measuring Devices
Gerald J. Hahn, Wayne B. Nelson · Technometrics · 1970
The comparison of two measuring devices whose readings are subject to random variations involves 1) comparing their means to determine if they differ significantly and 2) comparing their variances to determine if they differ significantly. For the problem considered, the available data consist of one reading with one device and two additional independent readings with a second device on each of a number of units. An estimate of the difference in means can be readily obtained from the difference in the average readings for the two devices, and an estimate of the reading error variance for the second device is obtained from the differences in the two readings with that device. A method is also developed for estimating the reading error variance for the measuring device with only a single reading per unit. Procedures are given for testing hypotheses concerning the average difference in readings between the two devices, for testing the hypothesis that the reading error standard deviations are identical, for obtaining estimates of the standard deviations and for establishing confidence bounds. The methods are illustrated by an example and an extension of the problem is considered. Generalizations to situations where there are more measllrements by one or both of the devices are also discussed.