A Method of Fitting Several Linear Functional Relations and of Testing for Differences between Them

J. Taylor

Journal of the Royal Statistical Society Series C, 1973, vol. 22, issue 2, 239-248

Abstract: The relation between readings on two instruments may be represented by a linear functional relation with errors of observation in both variables. We may compare a number of instruments under test with a standard. This paper describes a method of simultaneously fitting all the relations, and of testing whether they are parallel lines or a single line, in the case in which some replicate observations are available for each instrument. Maximum‐likelihood estimates are used. A simulation investigation has shown that the slopes are estimated with little bias in small experiments. The asymptotic estimates of the variances of slopes are usually underestimates. Differences between slopes and origins may be tested using likelihood ratios, but it is recommended that χ2 tests on these should be done with nominal significance levels of one‐half of the desired level.

Date: 1973
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