Procedures for the statistical evaluation of method comparisons and Instrument tests often have a requirement for distributional properties of the experimental data, but this requirement is frequently not met. In our paper we propose a new linear regression procedure with no special assumptions regarding the distribution of the samples and the measurement errors. The result does not depend on the assignment of the methods (instruments) to X and Y. After testing a linear relationship between X and confidence limits are given for the slope and the intercept a; they are used to determine whether there is only a chance difference between and l and between and 0. The mathematical background is amplified separately in an appendix.