Comparison of alternative measurement methods: determination of the minimal number of measurements required for the evaluation of the bias by means of interval hypothesis testing

The classical approach of hypothesis testing for the detection of bias has a major disadvantage in that the risk of adopting a method that has an unacceptable bias is not well controlled. To control this risk, interval hypothesis testing was introduced in method validation [S. Kuttatharmmakul, D.L. Massart, J. Smeyers-Verbeke, Anal. Chim. Acta, 391 (1999) 203; C. Hartmann, J. Smeyers-Verbeke, W. Penninckx, Y. Vander Heyden, P. Vankeerberghen, D.L. Massart, Anal. Chem., 67 (1995) 4491]. However, the application of interval hypothesis testing in the evaluation of bias can lead to the false rejection of a method, which, in reality, has an acceptable bias. To limit this risk (of false rejection), an appropriate number of measurements is required. Formulae to determine this sample size are proposed. However, the required number of measurements depends on the precision of the analytical method(s), the bias that analysts are prepared to accept with a high probability and the risk that one is willing to take of incorrectly rejecting a method that has an acceptable bias. An evaluation of the equations proposed was undertaken by means of simulations. liability of the formulae proposed depends on the quality of the precision estimates used in the formulae. When the precision estimates applied correspond well with the true precision parameters, the sample size determined assures that the risk of incorrectly rejecting the alternative method that has an acceptable bias does not exceed the specified level. When the true precision is worse than the precision estimates used in the formulae, the probability that a method with an acceptable bias will be rejected is much higher than the specified level.