Uniformity test of bias when the reference value contains experimental error

The uniformity test of biases for analytical methods must address uncertainties in the reference method. If the uncertainty associated with the estimates of true values is significant but ignored in the test of bias equality, the type I error can exceed the prespecified error rate. In general, when biases at each concentration level are confounded with a random component (confounding bias), the usual test of bias equality tests the uniformity of the combined bias, rather than the uniformity of fixed bias-the bias without the random component. Based on a confounding model that takes both the fixed and the confounding biases into account, the actual type I error rate of the uniformity test can be calculated. To eliminate the impact of confounding bias on the uniformity test of fixed biases, a new F'-test is proposed. The new F'-test is simply adding a correction factor to the conventional F-test. The correction factor is directly related to the uncertainty associated with the estimates of true values. A simulation study is conducted to show that the proposed test can bring the type I error rate down to the prespecified level. Data from two aldehyde methods are used to demonstrate how the proposed F'-test works. Recommendations on optimal sample allocation are also provided.