Evaluation between Statistical Methods Related to the z Score for Use in Proficiency Testing

In this paper, we propose two evaluation tools to understand statistical methods related to the z score for use in proficiency testing by interlaboratory comparisons. In the case that the distribution of the test result in the laboratory proficiency testing with a single test item is different from the normal distribution, we propose a new method of the z score based on the lognormal distribution. Because the criteria based on the normal distribution can be adjusted in this case, this technique can be similarly used in interlaboratory comparisons based on two examination materials. When a laboratory uses a method, control charts offer an easy way to keep a running check on work. We consider the simultaneous control of two related variables. For repeatedly performed interlaboratory comparison tests, the Youden approach may provide a useful solution. The simple principle is to test only two nearly identical samples and to compare the difference. However, in many cases there is a large difference in the concentration in examinations that use two examination materials. In such a situation, we consider an alternative approach. We suggest that two variables in which the relations between new variables that measure the bias between laboratories and within laboratory become no correlations are converted. We make a new orthogonal coordinate system. After converting these variables, we construct a new z score on the newly defined orthogonal coordinate system. This z socre is closely related to the control ellipse on the Youden plot.