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Figure 4: Overview of Z scores of FDA PT: Arsenic in Apple Juice 3/14 eFOOD-Lab international 11 feedback regarding analytical competence within analytical peer group (identical method, identical equipment) and between different types of equipment and different analytical methods. The following example illustrates two ways of presenting results in a PT performed by the German BVL, Manganese in green cabbage. In this example participants used one of two methods, and the results for AES/ICP turned out to be lower than the results for ICP/MS. The same results can also be used to examine whether the analytical methods can be considered equivalent or not, see Figure 2. In this test on equivalence, two aspects are considered, (1) whether results are significantly different and (2) whether the difference is significantly lower than a maximum tolerance limit. PTs can also be used to give updates of bias and precision data by country, method and sector. In addition, PTs can be used to characterize the measurement uncertainty of the overall mean and to derive the reference value of a test material. ProLab Plus, the PT software package, provides a number of statistical methods which conform to the prescriptions of several international standards to do just this. Z scores PT data can also be used to derive z scores. Z scores make it possible to identify deviating results and represent the standardized deviation between the test result x of the participant and the assigned value m: z = (x-m)/s, where s = target standard deviation. As different PT programs differ in the determination of the assigned value m and the target standard deviation s, z scores from different PT programs are not always comparable. This is demonstrated in the following figure (Aluminum in green cabbage, BVL). Variability was relatively high, so that the robust standard deviation based on Q/Hampel is clearly higher than the Horwitz standard deviation. The consequence is that the absolute value of z scores based on Horwitz are 1.7 times higher than that of z scores calculated with Q/Hampel. In this example, the Horwitz standard deviation leads to 6 out of 23 participants having unsatisfactory z scores (marked yellow and red), whereas the more realistic Q/Hampel standard deviation leads to only one laboratory lying outside the limits. This example demonstrates that it is crucial to use harmonized methods for the calculation of assigned value and target standard deviation. It is recommended to apply highly robust and efficient statistical methods for the calculation of assigned value and target standard deviation (e.g. Q/Hampel method - to come in the revised version of ISO 13528) in order to avoid misleading z scores: z < -2: significant deviation (too low) -2 < z < 2: no significant deviation z > 2: significant deviation (too high) “Significant deviation” means that something in the measurement process of the participant is different from the majority of the labs. Z scores can be used not only to assess the analytical competence of participants but also in order to provide an overview of results across analytes and samples, as illustrated in the following figure. Displaying deviations across laboratories, samples and analytes can provide information as to error correlation and possible reasons for bias, e.g. detection method, sample preparation etc. The same data can also be used to assess the random component and the systematic component of the lab bias across samples and analytes, as illustrated in Figure 5. The RSZ parameter is a measure of the systematic bias across samples and analytes, and thus provides information which the individual z scores, considered in and of themselves, do not reveal. Similarly, the RLP is a measure of a laboratory’s random error across samples and analytes: the Figure 5: Combination scores RLP and RSZ in PT: Arsenic in apple juice; US-FDA. Each number represent one participant. Results are satisfying or better if they are in the green rectangle.


eFOODLab_International_03_2014
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