Statistical Evaluation of Analytical Results

Both qualitative observations and quantitative measurements cannot be reproduced with absolute reliability. By reason of inevitable deviations, measured results vary within certain intervals and observations, mostly in form of decision tests, may fail. The reliability of analytical tests depends on the sample or the process to be controlled and the amount of the analyte, as well as on the analytical method applied and on the economical expenditure available. 

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Several overall conclusions can be drawn based on the statistical evaluation of the data submitted by the participants of the DR CALUX intra-and interlaboratory validation study. First, differences in expertise between the laboratories are apparent based on the results for the calibration curves (both for the curves as provided by the coordinator and for the curves that were prepared by the participants) and on the differences in individual measurement variability. Second, the average results, over all participants, are very close to the true concentration, expressed in DR CALUX 2,3,7,8-TCDD TEQs for the analytical samples. Furthermore, the interlaboratory variation for the different sample types can be regarded as estimates for the method variability. The analytical method variability is estimated to be 10.5% for analytical samples and 22.0% for sediment extracts. Finally, responses appear dependent on the dilution of the final solution to be measured. This is hypothesized to be due to differences in dose-effect curves for different dioxin responsive element-active substances. For 2,3,7,8-TCDD, this effect is not observed. Overall, based on bioassay characteristics presented here and harmonized quality criteria published elsewhere (Behnisch et al., 2001a), the DR CALUX bioassay is regarded as an accurate and reliable tool for intensive monitoring of coastal sediments. 

Similar to the PARCC parameters, acceptance criteria are expressed in qualitative and quantitative terms. Some of them are statistically derived values, while others are purely qualitative and represent industry standards and accepted practices. Quantitative parameters (precision, accuracy, and completeness) are evaluated mathematically and compared to numerical acceptance criteria representativeness, which is a qualitative parameter, is established by comparing documented field and laboratory procedures to applicable standards and specifications. Comparability is estimated as the closeness of analytical results obtained at two different laboratories, and is usually expressed qualitatively. In environmental project work, acceptance criteria for the PARCC parameters are documented in the SAP. 

The availability of fast, cheap and accessible data processing is encouraging analysts to employ standard statistical evaluation of results, which previously have been very time-consuming to undertake, and to explore new ways of extracting the maximum amount of chemical information from the analytical data. This last is a... 

If an ALMERA member wants to keep the evaluation result of his/her participation anonymous, he/she will have the option to only take part in the IAEA world-wide open proficiency test. In this case, his/her results will not be included in the ALMERA report. In addition, the statistical approach used to evaluate the analytical results of the ALMERA network proficiency test will be adapted in the future to take the reporting time into consideration. 

In analytical sciences, measurement uncertainty narrows down the differences between the actual measured value and the true value of a concentration of analyte. The actual measured value consists of two parts, the estimate of the true value and uncertainty associated with this estimation. Uncertainty of measurement is made of every component that is critical to the measured value, some of which may be evaluated from statistical distribution of the results of a series of measurements and can be characterised by standard deviations. The actual measured value does not coincide with the true value and may be considered as an estimate that may be larger or smaller than the true value. This is not an error but rather an inherent part of any measurement. Hence it is true to state that ... 

The last type of precision study is reproducibility (q.v.), which is determined by testing homogeneous samples in multiple laboratories, often as part of interlaboratory crossover studies. The evaluation of reproducibility results often focuses more on measuring bias in results than on determining differences in precision alone. Statistical equivalence is often used as a measure of acceptable interlaboratory results. An alternative, more practical approach is the use of analytical equivalence, in which a range of acceptable results is chosen before the study and used to judge the acceptability of the results obtained from the different laboratories. 

The aims of a particular scheme should be described by the coordinator of the EQAS. In principle, the coordinator of a scheme on a regular basis distributes sample(s) to the participants. The laboratory measures the sample(s) and within a given time reports the resultfs) to the organizing laboratory or coordinator, which carries out the statistical analysis of the results. Afterward, the participating laboratories receive an evaluation report of their analytical performance in comparison with the other participants. The typical structure of the scheme is as follows (1) preparation of samples (2) distribution of samples (3) analysis of samples and submission of results and (4) statistical analysis of results and performance characteristics assessed. 

One of the most important properties of an analytical method is that it should be free from systematic error. This means that the value which it gives for the amount of the analyte should be the true value. This property of an analytical method may be tested by applying the method to a standard test portion containing a known amount of analyte (Chapter 1). However, as we saw in the last chapter, even if there were no systematic error, random errors make it most unlikely that the measured amount would exactly equal the standard amount. In order to decide whether the difference between the measured and standard amounts can be accounted for by random error, a statistical test known as a significance test can be employed. As its name implies, this approach tests whether the difference between the two results is significant, or whether it can be accounted for merely by random variations. Significance tests are widely used in the evaluation of experimental results. This chapter considers several tests which are particularly useful to analytical chemists. 

The raw data collected during the experiment are then analyzed. Frequently the data must be reduced or transformed to a more readily analyzable form. A statistical treatment of the data is used to evaluate the accuracy and precision of the analysis and to validate the procedure. These results are compared with the criteria established during the design of the experiment, and then the design is reconsidered, additional experimental trials are run, or a solution to the problem is proposed. When a solution is proposed, the results are subject to an external evaluation that may result in a new problem and the beginning of a new analytical cycle. 

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