Trueness statistics

When specifying atomic coordinates, interatomic distances etc., the corresponding standard deviations should also be given, which serve to express the precision of their experimental determination. The commonly used notation, such as d = 235.1(4) pm states a standard deviation of 4 units for the last digit, i.e. the standard deviation in this case amounts to 0.4 pm. Standard deviation is a term in statistics. When a standard deviation a is linked to some value, the probability of the true value being within the limits 0 of the stated value is 68.3 %. The probability of being within 2cj is 95.4 %, and within 3ct is 99.7 %. The standard deviation gives no reliable information about the trueness of a value, because it only takes into account statistical errors, and not systematic errors. 

II the difference approach, which typically utilises 2-sided statistical tests (Hartmann et al., 1998), using either the null hypothesis (H0) or the alternative hypothesis (Hi). The evaluation of the method s bias (trueness) is determined by assessing the 95% confidence intervals (Cl) of the overall average bias compared to the 0% relative bias value (or 100% recovery). If the Cl brackets the 0% bias then the trueness that the method generates acceptable data is accepted, otherwise it is rejected. For precision measurements, if the Cl brackets the maximum RSDp at each concentration level of the validation standards then the method is acceptable. Typically, RSDn> is set at <3% (Bouabidi et al., 2010),... 

International Organization for Standardization (ISO), Statistical methods for quality control, Vol. 2, 4th Edition, Accuracy (trueness and precision) of measurement methods and results - Part 2 Basic method for the determination of repeatability and reproducibility of a standard measurement method, ISO 1994(E), 5725-2. 

Includes all information on analytical quality control, such a precision clauses (repeatability and reproducibility data), table of statistical data outlining accuracy (trueness and precision) of method... 

Two aspects are important for IQC (1) the analysis of control materials such as reference materials or spiked samples to monitor trueness and (2) replication of analysis to monitor precision. Of high value in IQC are also blank samples and blind samples. Both IQC aspects form a part of statistical control, a tool for monitoring the accuracy of an analytical system. In a control chart, such as a Shewhart control chart, measured values of repeated analyses of a reference material are plotted against the run number. Based on the data in a control chart, a method is defined either as an analytical system under control or as an analytical system out of control. This interpretation is possible by drawing horizontal lines on the chart x(mean value), x + s (SD) and x - s, x + 2s (upper warning limit) and x-2s (lower warning limit), and x + 3s (upper action or control limit) and x- 3s (lower action or control limit). An analytical system is under control if no more than 5% of the measured values exceed the warning limits [2,6, 85]. 

Results verification is totally different from results validation. Results validation (point 4.7.5. and 5.9. of NBN-EN-ISO-CEI 17025 standard) shows, each year, or when it is judged necessary, that a given laboratory has the capacity to apply a particular method, repetitively, in respect of obtained data during initial validation. Trueness and statistical dispersion of results are the basis of the definition of the uncertainty of the standard of measurement [16] and, in some cases, the basis for the definition of the limit of detection and quantification. Management of data from validation results, as control card, could permit the detection and control of eventual deviation. Validation of results is the internal quality control procedure which verifies the stability of performance of the methods for which accreditation is sought, in the limited-scope procedural context. 

Precision may be defined as the closeness of agreement between independent results of measurements obtained under stipulated conditions.The degree of precision is usually expressed on the basis of statistical measures of imprecision, such as the SD or CV (CV = SD/x, where x is the measurement concentration), which thus is inversely related to precision. Imprecision of measurements is solely related to the random error of measurements and has. no relation to the trueness, of measurements. 

The validation has the objective to identify, during the method development process, all sources of error and eliminate them or to quantify their contribution to the total uncertainty of the determination. For trace organic determinations particular attention must be given to the quantitative extraction and clean-up of all PCBs. Several types of adapted materials must be prepared to test all steps of the process (from simple calibrant solutions or mixtures, spiked extracts, to spiked soil material). CRMs should be used for validating trueness. Laboratory RMs must be prepared for the establishment of control charts when the method is under statistical control. 

X" table values can be found in the tables given in all statistical textbooks. If the precision is sufficient, it is worthwhile to verify the degree of trueness of the method. 

As already mentioned, the main advantage of CRMs lies in the availability of the true value . In other words, it is a reference value that is considered as the best estimate analytical sciences can give for the real content of the substance in the particular material. As such CRMs represent the only way to check trueness easily. The verification of trueness will consist in a statistical comparison of the value determined by the operator on the CRM and the certified value. Again it must be stressed that this has no sense if the method s precision is too large. The trueness of a method can be verified within the laboratory or through an interlaboratory study, in particular when a reference standard or an official method is concerned. 

International Organization for Standardization (ISO) (1994(E)) Statistical methods for quality control, Accuracy (trueness and precision) of measurement... 

These experiments are designated as phases II and III of a method validation or an analyst familiarization for those using the approach recommended in the USDA/FSIS Chemistry Laboratories Guidebook (see QA section of the posted methods)7 The results provide an assessment of the recovery (trueness) and the analyst precision attained with the method under routine conditions of use. In addition, the data generated may be used to calculate statistical estimates of the reliability of the results, including estimates of MU. i ... 

Trueness Trueness is measured in terms of the systematic error (bias) in a measurement result and is the difference between a result obtained by the analyst and the true value of the measurand. For a measurement result, which is the mean of a series of analyses carried out within a single run, the bias so defined has three components, arising from the method, the laboratory, and the particular run. Assuming the method is in statistical control, the within run variation should be from a normal population with expectation zero. Figure 3 shows these contributions to trueness. It would also be hoped that the laboratory could achieve a zero run bias. The systematic effect from the laboratory and method combined can be measured by analyzing a certified reference material (CRM) at least 10 times in several runs (assuming such material is available). 

In addition, information about precision and trueness may also be gained by using statistical tests for trends in control measurements [31]. 

A potentially more appropriate statistical tool, the Durbin-Watson statistic [29], can be used to assess the linearity of the NIR quantitative method. This statistic allows the analyst to establish the lack of intercorrelation between data points in the regression. The correlation coefficient R only describes the tendency of the line, not the trueness cffit to a linear model. If there is no intercorrelation of the residuals described by the Durbin-Watson statistic, then a linear model is appropriate and may be used. 

---