Statistical Evaluations

A statistical analysis of the data from an interlaboratory study cannot explain deviating results nor can it alone give any information on the accuracy of the results. Statistics only treat a population of the data and provide information on the statistical characteristics of this population. The results of the statistical treatment may raise discussions on particular data not belonging to the rest of the population, but outlying data can sometimes be closer to the true value than the bulk of the population [67]. 

In case a given protocol is to be followed, the statistical treatment should be applied only to the data which correspond strictly to the use of this protocol (e.g. standardized method). 

If no systematic errors affect the population of data, various statistical tests may be applied to the results, which can be treated either as individual data or as means of laboratory means. When different methods are applied, the statistical treatment is usually based on the mean values of replicate determinations. 

The statistical treatment involves tests, e.g. to assess the conformity of the distributions of individual results and of laboratory means to normal distributions (Kolmogorov-Smimov-Lilliefors tests), to detect outlying values in the population of individual results and in the population of laboratory means (Nalimov test), to assess the overall consistency of the variance values obtained in the participating laboratories (Bartlett test), and to detect outlying values in the laboratory variances (s ) (Cochran test). One-way analysis of variance (F-test) may be used to compare and estimate 

Together with the technical evaluation of the results, the statistical evaluation forms the basis for the conclusions to be drawn and the possible actions to be taken. 

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Gordus, A. A. Statistical Evaluation of Glass Data for Two Buret Readings, /. Chem. Educ. 1987, 64, 516-511. 

More fundamental treatments of polymer solubihty go back to the lattice theory developed independentiy and almost simultaneously by Flory (13) and Huggins (14) in 1942. By imagining the solvent molecules and polymer chain segments to be distributed on a lattice, they statistically evaluated the entropy of solution. The enthalpy of solution was characterized by the Flory-Huggins interaction parameter, which is related to solubihty parameters by equation 5. For high molecular weight polymers in monomeric solvents, the Flory-Huggins solubihty criterion is X A 0.5. 

Sulcer and Denson (Ref 19) used the gas chromatographic—B .T. procedure for the analysis of Class I A1 powder (45 u max dia) which cannot be tested satisfactorily by sedimentation methods because of the presence of aggregates. A rough statistical evaluation of this procedure was made by running twelve determinations and calculating the standard deviation as shown in Table 14 ... 

Figure 34. PMC lifetime map of n-type silicon/polymer (poly(epichlorhydrine-co-ethylenoxide-co-allyl-glycylether plus iodide) junction at -10 V potential (mostly dropping across the polymer layer), after Li+ insertion has changed the silicon interface. The statistical evaluation shows the drastic drop in the PMC lifetime. For color version please see color plates opposite p. 453.

Alternatively, the experimental error can be given a particular value for each reaction of the series, or for each temperature, based on statistical evaluation of the respective kinetic experiment. The rate constants are then taken with different weights in further calculations (205,206). Although this procedure seems to be more exact and more profoundly based, it cannot be quite generally recommended. It should first be statistically proven by the F test (204) that the standard errors in fact differ because of the small number of measurements, it can seldom be done on a significant level. In addition, all reactions of the series are a priori of the same importance, and it is always a... 

A systematic difference is found, supported by indirect evidence that from experience precludes any explanation other than effect observed. This case does not necessarily call for a statistical evaluation, but an example will nonetheless be provided in the elemental analysis of organic chemicals (CHN analysis) reproducibilities of 0.2 to 0.3% are routine (for a mean of 38.4 wt-% C, for example, this gives a true value within the bounds 38.0. .. 38.8 wt-% for 95% probability). It is not out of the ordinary that traces of the solvent used in the... 

Overall, the story shows that a manufacturer must go to extreme lengths to establish a satisfactory QA-network without the effort, statistical evaluations... 

Davies, P. L., Statistical Evaluation of Interlaboratory Tests, Fresenius Z. Anal. Chem. 331, 1988, 513-519. 

Porter, W. R., Proper Statistical Evaluation of Calibration Data, Anal. Chem. 55, 1983, 1290A (letter). 

Statistical evaluation shows that the experimental data are better correlated with Eqs. 7 and 8, i. e., an autocatalytic process, than with Eq. 9 although it is not possible to rule out the superposition of both mechanisms. 

All predictions must be taken for what they are, namely, generalizations based on current knowledge and understanding. There is a temptation for a user to assume that a computer-generated answer must be correct. To determine whether this is in fact the case, a number of factors concerning the model must be addressed. The statistical evaluation of a model was addressed above. Another very important criterion is to ensure that a prediction is an interpolation within the model space, and not an extrapolation outside of it. To determine this, the concept of the applicability domain of a model has been introduced [106]. 

Trone, M. D., Khaledi, M. G. Statistical evaluation of linear solvation energy relationship models used to characterize chemical selectivity in micellar electrokinetic chromatography. J. Chromatogr. A 2000, 886, 245-257. 

Evaluation of the results Evaluation of the results consists of (i) technical scrutiny of the consistency and of the quality of the data the acceptance, on technical (not statistical) grounds, of data to be used to calculate the certified value and its uncertainty, (2) the calculation (using the appropriate statistical techniques) of the certified value and its uncertainty. The approach indudes technical discussion of the results among all cooperators, rejection of outliers, statistical evaluation, and calculation of the certified value and uncertainties. 

Fig. 3-1 Data sets for Cu in CRM 482 Lichen accepted after the technical and statistical evaluation. The laboratory codes are indicated with the methods used (Quevauviller et al. 1996b).

Kurfurst U, Pauwels J, Grobecker KH, Stoeppler M, Muntau M (1993) Micro-heterogeneity of trace elements in reference materials - determination and statistical evaluation. Fresenius J Anal Chem 345 112-120. 

The homogeneity determination of the bacteria in the materials is performed by viable count followed by statistical evaluation of the cormts of sub-samples from the same capsule solution and of total counts of different capsules of one batch. An example for the homogeneity determination for a batch of capsules containing Enterococcus faecium is also presented in (Janning et al. 1995). 

Acute Toxicity. The LD50 following oral administration of parathion, either in propylene glycol solutions or in aqueous suspensions of the 15% wettable powder, has been determined for rats, mice, and guinea pigs. The lethal dose was approximated for rabbits and dogs. The results of these experiments are summarized in Table I. Statistical evaluation was by the method of Wilcoxon and Litchfield (11). 

In the following, the stages of the analytical process will be dealt with in some detail, viz. sampling principles, sample preparation, principles of analytical measurement, and analytical evaluation. Because of their significance, the stages signal generation, calibration, statistical evaluation, and data interpretation will be treated in separate chapters. 

The correction displayed is negligible relative to 1, in the macroscopic limit. The independence in the thermodynamic limit of the PDT on a choice of simulation ensemble used for statistical evaluation is a difference from the partition functions encountered in Gibbsian statistical thermodynamics. 

Pohl, E., F. Steinhausler, W. Hofmann, and J. Pohl-Ruling, Methodology of Measurements and Statistical Evaluation of Radiation Burden to Various Population Groups From All Internal and External Natural Sources, in Proceedings of Biological and Environmental Effects of Low-Level Radiation, International Atomic Energy Agency), Vol.II, pp. 305-315, Vienna, Austria (1976). 

Statistical evaluation of HPLC UV MS[19] and CE UV MS[20] methods proves that MS detection of anthraquinone dyes is more sensitive than UV, especially in the case of chromatographic analysis of laccaic acids (almost 20 times) and purpurin (almost 40 times). However, detection limits of HPLC ESI MS determination of alizarin and purpurin (0.03 gg ml ) are about 20 times lower than those of CE ESI MS (0.52 0.58 gg ml x). 

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