Statistical Terms and Data Handling

Standardized long-term measurements provide reliable information on statistical behavior of atmospheric aerosols, far beyond what could be obtained in short-term campaign-wise measurements. Although data from a period of only two years is shown, the results already provide a previously unavailable variety of information on the sub-micron aerosol physical properties and variability in Europe. Such information would also be hard to achieve based on information collected from separately managed stations, especially if the instrumentation and data handling are not harmonized. 

This text aims at a sfightly different need that lies beyond the basic use of chromatographic instrumentation. The commonplace use of chromatographic techniques in analyzing regulated products places an additional burden on the analyst the proficient use of the basic data-handling terms is also expected. Therefore, the definitions of some fundamental statistical terms and concepts are included. 

Consideration of the results from a simple multi-element analysis will serve to illustrate terms and parameters associated with the techniques used. This example will also introduce some features of matrix operators basic to handling multivariate data. In the scientific literature, matrix representation of multivariate statistics is common. For those readers unfamiliar with the basic matrix operations, or those who wish to refresh their memory, the Appendix provides a summary and overview of elementary and common iriatrix operations. 

Although the steps in solving analytical problems usually follow the order listed above, knowledge of basic statistics is useful not just for handling the data and method validation but is required for proper sampling and selection of an analytical method. The statistics and definitions needed to understand what is meant by accuracy, precision, error, and so on are covered in Section 1.3. Students not familiar with these terms and concepts may want to read Section 1.3 at this point. Steps (1) and (2) are covered in this section, while steps (3) through (5) are discussed in the sections following Section 1.3. 

The systematic study of electrolyte solutions by van t Hoff and Arrhenius (1887) established physical chemistry as a scientific discipline. Electrolytes are important not only in solution chemistry and in the chemistry of electrode processes, but also in geochemistry and oceanography and in many areas of biophysics and biochemistry. Salt solutions , as they are often referred to by chemists, are ubiquitous they are easily handled in the laboratory and their properties accurately measured. Reams of experimental data on these solutions have been collected but their explanation and correlation in terms of the molecular (or microscopic) properties of the system continue to present major challenges to theoretical chemists. This has also lead to the formulation of sophisticated new techniques in statistical mechanics and the extensive use of computer simulation to study ionic fluids. 

Once the regulatory submission has been made there will inevitably be questions and issues coming back from the regulators. There may be concerns about the way the data has been handled from a statistical point of view. There may be requests for additional specific analyses to resolve uncertainty. There may be more open issues that the regulators are unhappy with which may require a substantial amount of further analysis. At the extreme end there may be outright rejection and the company may then be back to the drawing board in terms of the product. In all of these cases there will usually be a need for further statistical considerations. 

Numerous problems remain to be solved before it will be possible to quantify the sensitivity of explosives to impact and friction in terms that express an intrinsic property of the chemical substances. The need for more refined tests, a better understanding of the phenomena that occur during the test procedures, and improved statistical approaches to the treatment of low-probability events are paramount requirements for more meaningful data. Even then it will continue to be difficult to relate measurements in laboratory apparatus to the conditions encountered in the industrial handling and field utilization of azides. 

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