Statistical techniques analysis

For the analysis of data the laboratory shall employ appropriate statistical techniques. Analysis of the data can help to determine the root canse of existing or potential problems, and therefore indicate the corrective and preventive actions needed for improvement. 

Graham R C 1993. Data Analysis for the Chemical Sciences. A Guide to Statistical Techniques. New York, VCH Publishers. 

Moore, D. S., Statistics Concepts and Controversies, W. H. Freeman, New York, 1985. MuUiolland, H., and C. R. Jones, Fundamentals of Statistics, Plenum Press, New York, 1968. Taylor, J. K., Statistical Techniques for Data Analysis, Lewis, Boca Raton, FL, 1990. 

What statistical techniques are required for the analysis of the resulting data, and can these tools be rapidly brought to bear after the experiment has been conducted ... 

The use of various statistical techniques has been discussed (46) for two situations. For standard air quality networks with an extensive period of record, analysis of residuals, visual inspection of scatter diagrams, and comparison of cumulative frequency distributions are quite useful techniques for assessing model performance. For tracer studies the spatial coverage is better, so that identification of meiximum measured concentrations during each test is more feasible. However, temporal coverage is more limited with a specific number of tests not continuous in time. 

Statistical techniques can be used for a variety of reasons, from sampling product on receipt to market analysis. Any technique that uses statistical theory to reveal information is a statistical technique, but not all applications of statistics are governed by the requirements of this part of the standard. Techniques such as Pareto Analysis and cause and effect diagrams are regarded as statistical techniques in ISO 9000-2 and although numerical data is used, there is no probability theory involved. These techniques are used for problem solving, not for making product acceptance decisions. 

Market analysis - a technique for establishing product characteristics where the customer requirements are revealed by market survey and determined by statistical techniques for inclusion in specifications. 

Sec. 820.50 Statistical techniques - Use appropriate statistical methods for data analysis and... 

Prediction of the useful life, or the remaining life, of coatings from physical or analytical measurements presents many problems in data analysis and interpretation. Two important considerations are that data must be taken over a long period of time, and the scatter from typical paint tests is large. These considerations require innovative application of statistical techniques to provide adequate prediction of the response variables of interest. 

The precision of time series predictions far into the future may be limited. Time series analysis requires a relatively large amount of data. Precautions are necessary if the time intervals are not approximately equal (9). However, when enough data can be collected, for example, by an automated process, then time series techniques offer several distinct advantages over more traditional statistical techniques. Time series techniques are flexible, predictive, and able to accommodate historical data. Time series models converge quickly and require few assumptions about the data. 

Since that time thousands of QSARs, covering a wide and diverse range of end points, have been published [9] most of these have used MLR, but numerous other statistical techniques have also been used, such as partial least squares, principal component analysis, artificial neural networks, decision trees, and discriminant analysis [f4]. 

This approach did not seem to be as satisfactory for those sulfamates having heteroatom substituents (hetero-sulfamates). Spillane suggested that the various electronic effects of the hetero-atoms probably introduce an additional variable that is apparently absent, or constant, for the carbosulfamates. Because molecular connectivity correlates structure with molecular volume and electronic effects, Spillane included molecular connectivity, (computed for the entire molecule, RNHSOO to the four variables, x, y, z, and V, and applied the statistical technique of linear-discrimination analysis to 33 heterosulfamates (10 sweet, 23 not sweet). A correlation of >80% was obtained for the x, z, x subset 5 of the 33... 

The design of this fish study centered on sample collection, preservation, preparation, analysis, and QA/QC. There was no discussion of the effect of compositing on the sample population. No description was given of statistical techniques to be applied to the data for reporting results and for comparison with action levels and future data. Unfortunately, the omission of a statistical framework during planning of the field study is the rule rather than the exception in hazardous waste investigations. 

Factor analysis is a statistical technique that has been used to interpret numerous types of data. Hamer (1989), Rastogi et al. (1990, 1991, 1992), Fotopoulos et al. (1994), and Bonvin and Rippin (1990) have used it successfully for the identification of stoichiometries of complex reactions. The technique is applied to Eqn. (A-1) which are rewritten in matrix form ... 

However, there is a mathematical method for selecting those variables that best distinguish between formulations—those variables that change most drastically from one formulation to another and that should be the criteria on which one selects constraints. A multivariate statistical technique called principal component analysis (PCA) can effectively be used to answer these questions. PCA utilizes a variance-covariance matrix for the responses involved to determine their interrelationships. It has been applied successfully to this same tablet system by Bohidar et al. [18]. 

H.A. Guess and K.S. Crump. "Low Dose Extrapolation of Data from Animal Carcinogenicity Experiments - Analysis of a New Statistical Technique." Math. Biosciences, 32, 1976, pp. 15-36. 

Examples of statistical analysis for QSAR developing using different techniques is given in Table 2 that shows the prediction of the Daphnia magna toxicity for allelochemicals (BOA, DIMBOA and MBOA) using QSARs models obtained with different statistical techniques (PLS, MLR, and Neural Networks). 

To understand these processes and correlate residue profiles with specific toxic responses required congener-specific methods of analysis and complex statistical techniques (principal component analysis). Using these techniques, it was established that eggs of Forster s terns of two colonies differed significantly in PCB composition (Schwartz and Stalling 1991). Similar techniques were used to identify various PCB-contaminated populations of harbor seals (Phoca vitulina) in Denmark (Storr-Hansen and Spliid 1993). 

Scaife, B., Budd, P., McDonnell, J.G., Pollard, A.M. and Thomas, R.G. (1996). A new statistical technique for interpreting lead isotope analysis data. In Archaeometry 94. Proceedings of the 29th International Symposium on Archaeometry, ed. Demirci, ., Ozer, A.M. and Summers, G.D., Tubitak, Ankara, pp. 301-307. 

The training of most pathologists in statistics remains limited to a single introductory course which concentrates on some theoretical basics. As a result, the armertarium of statistical techniques of most toxicologists is limited and the tools that are usually present (t-tests, chi-square, analysis of variance, and linear regression) are neither fully developed nor well understood. It is hoped that this chapter will help change this situation. 

The application of statistical techniques generally requires somewhat tedious calculations. The analysis of results to make predictions is likely to involve curve fitting and the... 

Linear regression analysis is a statistical technique to determine the equation for the straight line that best describes the relationship between two variables. 

Monte Carlo—A statistical technique commonly used to quantitatively characterize the uncertainty and variability in estimates of exposure or risk. The analysis uses statistical sampling techniques to obtain a probabilistic approximation to the solution of a mathematical equation or model. 

However, the graphical approach is not appropriate for finding the absolute accuracy between more than two properties. The well-established statistical technique of regression analysis is more pertinent to determining the accuracy of points derived from one property and any number of other properties. There are many instances in which relationships of this sort enable properties to be predicted from other measured properties with as good precision as they can be measured by a single test. It would be possible to examine in this way the relationships between aU the specified properties of a product and to establish certain key properties from which the remainder could be predicted, but that would be a tedious task. 

This paper describes the use of statistical techniques to improve precision in routine chemical analysis at a modest extra cost and to measure the precision of such analyses. 

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