Statistical Treatment of Data

Most of the topics covered in this text are of interest to many others as well as to analytical chemists. Of these, however, statistical concepts are clearly the most generally applicable and widely encountered. For all experimental scientists, the evaluation of reliability of their results is of paramount interest. Except for pure numbers, numerical values are virtually meaningless when not accompanied by a specified estimate of their reliability. 

In addition to evaluation of new methods (how well do the analyses agree with each other as well as with older methods), or new people s ability to follow established methods (how well do student data agree with it), questions about the validity (i.e., representativeness) of samples must be addressed not only by analytical chemists, but all experimental scientists and engineers, by epidemiologists, marketers, journalists, politicians, and others interested in opinion surveys. 

Let us begin by defining some essential terms dealing with expressions of describing central tendency and scatter in data, of reliability, precision, and accuracy. 

In all measurements there are errors that may be determinate or indeterminate. Indeterminate errors are random errors that cannot be eliminated and are inherent in the analytical technique. When indeterminate errors are minimized, high precision is possible. Determinate errors are errors whose cause and magnitude can be determined. If the determi- 

As a supplemental approach to determine the linearity of calibration curves that span a wide concentration range, many analytical chemists replot the data on a log-log scale. Although that approach makes the data points at the lower end of the concentration scale easier to see, the data are displayed in a nonlinear system which distorts the patterns that existed in a linear scale.24 The tendency, however, is to interpret the curve using a linear scale, so log-log plots are easily misinterpreted. 

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The LIMS software is essentially a database for tracking, reporting, and archiving lab data as well as scheduling and guiding lab activities. Graphical and statistical treatment of data for improved process control (qv) as well as preparation of certificates of analysis (COA) for the customer are some of the other features of a comprehensive LIMS package (30). 

Ludwig KR (2003) Mathematical-statistical treatment of data and errors for °Th/U geochronology. Rev Mineral Geochem 52 631-636... 

Lovley D, Philhps EJP, Gorby YA, Landa ER (1991) Microbial reduction of itraniitm. Nature 350 413-416 Lowson RT, Short SA, Davey BG, Gray DJ (1986) " U/ U and °Th/ " U activity ratios in mineral phases of a lateritic weathered zone. Geochim Cosmochim Acta 50 1697-1702 Ludwig KR (2003) Mathematical-statistical treatment of data and errors for h/U geochronology. Rev Mineral Geochem 52 631-636... 

Mathematical-Statistical Treatment of Data and Errors for Th/U Geochronology... 

Helsel DR (1990) Less than obvious statistical treatment of data below the detection limit. Environm Sci Technol 24 1756... 

Statistical Treatment of Data. Each dose ratio point was the mean of three determinations. SrTly points between 20 and 80% on the dose response curves were utilized for the calculation of the dose ratio. After the dose was converted to a log value and the response to percent of the maximum, a best fit line was determined by linear regression. 

Helsel, D.R. (1990). Less than obvious-statistical treatment of data below the detection limits. Environ. Sci. Technol., 24 1766-1774. Helsel, D.R. and R.M. Hirsch (1992). Statistical Methods in Water Resources. New York Elsevier Science. 

There is statistical treatment of data generated from study. 

We will illustrate the use of the statistical treatment of data suspected of being expressed in the form y = a -t- bx with the data partially (there are actually 30 pairs of observations) given by... 

IAEA (1992) Statistical treatment of data on environmental isotopes in precipitation. IAEA, Technical Report Series no. 331, Vienna, 720pp. 

If the errors in the experimental parameters can be estimated or are known for a given experimental measurement, then the errors obtained in parameters from a specific experiment can be compared with these values and the quality of the results from a specific experiment evaluated. The known errors are designated ct(o). In the statistical treatment of data this is designated as the true standard deviation, while the standard deviation from a given experiment is designated with the symbol s or cr (ext). 

Reviews of the association of chemical and sensory aspects were published as early as 1965 by Wick and later, for instance, by Vernin (1981), who gave examples of odor-structure relationship. Different structures can be related to similar odors, similar structures to different odors, and similar structures to similar odors. A statistical treatment of data became necessary to correlate analytical results with those obtained by sensory analysis, as stated by Adda and Jounela-Eriksson (1979). Since then, correlation between sensory analysis and instrumental analysis has been the subject of important sessions of the Weurman Flavor Research Symposia, for instance in the chapters on Sensory science in flavor research (Weurman 5th Meeting, 1987) or Correlation between sensory and instrumental analysis (Weurman 7th meeting, 1993). 

Sweetness cannot yet be determined by chemical or instrumental means. Estimates of the relative sweetness of different substances remain dependent upon statistical treatment of data obtained subjectively by means of taste panels. Reduction of such results to practical application appears simple, but may indeed become illegitimate. 

Silver acetate dissolved in n-butyl amine was proposed as a coating (42). Although the reaction is irreversible, a linear calibration curve was obtained over the concentration range 10 ppb -10 ppm, and no statistical treatment of data was reported. 

These techniques often involve statistical treatment of data in a largely retrospective manner which is further limited by the arbitrary choice of common substructures, pharmacophores, binding points, and molecular overlays. In classical QSAR the limitations can be quite severe in that regressions are confined to a series of closely related structures often differing in relatively minor ways. More recent innovations Involve molecular shape analysis (13) and distance geometry methods (14). These techniques represent significant steps toward a true three-dimensional SAR with some predictive... 

Technometrics. Vol. 11, pp. 1-21. ISSN 0040-1706 Helsel, D.R. (1990).Less than obvious Statistical treatment of data below the detection limit. Environmental Science Technology. Vol. 24, pp. 1766-1774. ISSN 1520-5851... 

Health Canada and Environment Canada (1998) National ambient air quality objectives for particulate matter. Executive summary. Part 1 science assessment document. A report by the CEPA/FT AC Working Group on Air Quality Objectives and Guidelines. Public Works and Government Services Ottawa, ON, Canada, p 25 Helsel DR (1990) Less than obvious statistical treatment of data below the detection limit. Environ Sci Technol 24 1766-1774... 

Quantitative Analysis emphasis on standards preparation techniques statistical treatment of data environmental sampling techniques learning to operate the UV-vis spectrophotometer learning to operate the flame atomic absorption (A A) spectrophotometer no write-up required... 

Quantitative Analysis unknown sample analysis statistical treatment of data write-up required... 

The centerpiece of statistical treatment of data is the Gaussian Error function which gives mathematical expression for the behavior of random... 

No statistical treatment of data (usually only single values taken). 

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