Statistical methods bivariate analysis

The goal of EDA is to reveal structures, peculiarities and relationships in data. So, EDA can be seen as a kind of detective work of the data analyst. As a result, methods of data preprocessing, outlier selection and statistical data analysis can be chosen. EDA is especially suitable for interactive proceeding with computers (Buja et al. [1996]). Although graphical methods cannot substitute statistical methods, they can play an essential role in the recognition of relationships. An informative example has been shown by Anscombe [1973] (see also Danzer et al. [2001], p 99) regarding bivariate relationships. 

Statistical methods for assessing bivariate data (two dimensional data where one parameter is measured as a function of another) are used to performr ression analysis of calibration data and to determine the goodness of fit of the calibration curve. A simple, linear equation is desirable when fitting quantitative calibration data for several reasons i) only two fitting parameters (A = intercept and B = slope) need to be calculated ii) it is straightforward to invert the equation so as to calculate an unknown value of x (e.g., analyte concentration) from a measured value of Y (e.g. mass spectrometer response), i.e. Xj = (Yj —A)/B and iii) relatively few experimental measurements (Xj,Yj) are required to establish reliable values of A and B in the catibration equation... 

The NAA method for the determination of firearm discharge residue has been generally accepted, but applications have been limited to just a few laboratories. In the process of establishing NAA capability for the State of Illinois crime laboratories we re-examined the standard techniques (10). In the course of our work it became clear that post-irradiation is the cause of several constraints which have discouraged a more widespread use of NAA. The inherent time limitation due to the 87 min. half-life of 139Ba necessitates fast manipulations of radioactive solutions which in turn requires an experienced radiochemist. In addition to an ever present danger of overexposure and contamination, typically only a dozen samples can be irradiated per batch, which makes the method quite expensive. The developed statistical bivariate-normal analysis (11) is convenient for routine applications. With this in mind, a method was developed which a) eliminates post-irradiation radiochemistry and thus maximizes time for analysis b) accommodates over 130 samples per irradiation capsule (rabbit) c) does not require a collection of occupational handblanks and d) utilizes a simplified statistical concept based on natural antimony and barium levels on hands for the interpretation of data. The detailed procedure will be published elsewhere (15). 

Statistical indices are fundamental numerical quantities measuring some statistical property of one or more variables. They are applied in any statistical analysis of data and hence in most of Q S AR methods as well as in some algorithms for the calculation of molecular descriptors. The most important univariate statistical indices are indices of central tendency and indices of dispersion, the former measuring the center of a distribution, the latter the dispersion of data in a distribution. Among the bivariate statistical indices, the correlation measures play a fundamental role in all the sciences. Other important statistical indices are the diversity indices, which are related to the injbrmationcontentofavariahle,the —> regressiowparameters, used for regression model analysis, and the —> classification parameters, used for classification model analysis. 

The main example of bivariate statistics in this book involves simple linear regression and its application to calibration of the response of an analytical instrument with respect to concentration (or amount) of a target analyte values of the dependent variable (e.g., instrument response) are recorded as a function of an experimental (independent) variable (e.g., amount of analyte injected) under fixed instrumental conditions the most useful circumstance involves a linear relationship between the two, and the relevant statistical approach is linear regression analysis (Sections 8.3.2 and 8.3.5). Another example would involve a series of repeated analyses of the same sample (typically a laboratory QC sample) as a function of the time (date) of analysis, as a monitor of stability and reproducibihty of the instrument or complete analytical method. 

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