Applied statistics univariate analysis

More sophisticated statistical treatments of sensory data have been more commonly applied in studies of multiple factors of Upid oxidation on quality of foods, including Multivariate and Principal Component analyses. These procedures attempt to simplify complex relationships of several factors and sets of data into more understandable levels. Multivariate analysis is based on the fact that one measured property generally depends on more than one factor and the classical statistical univariate methods dealing with just one variable at a time are inadequate to analyse complex data. 

Principal Component Analysis (PCA) is performed on a human monitoring data base to assess its ability to identify relationships between variables and to assess the overall quality of the data. The analysis uncovers two unusual events that led to further investigation of the data. One, unusually high levels of chlordane related compounds were observed at one specific collection site. Two, a programming error is uncovered. Both events had gone unnoticed after conventional univariate statistical techniques were applied. These results Illustrate the usefulness of PCA in the reduction of multi-dimensioned data bases to allow for the visual inspection of data in a two dimensional plot. 

Data have been collected since 1970 on the prevalence and levels of various chemicals in human adipose (fat) tissue. These data are stored on a mainframe computer and have undergone routine quality assurance/quality control checks using univariate statistical methods. Upon completion of the development of a new analysis file, multivariate statistical techniques are applied to the data. The purpose of this analysis is to determine the utility of pattern recognition techniques in assessing the quality of the data and its ability to assist in their interpretation. 

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. 

A combination of univariate statistics and plots allow exploration of a candidate model relative to these last two requirements. Bacterial bioluminescence 15-minute EC50 data for 20 metal ions (McCloskey et al. 1996, Appendix 8.1) and the recently developed softness index (Kinraide 2009) can be applied to illustrate this approach. The following statistical analysis system (SAS) code implements analyses with normality plots and tests of regression residuals (Figure 8.1 top). It also plots predicted and observed data (Figure 8.1 middle) and regression residuals versus the explanatory variable, 0, 0 (Figure 8.1 bottom). 

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