Statistical univariate methods

While in classical statistics (univariate methods) modelling regards only quantitative problems (calibration), in multivariate analysis also qualitative models can be created in this case classification is performed. 

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. 

Univariate methods are among the simplest and most commonly used methods that compose a broad family of statistical approaches. Based on... 

The most commonly employed univariate statistical methods are analysis of variance (ANOVA) and Student s r-test [8]. These methods are parametric, that is, they require that the populations studied be approximately normally distributed. Some non-parametric methods are also popular, as, f r example, Kruskal-Wallis ANOVA and Mann-Whitney s U-test [9]. A key feature of univariate statistical methods is that data are analysed one variable at a rime (OVAT). This means that any information contained in the relation between the variables is not included in the OVAT analysis. Univariate methods are the most commonly used methods, irrespective of the nature of the data. Thus, in a recent issue of the European Journal of Pharmacology (Vol. 137), 20 out of 23 research reports used multivariate measurement. However, all of them were analysed by univariate methods. 

However, by definition, these univariate methods of hypothesis testing are inappropriate for multispecies toxicity tests. As such, these methods are an attempt to understand a multivariate system by looking at one univariate projection after another, attempting to find statistically significant differences. Often the power of the statistical tests is quite low due to the few replicates and the high inherent variance of many of the biotic variables. 

The tools of chemometrics encompass not only the familiar (univariant) methods of statistics, but especially the various multivariant methods, together with a package of pattern-recognition methods for time-series analyses and all the known models for signal detection and signal processing. Chemometric methods of evaluation have now become an essential part of environmental analysis, medicine, process analysis, criminology, and a host of other fields. 

The overall objective of the system is to map from three types of numeric input process data into, generally, one to three root causes out of the possible 300. The data available include numeric information from sensors, product-specific numeric information such as molecular weight and area under peak from gel permeation chromatography (GPC) analysis of the product, and additional information from the GPC in the form of variances in expected shapes of traces. The plant also uses univariate statistical methods for data analysis of numeric product information. 

In this chapter, we provide a general overview of the field of chemometrics. Some historical remarks and relevant literature to this subject make the strong connection to statistics visible. First practical examples (Section 1.5) show typical problems related to chemometrics, and the methods applied will be discussed in detail in subsequent chapters. Basic information on univariate statistics (Section 1.6) might be helpful to understand the concept of randomness that is fundamental in statistics. This section is also useful for making first steps in R. 

This paper presents a method to decide the handling of seemingly Inconsistent data (outliers). The univariate and multivariate methods recommended are strongly based on statistics and the experience of the author In using them. 

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. 

In other words, the application of univariate statistical methods to multivariate data often results in a considerable loss of information and, hence, a loss of power. This is because the assumptions on which the univariate analysis rely are seldom fulfilled (for example, independence between variables). 

Multivariate statistical methods should be preferred for evaluating such multidimensional data sets since interactions and resulting correlations between the water compounds have to be considered. Fig. 8-1, which shows the univariate fluctuations in the concentrations of the analyzed compounds, illustrates the large temporal and local variability. Therefore in univariate terms objective assessment of the state of pollutant loading is hardly possible. 

Sediment analyses are useful for characterization of pollution over a long period [MULLER, 1981]. Assessment of the state of a river and of the interactions between the components can be made by application of multivariate statistical methods only, because the strongly scattering territorial and temporal courses [FORSTNER and MULLER, 1974 FORSTNER and WITTMANN, 1983] are not compatible with many univariate techniques. FA shall serve as a tool for the recognition of variable structures and for the differentiated evaluation of the pollution of both river water and sediment [GEISS and EINAX, 1991 1992],... 

The state of pollution of the soil can be more objectively described by means of geostatistical methods. The computation of semivariograms and the use of kriging uncover spatial structures which are not discernible by means of simple univariate statistical tests. 

Statistical methods based on histograms, cumulative frequency probability curves (see above), univariate and multivariate data analysis (Miesh, 1981 Sinclair, 1974, 1976, 1991 Stanley, 1987) are widely used to separate geochemical baseline (natural and/or anthropogenic) values from anomalies. 

Exploratory data analysis (EDA). This analysis, also called pretreatment of data , is essential to avoid wrong or obvious conclusions. The EDA objective is to obtain the maximum useful information from each piece of chemico-physical data because the perception and experience of a researcher cannot be sufficient to single out all the significant information. This step comprises descriptive univariate statistical algorithms (e.g. mean, normality assumption, skewness, kurtosis, variance, coefficient of variation), detection of outliers, cleansing of data matrix, measures of the analytical method quality (e.g. precision, sensibility, robustness, uncertainty, traceability) (Eurachem, 1998) and the use of basic algorithms such as box-and-whisker, stem-and-leaf, etc. 

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