Exploratory data analysis description

Because of the limited space we focus on a user-oriented description of basic aspects of principal component analysis (PCA). PCA is an excellent tool for exploratory data analysis in chemistry. A number of surveys on the subject have already been published and it is strongly recommended to refer to a selection of them (ref. 1-7). 

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. 

Options should include descriptive statistics and exploratory data analysis techniques. 

The heights of the bars or columns usually represent the mean values for the various groups, and the T-shaped extension denotes the standard deviation (SD), or more commonly, the standard error of the mean (discussed in more detail in Section 7.3.2.3). Especially if the standard error of the mean is presented, this type of graph tells us very litde about the data - the only descriptive statistic is the mean. In contrast, consider the box and whisker plot (Figure 7.2) which was first presented in Tukey s book Exploratory Data Analysis. The ends of the whiskers are the maximum and minimum values. The horizontal line within the central box is the median, fhe value above and below which 50% of the individual values lie. The upper limit of the box is the upper or third quartile, the value above which 25% and below which 75% of fhe individual values lie. Finally, the lower limit of the box is the lower or first quartile, the values above which 75% and below which 25% of individual values lie. For descriptive purposes this graphical presentation is very informative in giving information about the distribution of the data. 

Data generated with the EOS are elaborated by Exploratory Data Analysis (EDA) software, a written-in-house software package based on MATLAB [22]. The EDA software includes the usual (univariate or multivariate) descriptive statistics functions among which Principal Component Analysis (PCA) [23], with the additional utilities for easy data manipulation (e.g. data sub sampling, data set fusion) and plots customization. 

The tasks that require multivariate statistics can be divided into descriptive, predictive, and classification. The term "exploratory data analysis" (EDA) is sometimes used to describe such multivariate applications. The discipline within chemistry that focuses on the analysis of chemical data, EDA, and modeling is called chemometrics. 

Exploratory factor analysis (EFA) would discern the thematic patterns of mFSMAS on the basis of the sample data. However, as the sample size is limited to N =29, which means the sample to variable ratio is less than 3 1 (please see Brown and Onsman 2013) for arguments on sampling adequacy for factor analysis), the data is not sufficient to run EFA. Therefore, the factorial structure of an earlier study of mFSMAS on Turkish students in the context of chemistry education is used as a reference for the analysis (Kahveci, 2009). Table 1 shows the item-based factorial categories as drawn from Kahveci (2009) and Cronbach alpha values and the standardized descriptive statistics for the current sample N = 29) in the context of PChem II. There were six factors applied to this research as follows (1) confidence in learning physical chemistry, (2) satisfaction, (3) relevance, (4) personal ability, (5) gender difference, and (6) interest. 

The second part of the book—Chapters 9-12— presents some selected applications of chemometrics to different topics of interest in the field of food authentication and control. Chapter 9 deals with the application of chemometric methods to the analysis of hyperspectral images, that is, of those images where a complete spectrum is recorded at each of the pixels. After a description of the peculiar characteristics of images as data, a detailed discussion on the use of exploratory data analytical tools, calibration and classification methods is presented. The aim of Chapter 10 is to present an overview of the role of chemometrics in food traceability, starting from the characterisation of soils up to the classification and authentication of the final product. The discussion is accompanied by examples taken from the different ambits where chemometrics can be used for tracing and authenticating foodstuffs. Chapter 11 introduces NMR-based metabolomics as a potentially useful tool for food quality control. After a description of the bases of the metabolomics approach, examples of its application for authentication, identification of adulterations, control of the safety of use, and processing are presented and discussed. Finally, Chapter 12 introduces the concept of interval methods in chemometrics, both for data pretreatment and data analysis. The topics... 

The second task involves defining the boundaries within which the model was derived and can be expected, without further motivation, to be an adequate description of the data. Within these bounds the model can replace the raw data (after all, the model is supposed to capture all salient features of the data), which will be useful when presenting the knowledge summarized by the developed model to nonpharmacometricians. The definition of these bounds can be based on the inclu-sion/exclusion criteria of the study or the realized covariate distribution. In the latter case, some of the exploratory plots from the before-analysis phase are useful. 

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