Real data analysis multiple samples

Most of the popular spreadsheet programs can perform multiple regression analysis, and most of the information that is needed can be obtained from this process. Regression analysis as well as other techniques that deal with normal statistics are based on two basic assumptions that are seldom completely accurate these are (1) independent variables upon which dependent variables are r ressed are truly independent, or not associated with each other in any way, and (2) the values of the independent variables are fixed (that is, each one is not just a sample of a distribution of values and thus is not subject to error). In the real world of corrosion research, it is extremely difficult to design or conduct an experiment where these criteria are met. Thus, it is necessary to evaluate how these assumptions might affect the data analysis. The different statistical techniques discussed in the foUowing paragraphs consider the effects of these assumptions. 

Multivariate methods, on the other hand, resolve the major sources by analyzing the entire ambient data matrix. Factor analysis, for example, examines elemental and sample correlations in the ambient data matrix. This analysis yields the minimum number of factors required to reproduce the ambient data matrix, their relative chemical composition and their contribution to the mass variability. A major limitation in common and principal component factor analysis is the abstract nature of the factors and the difficulty these methods have in relating these factors to real world sources. Hopke, et al. (13.14) have improved the methods ability to associate these abstract factors with controllable sources by combining source data from the F matrix, with Malinowski s target transformation factor analysis program. (15) Hopke, et al. (13,14) as well as Klelnman, et al. (10) have used the results of factor analysis along with multiple regression to quantify the source contributions. Their approach is similar to the chemical mass balance approach except they use a least squares fit of the total mass on different filters Instead of a least squares fit of the chemicals on an individual filter. 

The book is aimed at those who have to use statistics, but have no ambition to become statisticians per se. It avoids getting bogged down in calculation methods and focuses instead on crucial issues that surround data generation and analysis (sample size estimation, interpretation of statistical results, the hazards of multiple testing, potential abuses, etc.). In this day of statistical packages, it is the latter that cause the real problems, not the number-crunching. 

On the other hand, atomic emission spectra are inherently well suited for multivariate analysis due to the fact that the intensity data can be easily recorded at multiple wavelengths. The only prerequisite is that the cahbration set encompasses all likely constituents encountered in the real sample matrix. Calibration data are therefore acquired by a suitable experimental design. Not surprisingly, many of the present analytical schemes are based on multivariate calibration techniques such as multiple linear regression (MLR), principal components regression (PCR), and partial least squares regression (PLS), which have emerged as attractive alternatives. 

Calibration of peak position for accurate mass determination can be performed internally or externally to minimize systematic errors. Internal calibration can be conducted when compounds with known molecular weight (called calibration compounds or calibrants) are mixed with the sample prior to the introduction into the ion source. This calibration can be performed, for example, by adding the calibrant to the liquid-phase sample while diluting it prior to analysis. The best result is achieved when multiple calibration signals are used to interpolate the m/z of ions within the range of interest. In proteomics, a tryptic digest of albumin from horse heart is typically used as the calibrant because it covers a wide m/z range (e.g., m/z 800-3000) that is ideal for mass calibration of low- to medium-sized peptides. In external calibration, the calibrants are analyzed before the analysis of real samples. The peaks of the calibrants are used to create and set the calibration equation in the data acquisition software. This method provides less mass accuracy because the instrument condition may still vary between the calibration and analyses of real samples. However, external calibrations save time and calibration compounds, and such methods also make analyses of analytes free from interferences caused by calibrants. 

---