Data evaluation univariate analysis

Several applications of univariate statistical analysis for data evaluation in Py-MS are known [73]. One such application is the evaluation of reproducibility of a replicate of an analysis for the peak intensity at a given m/z value. If a series of measurements are made on identical specimens, this will provide a sample xi, X2...Xn. This sample will allow the calculation of parameters such as the mean m and the standard deviation s. By comparing the value s for different m/z values it is possible to select those m/z that are more reproducible (smaller s). 

In addition to the usual statistical methods based on univariate descriptors (mean, median, and standard deviation) and analysis of variance, multivariate techniques of statistics and chemometrics are increasingly being used in data evaluation. Whereas the former are more rigorous in theoretical background and assumptions, the latter are useful in the presentation of the data, pattern recognition, and multivariate calibrations. Several good monographs on chemometrics are available (see for example [58-61]). 

The initial multivariate analysis consisted of a principal component analysis on the raw data to determine if any obvious relationships were overlooked by univariate statistical analysis. The data base was reviewed and records containing missing data elements were deleted. The data was run through the Statistical Analysis System (SAS) procedure PRINCOMP and the results were evaluated. 

A typical multivariate set of data is generated when performing Py-MS. Each Py-MS trace is formed from a considerable number of peaks and each peak can be considered a measurable variable. The results from a set of samples to be evaluated by considering all these variables will generate a typical data matrix. The data matrix can be studied using multivariate data analysis. However, simple univariate data analysis can be applicable by selecting for analysis one single m/z value. 

The usefulness of univariate data analysis seems to be limited when analyzing Py-MS results because in each spectrum there is a significant number of peaks, each representing a measurement. However, if one mass peak is properly selected from the Py-MS spectrum, this can be used as a unique measurement for the given specimen, and univariate data analysis can be quite informative. Also, any peak can be selected separately, one at a time, for evaluation. This type of approach is less informative than multivariate data analysis, but has the advantage of being simpler. 

Analysis of full sheet data is useful for process performance evaluations and product value calculations. For feedback control or any other on-line application, it is necessary to continuously convert scanner data into a useful form. Consider the data vector Y ,k) for scan number k. It is separated into its MD and CD components as Y( , A ) = yM )( )+Yc )( , k) where Ymd ) s the mean of Y ,k) as a scalar and YcD -,k) is the instantaneous CD profile vector. MD and CD controllers correspondingly use these calculated measurements as feedback data for discrete time k. Univariate MD controllers are traditional in nature with only measurement delay as a potential design concern. On the other hand, CD controllers are multivariate in form and must address the challenges of controller design for large dimensional correlated systems. 

Contemporary spectrometers are able to produce huge amounts of data within a very short time. This development continues due to the introduction of array detectors for spectral imaging. The utilization of as much as possible of the enclosed spectral information can only be achieved by chemometric procedures for data analysis. The most commonly used procedures for evaluation of spectra are systematically arranged in Fig. 22.2 with the main emphasis on application, i.e. the variety of procedures was divided into methods for qualitative and quantitative analysis. Another distinctive feature refers to the mathematical algorithms on which the procedures are based. The dominance of multivariate over univariate methods is clearly discernible from Fig. 22.2. 

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