Confidence chemometrics

Workman, J. and Mark, H., Chemometrics in Spectroscopy Comparison of Goodness of Fit Statistics for Linear Regression - Part 3, Computing Confidence Limits for the Correlation Coefficient, Spectroscopy 19(7), 31-33 (2004). 

The t value is the number of standard deviations that the single value differs from the mean value. This t value is then compared to the critical t value obtained from a t-table, given a desired statistical confidence (i.e., 90%, 95%, or 99% confidence) and the number of degrees of freedom (typically iV-1), to assess whether the value is statistically different from the other values in the series. In chemometrics, the t test can be useful for evaluating outliers in data sets. 

Admittedly, navigating through a reference text on chemometrics can be a rather daunting task. There are many different tools in the toolbox, even though it is likely that you will only need a small subset of these to solve a specific problem. This chapter discussed many of the more commonly used and commonly available tools that are at your disposal. It is hoped that these discussions will improve your comfort level and confidence in chemometrics as an effective technology for solving your problems. 

Another type of classification is outlier selection or contamination identification. As an example, in Fig. 4.23(b), the butter is the desired material and bacteria the contamination. An arbitrary threshold for this image would be 0.02, in which all pixels >0.02 are considered suspect, and hopefully, because this is a food product, decontamination procedures are pursued. In these two examples of classification, only arbitrary thresholds have been defined and, as such, confidence in these classifications is lacking. This confidence can be achieved through statistical methods. Although this chapter is not the appropriate place for an involved discussion of application of statistics toward data analysis, we will give one example often used in chemometric classification. 

The reason for titis problem is that die infiuences of pH and temperature are not independent. In chemometric terms, they interact . In many cases, interactions are commonsense. The best pH in one solvent may be different to diat in another solvent. Chemistry is complex, but how to find the true optimum, by a quick and efficient manner, and be confident in die result Experimental design provides the chemist with a series of rules to guide the optimisation process which will be explored later. 

The use of the materials and the best chemical forms to be chosen have been discussed briefly in the section on validation. Details taken from Moody et al. and Wells are given in Tables 2.5a and b. The chemometric tools to be applied for the calibration of the signal and the calculation of the confidence interval of the calibration curve have been extensively detailed in several manuals and in particular the second book of Massart et al. [7] or in the text book of the FECS [48]. Modern automated spectrometers usually include adapted and properly validated calibration software. 

A very important and interesting field of chemometrics is the neural networks field, which can be successfully employed in nonlinear mapping, in nonlinear multivariate calibration, and in linear and nonlinear pattern classification. Also, confidence intervals are determined using calibration... 

Only if replicate measurements of y have been made for at least one point x model errors and experimental errors can be weighed against each other by LOF and complete analysis of varianees, ANOVA (- Chemometrics). Replicate measurements also reduce the width of the confidence band. 

Conlin AK, Martin EB, Morris AJ. Confidence limits for contribution plots. J Chemometr 2000 14 725-36. 

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