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Mark H.,Mark Electronics
Spectroscopy (Santa Monica) | Year: 2010

Several algorithms that are commonly used for analyzing data and especially those used for multivariate calibration are discussed. The relationship between the absorbance and analyte concentration can be found using least squares calculations such as the multiple linear regression (MLR). The classical least squares (CLS), inverse least squares (ILS), algorithms apply least squares calculations to the spectral data. The concentration of the components of a mixture based upon first principles such as the principal of absorbance being proportional to concentration, in accordance with Beer's law. The multiple linear regression (MLR) requires external reference laboratory values for the concentrations, while CLS requires spectra of the pure mixture components. Source


Mark H.,Mark Electronics
Spectroscopy (Santa Monica) | Year: 2010

Standard comparison of two methods, Bland-Altman Plot and Tukey Mean-Difference Plot involves regression plots of reference (X) versus test (Y) values and residual plots showing the errors (or differences) between the two methods. The Bland-Altman graphic consists of a residual or difference plot showing the mean of Method A and B for each sample analysis (X) versus the difference for Method A minus Method B for each sample analysis (Y). A good agreement between the methods is demonstrated by differences (residuals) near zero, or with a set of differences with nearly identical bias values for all sample analyses. The Tukey Mean-Difference plot (identical to the Bland-Altman plot) is more common for engineering research than for medical literature (10). It is exactly the same as the Bland-Altman plot but uses different X- and Y-axis labels, such as mean and difference. Source


Mark H.,Mark Electronics
Spectroscopy (Santa Monica) | Year: 2010

A team of researchers conducted a study to examine classical least squares (CLS) theory. They demonstrated that rays had a longer path-length through the sample than rays that pass through the sample perpendicular to the faces at high angles. The net effect led to the introduction of a nonlinearity in the spectroscopic response and the nonlinearity was greater at high absorbances. The equations for the CLS computations assumed that all the spectra responded in a strictly linear fashion to concentration and add together in exact proportion to their concentrations. There were at least two physical causes of nonlinearity in the spectra of the mixtures of these three materials that the researchers were working with. Equation 1 of the theory applied applies to a single component in a sample and the total absorbance was the sum of the absorbances of all the absorbing materials, at the wavelength of interest when there were multiple absorbing components. Source


Mark H.,Mark Electronics | Workman J.,Unity Scientific LLC | Workman J.,University of San Diego
Spectroscopy (Santa Monica) | Year: 2015

The science of statistics are concerned with the effects of the random portion of the uncertainty, not least because it can help discern and, even better, calculate the systematic errors so that they can be corrected. Over the years, statisticians have discovered much about the nature and behavior of random errors, and have learned how to specify bounds for what can legitimately be said about the data that are subject to these errors. One of the more important findings is that if the data are subject to fluctuations because of random error, then anything you calculate from those data will also be subject to fluctuations. To the statistician, a value calculated from a set of data subject to random fluctuations is what is known as a statistic. An important difference between samples and statistics is the distribution of the variations. The distribution of values of multiple measurements from a sample, or the distribution of values of measurements from multiple samples can be almost anything, and is determined by the physics or chemistry (or other applicable discipline) of the situation governing the behavior of the samples. Source


Mark H.,Mark Electronics
Spectroscopy (Santa Monica) | Year: 2011

Howard Mark and Jerome Workman, Jr., share their views on the connection between the mathematics of classical least squares (CLS) and the graphical displays that are conventionally used to present it. They have found that the absorbances of the various materials when added together wavelength by wavelength give the absorbances of the mixture. This process ties together the absorbances of the three different materials in a mathematical sense. The concentration of the materials in the mixture is exactly the information which they want to derive from the analysis. It is observed that this concentration is exactly the result of performing the least-squares calculations using the spectra of the pure materials against the spectrum of the mixture. Howard Mark and Jerome Workman, Jr also note that the information required by them is derived from the calibration calculations when they perform them the CLS way. Source

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