Statistics for chromatographers

A method successfully used for chromatographic data and capable to answer this and related questions is the SIMCA method (Statistical Isolinear Multiple Component Analysis). It has been constructed and developed by Svante Wold and his group at the University of Umea, Sweden. 

Many commercial statistical or chromatographic software packages also allow to set up a ruggedness test. This is for instance the case with Statgraphics Plus, Unscrambler II and DryLab for Windows . This list is far from complete. 

The shapes of chromatographic peaks often resemble the Gaussian distribution, though distorted to a variable degree. Theory seldom finds shape functions for chromatographic peaks in explicit form. More frequently, only the Laplace transform of the appropriate differential equation can be solved. Then, even if the solution cannot be inversed, it allows evaluation of the statistical moments of the distribution [4],... 

The use of Eq. (2.18) to quantitatively estimate the IDL for chromatographs and for spectrometers has been roundly criticized for more than 10 years. There have been reported numerous attempts to find alternative ways to calculate IDEs. This author will comment on this most controversial topic in the following manner. The approach encompassed in Eq. (2.18) clearly lacks a statistical basis for evaluation and, hence, is mathematically found to be inadequate. As if this indictment is not enough, IDEs calculated based on Eq. (2.18) also ignore the uncertainty inherent in the least squares regression analysis of the experimental calibration as presented earlier. In other words, what if the analyte is reported to be absent when, in fact, it is present (a false negative) In the subsections that follow, a more contemporary approach to the determination of IDEs is presented and starts first with the concept of confidence intervals about the regression line. 

Method of Moments The first step in the analysis of chromatographic systems is often a characterization of the column response to sm l pulse injections of a solute under trace conditions in the Henry s law limit. For such conditions, the statistical moments of the response peak are used to characterize the chromatographic behavior. Such an approach is generally preferable to other descriptions of peak properties which are specific to Gaussian behavior, since the statisfical moments are directly correlated to eqmlibrium and dispersion parameters. Useful references are Schneider and Smith [AJChP J., 14, 762 (1968)], Suzuki and Smith [Chem. Eng. ScL, 26, 221 (1971)], and Carbonell et al. [Chem. Eng. Sci., 9, 115 (1975) 16, 221 (1978)]. 

The curves show that the peak capacity increases with the column efficiency, which is much as one would expect, however the major factor that influences peak capacity is clearly the capacity ratio of the last eluted peak. It follows that any aspect of the chromatographic system that might limit the value of (k ) for the last peak will also limit the peak capacity. Davis and Giddings [15] have pointed out that the theoretical peak capacity is an exaggerated value of the true peak capacity. They claim that the individual (k ) values for each solute in a realistic multi-component mixture will have a statistically irregular distribution. As they very adroitly point out, the solutes in a real sample do not array themselves conveniently along the chromatogram four standard deviations apart to provide the maximum peak capacity. 

Sulcer and Denson (Ref 19) used the gas chromatographic—B .T. procedure for the analysis of Class I A1 powder (45 u max dia) which cannot be tested satisfactorily by sedimentation methods because of the presence of aggregates. A rough statistical evaluation of this procedure was made by running twelve determinations and calculating the standard deviation as shown in Table 14 ... 

These are most important realizations that will guide the evolution of multiple dimension chromatographic systems and detectors for years to come. The exact quantitative nature of specific predictions is difficult because the implementation details of dimensions higher than 2DLC are largely unknown and may introduce chemical and physical constraints. Liu and Davis (2006) have recently extended the statistical overlap theory in two dimensions to highly saturated separations where more severe overlap is found. This paper also lists most of the papers that have been written on the statistical theory of multidimensional separations. 

Not all of the above-described statistical quantities are chromatographically observable. For example, s, d, t, and m are not directly observable unless selective detectors as a mass spectrometer is employed (Campostrini et al., 2005) and thus they are hidden quantities. The point will be discussed in the third section of this chapter. 

Kublin and Kaniewska [52] used a gas chromatographic method for the determination of miconazole and other imidazole antimycotic substances. The conditions have been established for the quantitative determination of miconazole and the other drugs, which are present in pharmaceuticals such as ointments and creams. The column, packed with UCW-98 on Chromosorb WAW, and flame-ionization detector were used. The statistical data indicate satisfactory precision of the method, both in the determination of imidazole derivatives in substances and in preparation. 

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