Linear statistical comparison

Clarke, J.U. (1998). Evaluation of censored data methods to allow statistical comparisons among very small samples with below detection limits observations. Environmental Science Technology. Vol. 32, pp. 177-183. ISSN 1520-5851 Cole, R.A. Phelps, K. (1979). Use of canonical variate analysis in the differentiation of swede cultivars by gas-liquid chromatography of volatile hydrolysis products. Journal of the Science of Food and Agriculture. Vol. 30, pp. 669-676. ISSN 1097-0010 Coomans, D. Broeckaert, L Fonckheer, M Massart, D.L. Blocks, P. (1978). The application of linear discriminant analysis in the diagnosis of thyroid diseases. Analytica Chimica Acta. Vol. 103, pp. 409-415. ISSN 0003-2670 Coomans, D. Massart, D.L. Kaufman, L. (1979) Optimization by statistical linear discriminant analysis in analytical chemistry. Analytica Chimica Acta. Vol. 112, pp. 97-122. ISSN 0003-2670... 

A recent paper compares the performances of GC-MS in SIM mode to those of GC coupled to tandem mass spectrometry (GC-MS/MS), either using an ion-trap or a triple quadrupole (Kinani et al, 2006). The ion trap was not suitable for the PASs determination due to a high LOQ (up to 40 mg/kg), lack of linearity and high variability (up to 26% of standard deviation when re-injecting a standard at a concentration of 10 mg/kg). The statistical comparison of the GC-MS method (with a single column) with the triple quadrupole results shows, in the latter case, a lower risk of false positives and negatives. However, the authors conclude that none of the tested methods is fully satisfactory from this point of view. 

The results of a comparison between values of n estimated by the DRK and BET methods present a con. used picture. In a number of investigations linear DRK plots have been obtained over restricted ranges of the isotherm, and in some cases reasonable agreement has been reported between the DRK and BET values. Kiselev and his co-workers have pointed out, however, that since the DR and the DRK equations do not reduce to Henry s Law n = const x p) as n - 0, they are not readily susceptible of statistical-thermodynamic treatment. Moreover, it is not easy to see how exactly the same form of equation can apply to two quite diverse processes involving entirely diiferent mechanisms. We are obliged to conclude that the significance of the DRK plot is obscure, and its validity for surface area estimation very doubtful. 

The preceding equations will, of course, be somewhat in error owing to the neglect of intramolecular condensations. Very large species will be suppressed relatively more on this account. All conceivable errors can do no more, however, than to effect a distortion of the quantitative features of the predictions, which will be small in comparison with the vast difference between the branched polymer distribution and that usually prevailing in linear polymers. From this point of view, the statistical theory given offers a useful description of the state of affairs. 

A Scatchard plot of the data is shown in Figure 5.10C. For convenience, the fitted line is the regression of B/F on B (though, as noted earlier, this is statistically unsound) and provides an estimate for Bmax ( -intercept) of 0.654 fmol/mg dry wt. and an estimate for KL (-1/slope) of 132 pM. A Lineweaver-Burk (double-reciprocal) plot is provided for comparison in Figure 5.10D. Linear regression gives another estimate for Bmax (I v-intercept see Eq. (5.29)) of 0.610 fmol/mg dry wt. The estimate of KL from this plot (slope x Bmax) is 114 pM. 

Comparison of Goodness of Fit Statistics for Linear Regression Part 1 - Introduction... 

The scope of this chapter-formatted mini-series is to provide statistical tools for comparing two columns of data, X and Y. With respect to analytical applications such data may be represented for simple linear regression as the concentration of a sample (X) versus an instrument response when measuring the sample (Y). X and Y may also denote a comparison of the reference analytical results (X) versus predicted results (Y) from a calibrated instrument. At other times one may use X and Y to represent the instrument response (X) to a reference value (Y). Whatever data pairs one is comparing as X and Y, there are several statistical tools that are useful to assess the meaning of a change in... 

Workman, J. and Mark, H., Chemometrics in Spectroscopy Comparison of Goodness of Fit Statistics for Linear Regression - Part 1, Introduction , Spectroscopy 19(4), 32-35 (2004). 

Sections on matrix algebra, analytic geometry, experimental design, instrument and system calibration, noise, derivatives and their use in data analysis, linearity and nonlinearity are described. Collaborative laboratory studies, using ANOVA, testing for systematic error, ranking tests for collaborative studies, and efficient comparison of two analytical methods are included. Discussion on topics such as the limitations in analytical accuracy and brief introductions to the statistics of spectral searches and the chemometrics of imaging spectroscopy are included. 

Table XI presents the results of tests on the same materials in the NBS smoke chamber. It is immediately clear that these results do not correlate well with those measured on the RHR apparatuses. Furthermore, an attempt at a linear correlation between the flaming mode specific maximum optical density and the Cone calorimeter SmkPar at 20 kW/m2 yielded a correlation coefficient of ca. 1%, a coefficient of variation of 217% and statistically invalid correlations. A comparison between a Cone and OSU calorimeter correlation and one with the NBS smoke chamber is shown in Figure 4. This suggests that unrelated properties are being measured.

---