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Outliers detection in the statistical accuracy test of a pK a prediction

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Abstract

The regression diagnostics algorithm REGDIA in S-Plus is introduced to examine the accuracy of pK a predicted with four programs: PALLAS, MARVIN, PERRIN and SYBYL. On basis of a statistical analysis of residuals, outlier diagnostics are proposed. Residual analysis of the ADSTAT program is based on examining goodness-of-fit via graphical diagnostics of 15 exploratory data analysis plots, such as bar plots, box-and-whisker plots, dot plots, midsum plots, symmetry plots, kurtosis plots, differential quantile plots, quantile-box plots, frequency polygons, histograms, quantile plots, quantile-quantile plots, rankit plots, scatter plots, and autocorrelation plots. Outliers in pK a relate to molecules which are poorly characterized by the considered pK a program. Of the seven most efficient diagnostic plots (the Williams graph, Graph of predicted residuals, Pregibon graph, Gray L–R graph, Index graph of Atkinson measure, Index graph of diagonal elements of the hat matrix and Rankit Q–Q graph of jackknife residuals) the Williams graph was selected to give the most reliable detection of outliers. The six statistical characteristics, \({F_{\rm exp},R^{2},R_{\rm P}^{2},{\it MEP},{\it AIC}}\), and s in pK a units, successfully examine the specimen of 25 acids and bases of a Perrin’s data set classifying four pK a prediction algorithms. The highest values \({F_{\rm exp},R^{2},R_{\rm P}^{2}}\) and the lowest value of MEP and s and the most negative AIC have been found for PERRIN algorithm of pK a prediction so this algorithm achieves the best predictive power and the most accurate results. The proposed accuracy test of the REGDIA program can also be extended to test other predicted values, as log P, log D, aqueous solubility or some physicochemical properties.

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Authors and Affiliations

  1. Department of Analytical Chemistry, Faculty of Chemical Technology, Pardubice University, 532 10, Pardubice, Czech Republic

    Milan Meloun & Sylva Bordovská

  2. TriloByte Statistical Software, s.r.o., Jiráskova 21, 530 02, Pardubice, Czech Republic

    Karel Kupka

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  1. Milan Meloun
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  2. Sylva Bordovská
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  3. Karel Kupka
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Correspondence to Milan Meloun.

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Meloun, M., Bordovská, S. & Kupka, K. Outliers detection in the statistical accuracy test of a pK a prediction. J Math Chem 47, 891–909 (2010). https://doi.org/10.1007/s10910-009-9609-2

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  • DOI: https://doi.org/10.1007/s10910-009-9609-2

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