Root-mean-square-deviation computational analysis

After completion of the calculations182 on poly(Gly-Pro-Pro), it was learned that Okuyama et al.187 had carried out a single-crystal X-ray structure analysis of (Pro—Pro—Gly)10. The calculated structure (Figure 25) is in agreement with theirs, with a root-mean-square deviation of 0.3 A for all (nonhydrogen) atoms, based on a comparison between the X-ray coordinates (kindly provided by Professor M. Kakudo) and the computed coordinates. 

In those systems which could be analyzed by Equation 3, the parameters were determined by a least-squares analysis. The [17 ] matrix elements were those calculated by CFW. The error in the parameters was computed in the usual manner. The measure of the fitting is expressed by the root mean square (rms) deviation defined by... 

To demonstrate the accuracy, two dust and two soil reference materials were analyzed with the described method. The mean value of the correlation coefficients between the certified and the analyzed amounts of the 16 elements in the samples is r = 0.94. By application of factor analysis (see Section 5.4) the square root of the mean value of the communahties of these elements was computed to be approximately 0.84. As frequently happens in the analytical chemistry of dusts several types of distribution occur [KOM-MISSION FUR UMWELTSCHUTZ, 1985] these can change considerably in proportion to the observed sample size. In the example described the major components are distributed normally and most of the trace components are distributed log-normally. The relative ruggedness of multivariate statistical methods against deviations from the normal distribution is known [WEBER, 1986 AHRENS and LAUTER, 1981] and will be tested using this example by application of factor analysis. 

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