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Correlation of observations in the least-squares calculation for the analysis of gas electron diffraction data

1966; Wiley; Volume: 20; Issue: 5 Linguagem: Inglês

10.1107/s0365110x66001476

1600-8642

Yoshitada Murata, Yusuke Morino,

Calibration and Measurement Techniques

In an ordinary least-squares analysis of gas electron diffraction, the standard deviation for the most probable value of a parameter for a molecule depends on the interval of measurements As on a microphotometer recording, that is, on the number of observed points on an intensity curve.It is shown that a reasonable estimate of the standard deviation of a parameter can be obtained by taking into account the effect of 'correlation' among the points of observations.A general method and its simplified form for dealing with the correlation are developed by introducing off-diagonal elements into the weight matrix used in the least-squares fit of the observed values.The simplified method is applied, as an example, to the electron-diffraction data of silicon tetrachloride, and it is shown that the standard deviation of the most probable value estimated by using an infinite number of observations does not approach zero.At the same time, it is shown that when a diagonal weight matrix is used for simplicity there is an optimum interval for measurements in order to get a correct standard deviation.