Correlation in the statistical analysis of a reverse Fourier neutron time-of-flight experiment. Pt. 2

The significance of the correlation in the statistical analysis of reverse Fourier neutron time-of-flight observations has been evaluated by applying different methods of estimation to diffraction patterns containing peaks with Gaussian line shapes. Effects of the correlation between adjacent channels of a spectrum arise both from the incorrect weighting of the experiment's independent variables and from the misinterpretation of the number of independent observations in the data. The incorrect weighting bears the greatest effects on the width parameter of a Gaussian profile, and it leads to an increase in the relative weights of the broadest peaks of the diffraction pattern. If the correlation is ignored in the analysis, the estimates obtained for the parameters of a model will not be exactly the same as those evaluated from the minimum variance estimation, in which the correlation is taken into account. However, the differences will not be statistically significant. Nevertheless, the standard deviations will then be underestimated typically by a factor of two, which will have serious consequences on every aspect of the statistical inference. (orig.)