Statistics in Small-Angle Scattering Using Area Detectors

J.D. Barnes and T.J. Prosa
NIST Polymer Structure and Mechanics Group

This paper presents straightforward procedures that can be used to assess the statistical significance of small-angle scattering data obtained using area detectors. Such data invariably contain contributions from the Poisson character of the data collection process ("counting statistics"). Additional contributions from modeling errors in data reduction and uncontrolled instrumental factors should also be expected. While these latter sources can be described as "systematic errors" whose impact can be minimized through the careful design of SAS instrumentation and data handling procedures, it is nonetheless necessary to provide estimates for them in order to characterize the overall performance of a given SAS measuring system.

Simulations and model data sets are used to demonstrate ways in which 2 dimensional residual plots can aid in characterizing sources of systematic error in SAS data sets. It is concluded that all data sets that are used for public archiving or for comparisons of instrument performance should tabulate both the counting statistics and the "systematic errors.".

(posted 15-Oct-97 jw)