# 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)