  Small-angle X-ray and neutron scattering are widely used to investigate soft
matter and biophysical systems. The experimental errors are essential when
assessing how well a hypothesized model fits the data. Likewise, they are
important when weights are assigned to multiple data sets used to refine the
same model. Therefore, it is problematic when experimental errors are over- or
under-estimated. A method is presented, using Bayesian indirect Fourier
transformation for small-angle scattering data, to assess whether or not a
given small-angle scattering data set has over- or under-estimated experimental
errors. The method is effective on both simulated and experimental data, and
can be used to assess and rescale the errors accordingly. Even if the estimated
experimental errors are appropriate, it is ambiguous whether or not a model
fits sufficiently well, as the "true" reduced $\chi^2$ of the data is not
necessarily unity. This is particularly relevant for approaches where
overfitting is an inherent challenge, such as reweighting of a simulated
molecular dynamics trajectory against small-angle scattering data or ab initio
modelling. Using the outlined method, it is shown that one can determine what
reduced $\chi^2$ to aim for when fitting a model against small-angle scattering
data. The method is easily accessible via the web interface BayesApp.
