Correlation Map, a goodness-of-fit test for one-dimensional X-ray scattering spectra

Abstract

Assessing similarity between data sets with the reduced χ(2) test requires the estimation of experimental errors, which, if incorrect, may render statistical comparisons invalid. We report a goodness-of-fit test, Correlation Map (CorMap), for assessing differences between one-dimensional spectra independently of explicit error estimates, using only data point correlations. Using small-angle X-ray scattering data, we demonstrate that CorMap maintains the power of the reduced χ(2) test; moreover, CorMap is also applicable to other physical experiments.