Section 19.5.7.7. Evaluation

As in crystallography, fibre structures are evaluated by statistical measures, such as R values, and by the examination of difference maps. Fibre-diffraction R values are inherently lower than those expected in crystallography, particularly when large numbers of intensities have been superposed by cylindrical averaging (Stubbs, 1989). The largest likely R value for noncrystalline TMV at 3 Å resolution is about 0.31 and for polycrystalline DNA at 3 Å resolution it is about 0.41, both significantly less than the value of 0.59 to be expected from noncentric single-crystal analyses (Millane, 1989).

Comparison of R values alone is not necessarily a reliable way to discriminate between competing models. Such discrimination is often required for structures with small unit cells, for which alternative models are routinely refined (Sections 19.5.7.1 and 19.5.7.2). The relative merits of any pair of competing models can be assessed on the basis of several types of statistics (Arnott, 1980) using Hamilton's significance test (Hamilton, 1965), which considers not only residuals but also numbers of degrees of freedom (Section 19.5.7.3). Such a test is essential. There are many examples in the literature where R values have been lowered by the simple process of increasing the number of degrees of freedom; a decreased R value obtained in this way may or may not have any significance.

Difference Fourier maps have been used to evaluate crystalline fibre diffraction analyses for many years, for example, to reject the controversial Hoogsteen base pairing in double-stranded DNA (Arnott et al., 1965), and later to discriminate between 10- and 11-fold double helices of RNA (Arnott et al., 1967). Difference maps have been essential in the refinement of fibre structures with large unit cells (Namba et al., 1989; Wang & Stubbs, 1994), both to identify errors in early models and to confirm that the final structures contained no major errors or omissions.