|Isotropy||The property of being
directionally independent, implying no variation of specified physical
properties with direction.
|Anisotropy||The property of being
directionally dependent, implying variation of specified physical
properties with direction.
|Diffraction limit||The isotropic or
anisotropic limit on average of statistically significant data (also
known as the 'resolution limit'), depending on both the
properties of the crystal and the data-collection strategy.
|Threshold||Criterion used to make a decision
on rejection of data.
|Spherical shell||Region of reciprocal space
lying between two defined reciprocal-space radii (d*).  The
statistics of both isotropic and anisotropic properties are analyzed in
|Diffraction cut-off||Cut-off applied to all
diffraction data outside a single closed isotropic or anisotropic
surface in reciprocal space defining the assumed boundary between, on
average, statistically significant and insignificant data.  In the
case of an isotropic surface only one parameter is needed to define it,
i.e. the radius of the limiting sphere.  In the general case
the surface is anisotropic and one parameter (or even a small number of
parameters) is not sufficient.
|Possible data||All reflections inside the
greatest value of d* for diffraction cut-offs in all directions,
regardless of whether or not an intensity was measured (systematic
absences are excluded everywhere).
|Measured data||All possible reflections with
an experimental intensity and standard uncertainty.
|Unmeasured data||All possible reflections
without an experimental intensity and standard uncertainty.
|Observed data||All measured reflections
inside the diffraction cut-off surface and included in the statistical
tables and the reflection output file.
|Unobserved data||All measured reflections
outside the diffraction cut-off surface and excluded from the
statistical tables and the reflection output file.
|Observable data||All unmeasured reflections
inside the diffraction cut-off surface (i.e. expected to be
|Unobservable data||All unmeasured
reflections outside the diffraction cut-off surface (i.e.
expected to be unobserved).
|Fitted ellipsoid||Ellipsoid fitted by a
multi-dimensional search and weighted least squares algorithm to the
reflection data immediately neighboring the diffraction cut-off
surface.  Used to reduce the number of parameters required to define
the anisotropic diffraction cut-off surface and thereby estimate the
anisotropic diffraction limits and predict observable data.
|Debye-Waller factor||Attenuation factor of
each measured intensity and its standard uncertainty due to thermal
motion and/or static disorder: exp(-4 π2
sh) , where sh is the
reciprocal-lattice (column) vector,
shT is the same as a row vector and
U is the overall anisotropy tensor (= B / 8
|Intensity prior||Expected intensity,
estimated from a spherical intensity distribution obtained from
experimental data or from a model, combined with the symmetry
enhancement factor and the isotropic or anisotropic Debye-Waller factor.
|Anisotropy correction factor||The inverse
of the square root of the anisotropic Debye-Waller factor applied as a
multiplicative correction of the amplitudes after Bayesian estimation
from the intensities:  exp(2 π2
sh) where ΔU is the overall
anisotropy U tensor after subtraction of Ueq
from its diagonal elements, where Ueq is the isotropic
equivalent U (mean of the eigenvalues), so that the trace of
ΔU is zero.
|Completeness||Number of data as a fraction
of the number of possible data in any defined volume of reciprocal
space (e.g. within the intersection of a spherical shell with the
|Anisotropy ratio||Difference between the
largest and smallest eigenvalues of the overall anisotropy U
tensor divided by Ueq : (Emax -
Emin) / Ueq.  This metric lies
between zero (isotropic) and 3 (maximally anisotropic).
|Fractional anisotropy||The RMS deviation of
the eigenvalues from the mean, scaled to lie between zero and one:
√(1.5 Σi (Ei -
Ueq)2 / Σi
Ei2).  Unlike the anisotropy ratio this
metric takes into account all 3 eigenvalues.
|Anisotropic S/N ratio||The maximum value
over all observed reflections of the absolute deviation of the squared
anisotropy correction factor from 1, multiplied by the local mean
intensity / standard uncertainty ratio:
Maxh (| exp(4 π2
sh) - 1 | <Ih /
σ(Ih)>) .  Unlike the anisotropy
ratio and the fraction anisotropy this takes into account both the fact
that large anisotropies represent larger differences in intensity at
high d* and that there will be a greater contribution from
reflections with a high value of the local mean intensity / standard
uncertainty ratio.  This metric is zero in the isotropic case, with
no limit in the anisotropic case.
inverse-variance-weighted half-dataset Pearson product-moment
correlation coefficient, where the variances are those of the overall
inverse-variance-weighted mean intensities.  If the half-dataset
inverse-variance-weighted mean intensities are available (e.g.
from MRFANA), this is computed using the standard formula for the weighted correlation coefficient.  If the
half-dataset weighted mean intensities are not available it is computed
using a modification (i.e. using inverse-variance weighting as
above) of the 'σ-τ' method of Assmann et al.
|Fisher transformation of the weighted
CC½||This uses the standard formula.
|Kullback-Leibler divergence (a.k.a. 'relative
entropy')||This uses the standard formula with logarithms base 10 (so its unit
is the 'hartley' or 'ban').