Intensity statistics

Intensity statistics of twinned vs non-twinned vs pseudo-translation datasets

Question on CCP4BB (slightly edited):

The data I am working on has a strong translation vector (this can be found out e.g. using sfcheck).

On the cumulative intensity distribution plot, the theoretical and observed curves do not overlap. I did "detect_twinning" from CNS, and there is the result:

 <|I|^2>/(<|I|>)2  = 3.2236 (2.0   for untwinned, 1.5   for twinned)
 (<|F|>)2/<|F|^2>  = 0.6937 (0.785 for untwinned, 0.865 for twinned)

What does this mean?

Answer (slightly edited):

A normal data set has a unimodal intensity distribution with a predictable shape (for formulas and plots, see Centric and acentric reflections). When there is twinning the distribution remains unimodal but becomes sharper and this is picked up in the twinning analysis. When there is pseudo-translational symmetry, as you indicate you have, then the intensity distribution becomes bimodal with one set of reflections systematically strengthened and another systematically weakened. This makes the whole distribution broader, just the opposite of what twinning does, and therefore shows up as "negative twinning" in the analysis.

Mean intensity as a function of resolution

Please see Wilson plot.