Upon further consideration, I hereby retract my contention that reductions in anomalous signal throughout the course of a diffraction experiment will cause systematic negative CCanoms. Perhaps it has to do with the "random" selection of measurements for Dano calculations, as suggested by Clemens Vonrheim, or it may have to do with scaling. Can't figure it out just yet. I am, of course, assuming that the signs are not random.
Jacob -----Original Message----- From: Keller, Jacob Sent: Thursday, July 16, 2015 9:46 PM To: Keller, Jacob; CCP4BB@JISCMAIL.AC.UK Subject: RE: [ccp4bb] Negative CCanom [Sorry, typography was off a bit in the last one] Here is the answer, I think, to why twinning leads to negative CCanom: In fact, in any case in which the anomalous signal changes as a function of exposure, CCanom can be negative. The usual case is radiation damage: Consider, to start, four independent measurements of one reflection, two I+ and two I-. Call them A: not damaged, early-measured I+ a: damaged, late-measured I+ B: not damaged, early-measured I- b: damaged, late-measured I- CCanom is the correlation coefficient between anomalous differences (Dano's). From these four measurements of a given unique reflection, one can calculate two Dano's, and thus make one data point for a CC calculation. The possibilities for correlation pairs are: A-B and a-b: large value corresponds to a small value, i.e., negative correlation a-b and A-B: small corresponds to large, i.e., negative correlation A-b and a-B: both same size, so modest positive correlation a-B and A-b: both same size, so modest positive correlation Unique reflections as a population, then, will have equal proportions of these permutations. If the damage makes Dano go to zero (or indistinguishable from noise), then since A-B is double A-b, the first two combinations will outweigh the second two, leading to negative CCanom. I guess having a negative CCanom, then, is a mixed bag, since it implies that there is anomalous signal, but that there is also radiation damage. But the latter can be useful as well, so maybe not such a bad omen. Shifting to my case of twinning, although there was almost certainly negligible radiation damage, something else happened: since the twin fraction increased throughout the course of the dataset, this decreased the anomalous signal similarly to the case above. It could also be, if there was enough change in twin fraction, i.e., past the 50% mark, some anomalous differences might even flip their signs, making CCanom go really negative. Another corollary is that sufficient increases of anomalous signal over time would also produce negative CCanom, but I can't think of a case besides twinning in which that would happen. I think this explains the phenomenon, and I have to thank Clemens Vonrheim for explaining the calculation to me. But don't blame him if I've got it wrong. There is probably a good way to alter this feature of CCanom, perhaps by biasing the selection of measurements to encourage the latter two cases above. Or just continue using it, but in many cases there could be 0 CCanom when the damage and signal are counterbalanced. JPK
