ISa: Difference between revisions

What is that number? Scaling procedures (like the ones used in XDS, SCALA, SCALEPACK and DSCALEAVERAGE) scale (or rather, inflate) the variances of individual observations such that they match the experimental spread of symmetry-related observations. To this end, two contributions to the variance v(I) of a reflection are considered: the first component is random error, and the other component is systematic error. The two values a and b appearing in the variance-scaling formula v(I)=a*(v0(I)+b* <math>{I}^2</math>) are printed out by CORRECT. a scales the random error component, a*b scales the systematic error component. For strong and well-measured reflections, the variance is dominated by the systematic error a*b* <math>{I}^2</math> that is introduced by any beam /spindle / detector /cryo or other instability or malfunction. For weak reflections, a*v0(I), the variance from counting statistics, dominates.  

Versions of XDS since May 10, 2010 print out <math>{I/Sigma(I)}^{asymptotic}</math> = <math>I/\sqrt(a*b)</math> as "ISa". ISa is the I/sigma of an infinitely strong reflection. If there were no systematic error, ISa would be infinite. In the presence of systematic error, ISa is finite and is the upper limit of I/sigma of any observation in your dataset.  

As you can see from the formula, low values of a and b are ''good'' in the sense that a high upper limit of I/sigma(I) results. If e.g. the crystal is badly split or broken, or reflections are too close on the detector, or the data reduction is not good (wrong parameters), then the values of a and b are elevated.

If your crystal is good, then a and b will reflect the quality of the other components of the experimental setup (e.g. beamline stability).  

ISa is well suited to judge the quality of the experimental setup, because its value does not depend on random error, whereas the low-resolution <math>R_{meas}</math> does, and is thus influenced by crystal size and exposure. If you see a high value of the the low-resolution <math>R_{meas}</math>, you don't know if it is high because the crystal diffracted weakly, or because the beamline was broken. Conversely, a low value of ISa indicates that something is broken, no matter how small the crystal is or how weakly it was exposed.

On the other hand, I have sometimes obtained values less than 10 with good test crystals, clearly indicating strong systematic errors. It is always good to discuss this with the people who are responsible for the beamline. They might know what is broken, or might be able to find out what went wrong.