How can we know two SAXS profiles are same?

[Debarati92]

Do you feel that the pink and brown profiles below are the same?

Is there any way to establish similarity between SAXS profiles statistically rather than visual perception?

[andreashlarsen]

Important question! thank you.

there are some tools in ATSAS to do such comparison, see part 1 of the data reduction tutorial (the compare tool).

what do I feel? They are definitely not the same, but the question is: do the come from the same sample - and differ only by some statistical variation?
I feel they are not from exactly the same sample, but deviate significantly around log10(s) = 1.5. If you merge them, you could end up with systematically too small error bars - this would be my guess from a glance at the data.

what do I mean by the same sample? they could come from the same sample, but the sample may change slightly over time. Or some other factors could have changed sligthly - e.g. contamination of the capilary or slight beam damage.

[Debarati92]

Thanks Andreas! They are the same sample of same conc but prepared separately. I tried the compare tool in ATSAS and it shows difference :)