That leaves the question of how to label these statistics in a consistent, clear and concise way: suggestions?

Phil Evans

Here is a suggestion.  :)

FWIW, dtscaleaverage labels the mean I/sigmaI of the individual input reflections as "I/sig unavg". That is, before any averaging is
performed.

After scaling and adjustment of sigmas, the I/sigmaI for that unique hkl is calculated based on the weighted average of the
input observations that contribute to that unique hkl.
Then the mean I/sigmaI for these unique reflections as they appear
in the output reflection file is listed as well and labeled "I/sig avg".
That is, after any averaging is performed.

Here is the text the output file describing these two columns:
==========
I/sig unavg is the mean I/sig for the unaveraged reflections
in the input file.

I/sig avg   is the mean I/sig for the unique reflections
in the output file.
==========

I think these columns are consistent with the columns that appear in SCALA output. Rather than "I/sig unavg" or "I/sig avg", one could have
"I/sig in" and "I/sig out".

My issue is that errors, uncertainty and noise in the input reflections are treated as if they are normally distributed and random without a hint of systematic or erratic errors. This is wishful thinking in most cases.

Jim

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