Whoa! What is this "before we dichotomised it"? If you mean that your 0s
and 1s
are not the original ratings aren't you just throwing away information?
Anyway, I have never understood all the enthusiasm for kappa, which
despite its clear
definition is just a single summary measure. I have to suspect that the
lure of a single, supposedly simple summary, which comes wrapped up
nicely with a P-value attached, sometimes triumphs over the challenge of
looking at the fine structure of agreement (or more precisely
disagreement).
I don't know what your precise problem is but I have tackled what may be
similar ones. For example, in a couple of papers I have looked at
problems in the Earth sciences in which several methods were used to
measure what should be the same thing. Scientifically, putting a single
number on the strength of overall agreement has never seemed a terribly
useful thing to do. If overall agreement is extremely high, it is clear
that the methods do all agree very well, but what's more typical in my
experience is that the agreement is moderate or worse. In that situation
the real challenge is to try to identify (e.g.) whether one or two
methods are really out of line with the others. Naturally it need not be
a voting matter if one method is in some sense known to be very good
(even a 'gold standard') and the others are poor. Admittedly if you are
dealing with the ratings given by various medics then implying that one
or more may not be so competent could be a difficult matter.
There is more in the same spirit (statistically, not politically) at
SJ-4-3 gr0005 . . . . . Speaking Stata: Graphing agreement and
disagreement
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . N.
J. Cox
Q3/04 SJ 4(3):329--349 (no
commands)
how to select the right graph to portray comparison or
assessment of agreement or disagreement between data
measured on identical scales
which is now in the public domain via
http://www.stata-journal.com/sjpdf.html?articlenum=gr0005
and in
Cox, N.J. 2006. Assessing agreement of measurements and predictions in
geomorphology. Geomorphology 76: 332-346
doi:10.1016/j.geomorph.2005.12.001
which may or may not be accessible to you.
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