I've never used a binary-plus-doesn't-apply system for recording the
allocation of elements to constructs. I _have_ used a 5-point rating scale
system, without the "doesn't apply" response.
In which case, one computes % matching scores between the two constructs
a) both "as is", and
b) with one of them "reflected" (ratings being subtracted from r + 1 where
r is the maximum rating possible)
and reports max (reflected, unreflected) with pole labels reversed as
appropriate.
Matching scores are given by
MS% = 100 + ((-100 . Sigma d) / (e . r))
where r is as above, e is the number of elements, and Sigma d is the sum
of differences between corresponding ratings on each construct.
(Example: 5,4,2,1 and 5,2,3,4 gives as Sigma d of 6.)
I haven't thought it through, but your suggestion (3) would seem to
correspond to this in the case of a 2-point scale while elegantly
accounting for the "doesn't apply" response, which the approach I use can't
handle. Your procedure (1) would seem to confound a psychological
assumption with a purely statistical manipulation, viz., that reflections
are in some way related to the "Ideal Self" rating differently than they
are to ratings of other elements. As for your procedure (2), I'm a bit
cautious of using correlational measures when comparing ratings because
they can confound similarity of meaning with similarity of ratings in the
case of n-point scales where n > 2. (e.g. 2,1,2,2,5 and 4,3,4,4,5 are, one
imagines, reasonably correlated but, on a 5-point scale, 3 of the 5 ratings
on the first construct are aligned more with the left pole but none of 5
ratings on the second construct are aligned with the left pole, so to
interpret the correlation as indicating similar meaning would be erroneous;
a Sigma d-based score would seem to reflect the dissimilarity of meanings
better).
You might like to contact Mildred Shaw for further particulars; she has
tackled the "doesn't apply" rating issue, (and the "_both_ ends of the
scale apply" issue!) in preparing her yummy, user-friendly, Macintosh rep
grid package called REPGRID.
Kindest regards,
Devi Jankowicz
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