Regarding your question, I do not know Davis Cantor's work on multiple
sorting, could you send a reference regarding this? However, I would say
the question of whether to supply or let participants choose their own
elements should be determined by your hypothesis and the type of analysis
which you intend to use. For example, using common elements (although they
will not be construed identically) allows for a greater range of analyses to
be used. This may be necessary if you want to compare participants or
include all in one analysis, such as individual differences multidimensional
scaling. There is a literature on the issue of supplying versus letting
participants choose their own elements, as well as being general articles
which discuss this.
A second comment concerns your methodology, if you choose to compare groups
you need to consider your sample size. If you want to be able to generalise
about groups, you need more grids. Anyone who has completed a grid will
tell you that completing a grid can take an hour or so, even longer if the
participant does not understand the process or has difficulty. Also if I
were to make a guess, you may find differences within any group may be
greater than differences between the groups of interest to you.
Regarding your final point, Yorke has written a number of articles on constructs
which would be of relevance to you and Riemann has written on bipolarity of
constructs. My mail programme does not allow ready insertion of text from
other sources, however if you can read encoded attachments I could supply
some references.
Regards,
Bob Green
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