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Similarity, relatedness, dissimilarity, and distance
Data come in various forms. Of primary importance is the directonality of the data values. With similarity or relatedness, higher values mean more similar or more related pairs of items, and "similarity" or "similarities" should appear on the second line of a proximity data file. With dissimilarity or distance, lower values mean more related or smaller distance between pairs of items, and "distance" or "dissimilarity" should appear on the second line of a proximity data file.
JPathfinder algorithms use distances (or dissimilarities) rather than similarities so similarity data are inverted using the equation:
dis(i,j) = max  sim(i,j) + min
What is the Coherence
measure and when is it appropriate?
The
measure is based on a kind of transitivity assumption, i.e., if two
concepts have similar relationships with other concepts, then the two
concepts should be similar to one another. Now we know that
transitivity does not necessarily hold for all sets of concepts, but
failure of transitivity is the exception while transitivity is the
rule. The Coherence measure computes an indirect measure
of
similarity by correlating the distances for each item in a pair
with all of the other concepts  if we have 8 concepts (ABCDEFGH) then
for the pair AB we would correlate the ratings in the first two columns inthe following table. For the CF pair we would correlate the distances in the last two columns.
.........AB Pair............CF Pair.....
AC 
BC 
CA 
FA 


AD 
BD 
CB 
FB 

AE 
BE 
CD 
FD 

AF 
BF 
CE 
FE 

AG 
BG 
CG 
FG 

AH 
BH 
CH 
FH 
These correlations give the indirect similarity of AB  the extent to which A and B have
similar relationships with other concepts and likewise for the pair CF. If we do this for
all
pairs, we can construct a halfmatrix of indirect
similarities. Then, Coherence is the negative of the correlation between these
indirect measures and the original distances for each pair. A more consistent set of distance data will yield a higher
Coherence. One data set came from the study of physics
expertise
where Coherence increased monotonically with level of
expertise. Extremely low Coherence (less than .15) may
indicate
that the rater did not take the task seriously, or the rater did not understand the concepts very well.
The negative of the correlation of indirect similarities and distances is used because the indirect similarities have an opposite direction to the distance data itself, and greater Coherence should reflect greater consistency.