From: nichols@spss.com (David Nichols)
Subject: Response to Sue Anderson on CLUSTER
Date: Tue, 21 Jul 1992 21:50:11 CUT
Organization: SPSS Inc.

Sue Anderson asks:

I am using the CLUSTER procedure with a sample of 316 cases.  In
attempting to compare the results of using the WAVERAGE vs WARD
methods, I noticed that the values of the coefficients printed in the
agglomeration schedules vary quite a bit from one method to the other.

For example with WAVERAGE, I get:
  Stage    Cluster 1  Cluster 2   Coefficient
    310            2          3      5.392510
    311            1         13      5.749814
    312            5         14      6.314435
    313            2          5      7.502407
    314            1          2      8.621726
    315            1          6      9.946472

Whereas, with WARD, I get:
  Stage    Cluster 1  Cluster 2   Coefficient
    310            3         19    639.756470
    311            5         10    707.005676
    312            1         14    780.497070
    313            3          5    958.662842
    314            1          2   1190.600586
    315            1          3   1566.569336

The SPSS-X Advanced Statistics Guide explains that the actual value of
these coefficients depend on the clustering method and the distance
measure used.  I assume that means that it is NOT worthwhile to compare
these values from one method to the next.  Is that correct?  

Also, I find the size of the coefficients obtained from WARD to be
alarming.  The Advanced Guide explains that small coefficients indicate
that fairly homogeneous clusters are being merged and large
coefficients indicate that clusters containing dissimilar members are
being combined.  My question is... for each method/distance measure,
what should be considered "small" and what is "large?"

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It is a correct deduction that distance coefficients are generally not
comparable across measures and methods. The same data will give different
coefficients with different measures and may give very different results
with the same measure but with different methods. 

The coefficients given for the Ward method differ from all of the other
methods in that rather than being the distance at which two clusters
were joined, they represent the within cluster sums of squares after
joining the two clusters. 

I don't think any standard rules can be given for what is large and what
is small. This depends on the scale and other characteristics of the data.
The general guidelines for usage of these coefficients are that they can
be used to look for breaks, or places where joining two clusters produces
either a much larger within clusters sums of squares (for Ward's method)
or where clusters that are relatively much farther apart than those last
joined would have to be joined in order to continue.

--
 David Nichols           Statistical Support Specialist            SPSS, Inc.
 Phone: (312) 329-3684     Internet: nichols@spss.com     Fax: (312) 329-3657
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 Any correlation between my views and those of SPSS is strictly due to chance.