Example F

Title=Dichotomous Data Showing Exclusive Groupings and MDS Robustness
SubTitle=Strong results are possible using dissimilarity data with only two values.  (Press F4 to see the data.)

NObjects=15

Dissimilaritylist
0 .2 .2 .2 .2 .8 .8 .8 .8 .8 .8 .8 .8 .8 .8
.2 0 .2 .2 .2 .8 .8 .8 .8 .8 .8 .8 .8 .8 .8
.2 .2 0 .2 .2 .8 .8 .8 .8 .8 .8 .8 .8 .8 .8
.2 .2 .2 0 .2 .8 .8 .8 .8 .8 .8 .8 .8 .8 .8
.2 .2 .2 .2 0 .8 .8 .8 .8 .8 .8 .8 .8 .8 .8
.8 .8 .8 .8 .8 0 .2 .2 .2 .2 .8 .8 .8 .8 .8 
.8 .8 .8 .8 .8 .2 0 .2 .2 .2 .8 .8 .8 .8 .8 
.8 .8 .8 .8 .8 .2 .2 0 .2 .2 .8 .8 .8 .8 .8 
.8 .8 .8 .8 .8 .2 .2 .2 0 .2 .8 .8 .8 .8 .8 
.8 .8 .8 .8 .8 .2 .2 .2 .2 0 .8 .8 .8 .8 .8 
.8 .8 .8 .8 .8 .8 .8 .8 .8 .8 0 .2 .2 .2 .2
.8 .8 .8 .8 .8 .8 .8 .8 .8 .8 .2 0 .2 .2 .2
.8 .8 .8 .8 .8 .8 .8 .8 .8 .8 .2 .2 0 .2 .2
.8 .8 .8 .8 .8 .8 .8 .8 .8 .8 .2 .2 .2 0 .2
.8 .8 .8 .8 .8 .8 .8 .8 .8 .8 .2 .2 .2 .2 0

Teaching: This example shows that very coarse grained data can result in complex 
relationships that are stable and have relatively low stress values.  This is an important
conclusion that shows MDS's robustness.  If you have studied linear programming you 
will see the analogy.  Using many roughly defined cutting planes can pin-point a small 
feasible space.

Teaching: Once the results of this example become 'obvious' try the two Simplex cases
accessed via the Special Cases menu.  Again you will get stable results from extremely
crude input data, but this time the stability is entirely different.  A constant pattern evolves
but the relative positions of the objects within the pattern is random.

Program Note: The whole Dij matrix is entered simply because it was easier to do so.  
The data were available as a square matrix in a spreadsheet so it was imported 
in its original condition.  Only the lower triangle is required.
