The input for multidimensional scaling comes from the sort data--from what is called a group similarity matrix. The computer program automatically constructs the similarity matrix from the group sort data, but first, it must construct a binary symmetric similarity matrix for each individual.

That is, for each sorter included in the analysis, the computer internally must construct a square table with as many rows and columns as there are statements. (If there are 100 statements, the computer constructs a 100x100 table.) This table has only two values--zeros or ones. If an individual put statements 32 and 54 together in a category, the computer enters a “1” in the cell for Row 32 and Column 54 and in the cell for Row 54 and Column 32. If two statements were not put in the same category, their corresponding cell (i.e., row and column combination) will have a “0” in it. Each table is called a “binary symmetric similarity matrix.” It is “binary” because there are only two values possible for each cell (zero or one). It is “symmetric” because the cells with the same row-column pair will always have the same value (i.e., if Row 32, Column 54 = 1 then Row 54, Column 32 must also equal 1). It is a similarity matrix because higher values (i.e., 1s) indicate statements that are more like each other (were sorted into the same category). Note, also, that the diagonal of these individual matrices is always equal to 1s. That is, Row 1, Column 1 = 1; Row 2, Column 2 = 1; and so on. This is because a statement is automatically always put into a category with itself!

Once the computer has computed the binary symmetric similarity matrix for each individual, it constructs a group similarity table. This table also has as many rows and columns as there are statements. (If there are 100 statements, this will be a 100x100 table.) The values in each cell of this table are the sum of the values in the same cell across the individual matrices. Essentially, we are just summing across the individual matrices to get this group similarity table or matrix. Since the individual matrices can only have 0s or 1s, the group matrix essentially tells us the number of people who sorted each pair of statements together into a category. The diagonal of the group matrix is the number of people who sorted. This group similarity matrix is the input to the multidimensional scaling analysis.