Russel-Research-Method-in-Anthropology

Multivariate Analysis 685
TABLE 21.27
Pile Sort Data for an Individual Proximity Matrix
A List of 18 Fruits for a Pile Sort
1. Apple 10. Strawberry
2. Orange 11. Lemon
3. Papaya 12. Cantelope
4. Mango 13. Grapefruit
5. Peach 14. Plum
6. Blueberry 15. Banana
7. Watermelon 16. Avocado
8. Pineapple 17. Fig
9. Pear 18. Cherry
One Person’s Sorting of 18 Fruits
Pile 1: 2, 11, 13
Pile 2: 1, 5, 9, 14, 17, 18
Pile 3: 3, 4, 8, 15, 16
Pile 4: 6, 10
Pile 5: 7, 12
one person’s pile sort of 18 fruits (the names of the fruits are in the top half
of the table and the contents of each pile the informant made are in the bottom
half). Table 21.28 displays the pile-sort data as an individual proximity
matrix.
This particular proximity matrix is a similarity matrix. (Recall that the
matrix of cities was a dissimilarity matrix.) When the informant put items 2,
11, and 13 into a pile, he did so because he thought the items were similar. To
indicate this, there is a 1 in the matrix where items 2 and 11 intersect; another
1 in the cell where items 2 and 13 intersect; and another 1 in the cell where
11 and 13 intersect. And similarly for Pile 2: there is a 1 in the 1–5 cell, the
1–9 cell, the 1–14 cell, and so on There are zeros in all the cells that represent
no similarity of a pair of items (for this informant) and zeros down the diagonal
(we don’t count items as being similar to themselves). Also, notice that if
11 is similar to 13, then 13 is similar to 11, so this particular matrix is also
symmetric. The bottom and top halves of the matrix are identical.
The matrix in table 21.28 contains exactly and only the information in the
bottom half of table 21.27. There are no numerical operations here. The individual
proximity matrix in table 21.28 is just a convenient way to display the
symmetric similarities implied by the pile sort data. Figure 21.5 is a multidimensional
scaling of these similarity data, a visualization of how this infor-