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Analyzing Pile Sort Data: Aggregate Matrices

To test whether this pattern holds up, Ryan and I asked five more informants to do the pile sort exercise (Bernard and Ryan 2010:179). Each informant’s data produce an individual similarity matrix of 1s and 0s, like the matrix shown in table 16.2. Table 16.5 shows the aggregate similarity matrix for the six informants.

To produce table 16.5, just stack the six individual matrices on top of one another, count the number of 1s down the column for each cell, and divide by six. (This is all done

BOX 16.4

DIMENSIONS AND CLUSTERS IN MDS

Susan Weller (1983) asked 24 Guatemalan women—some urban, some rural—to do a pile sort of 27 illness names. Figure 16.7 shows the MDS graph of the illnesses for Weller's urban sample.

MDS representation of 27 illnesses for urban Guatemalan women.

Source: S. Weller, ''New Data on Intracultural Variability: The Hot-Cold Concept of Medicine and Illness,'' Human Organization, Vol. 42, pp. 249-57. © 1983. Reprinted with permission of the Society for Applied Anthropology.

FIGURE 16.7.

When you interpret an MDS graph, look for arrays, or dimensions as well as for clusters. There is a clump on the right that might be called ''gastrointestinal disorders.'' On the left there is a clump of ''childhood disorders.'' Those, at least, are the labels that struck Weller as appropriate. I agree with her intuition about this. What do you think?

How about the arrays, or dimensions? To me, it looks like informants distinguish between chronic and acute illnesses (from top to bottom in figure 16.7) and between infectious and noninfectious illnesses (from left to right). But remember: Interpretation of numerical results is always a brazen, flat-out qualitative exercise, a Rorschach test for social scientists—which is why I like it so much. Use every technique you can think of in data analysis, and let your experience guide your interpretation. Interpretation of results is where data analysis in all science ultimately becomes a humanistic activity.

instantly with a computer program, like ANTHROPAC or UCINET.) That tells you the percentage of people who put each pair of fruits together in a pile. Because there are six informants here, the numbers in the cells of table 16.5 can be 0.00 (none out of six), 0.17 (one out of six), 0.33 (two out of six), 0.50 (three out of six), 0.67 (four out of six), 0.83 (five out of six), and 1.00 (six out of six).

Table 16.5 Aggregate Similarity Matrix from Six Pile Sorts of the 18 Fruits in Figure 16.2

ap

or

pap

man

pea

blu

wat

pin

per

str

lem

can

9Pf

plu

ban

a vc

fig

chr

Apple

1.00

0.00

0.00

0.00

0.83

0.00

0.17

0.00

0.83

0.00

0.00

0.00

0.00

0.83

0.17

0.00

0.17

0.33

Orange

0.00

1.00

0.17

0.17

0.00

0.00

0.17

0.17

0.00

0.00

0.83

0.17

1.00

0.00

0.00

0.17

0.00

0.00

Papaya

0.00

0.17

1.00

0.67

0.17

0.00

0.17

0.50

0.17

0.00

0.00

0.17

0.17

0.17

0.33

0.67

0.17

0.00

Mango

0.00

0.17

0.67

1.00

0.00

0.00

0.17

0.50

0.00

0.00

0.00

0.33

0.17

0.00

0.33

0.67

0.00

0.00

Peach

0.83

0.00

0.17

0.00

1.00

0.00

0.00

0.00

1.00

0.00

0.00

0.00

0.00

1.00

0.17

0.17

0.17

0.33

Blueberry

0.00

0.00

0.00

0.00

0.00

1.00

0.00

0.00

0.00

0.83

0.00

0.00

0.00

0.00

0.00

0.00

0.50

0.67

Watermelon

0.17

0.17

0.17

0.17

0.00

0.00

1.00

0.17

0.00

0.00

0.00

0.83

0.17

0.00

0.00

0.17

0.00

0.00

Pineapple

0.00

0.17

0.50

0.50

0.00

0.00

0.17

1.00

0.00

0.00

0.00

0.17

0.17

0.00

0.50

0.50

0.00

0.00

Pear

0.83

0.00

0.17

0.00

1.00

0.00

0.00

0.00

1.00

0.00

0.00

0.00

0.00

1.00

0.17

0.17

0.17

0.33

Strawberry

0.00

0.00

0.00

0.00

0.00

0.83

0.00

0.00

0.00

1.00

0.00

0.00

0.00

0.00

0.00

0.00

0.50

0.50

Lemon

0.00

0.83

0.00

0.00

0.00

0.00

0.00

0.00

0.00

0.00

1.00

0.00

0.83

0.00

0.00

0.00

0.00

0.00

Cantaloupe

0.00

0.17

0.17

0.33

0.00

0.00

0.83

0.17

0.00

0.00

0.00

1.00

0.17

0.00

0.00

0.17

0.00

0.00

Grapefruit

0.00

1.00

0.17

0.17

0.00

0.00

0.17

0.17

0.00

0.00

0.83

0.17

1.00

0.00

0.00

0.17

0.00

0.00

Plum

0.83

0.00

0.17

0.00

1.00

0.00

0.00

0.00

1.00

0.00

0.00

0.00

0.00

1.00

0.17

0.17

0.17

0.33

Banana

0.17

0.00

0.33

0.33

0.17

0.00

0.00

0.50

0.17

0.00

0.00

0.00

0.00

0.17

1.00

0.33

0.00

0.00

Avocado

0.00

0.17

0.67

0.67

0.17

0.00

0.17

0.50

0.17

0.00

0.00

0.17

0.17

0.17

0.33

1.00

0.00

0.00

Fig

0.17

0.00

0.00

0.00

0.17

0.50

0.00

0.00

0.17

0.50

0.00

0.00

0.00

0.17

0.00

0.00

1.00

0.50

Cherry

0.33

0.00

0.00

0.00

0.33

0.67

0.00

0.00

0.33

0.50

0.00

0.00

0.00

0.33

0.00

0.00

0.50

1.00

SOURCE: H. R. Bernard and G. W. Ryan, Analyzing Qualitative Data: Systematic Approaches. Los Angeles: Sage Publications. 2010. p. 179. Used by permission.

For example, reading across the top row in table 16.5, we see that five out of six informants (83%) put apple and pear in the same pile. Reading across the third row, we see that four out of six people (67%) put papaya and mango in the same pile. And so on. Just like table 16.2, table 16.5 is symmetric (check it and see for yourself).

 
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