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The Balanced Incomplete Block Design for Triad Tests

Typically, the terms that go into a triad test are generated by a free list, and typically the list is much too long for a triad test. As you can see from formula 10.1, with just 9 terms, there are 84 stimuli in a triad test containing nine items. But with 15 items, just 6 more, the number of decisions an informant has to make jumps to 455. At 20 items, it’s a mind-numbing 1,140.

Free lists of illnesses, ways to prevent pregnancy, advantages of breast-feeding, places to go on vacation, and so on easily produce 60 items or more. Even a selected, abbreviated list may be 20 items.

This led Michael Burton and Sara Nerlove (1976) to develop the balanced incomplete block design, or BIB, for the triad test. BIBs take advantage of the fact that there is a lot of redundancy in a triad test. Suppose you have just four items, 1, 2, 3, 4 and you ask informants to tell you something about pairs of these items (e.g., if the items were vegeta?bles, you might ask ‘‘Which of these two is less expensive?’’ or ‘‘Which of these two is more nutritious?” or ‘‘Which of these two is easier to cook?’’). There are exactly six pairs of four items (1-2, 1-3, 1-4, 2-3, 2-4, 3-4), and the informant sees each pair just once.

But suppose that instead of pairs you show the informant triads and ask which two out of each triple are most similar. There are just four triads in four items (1-2-3, 1-2-4, 2-3-4, 1-3-4), but each item appears (n-1)(n —2)/2 times, and each pair appears n — 2 times. For four items, there are n(n—1)/2 = 6 pairs; each pair appears twice in four triads, and each item on the list appears three times.

It is all this redundancy that reduces the number of triads needed in a triads test. In a complete set of 84 triads for 9 items, each pair of items appears n — 2, or seven times. If you have each pair appear just once (called a lambda 1 design), instead of seven times, then, instead of 84 triads, only 12 are needed. If you have each pair to appear twice (a lambda 2 design), then 24 triads are needed. For analysis, a lambda 2 design is much better than a lambda 1. Table 10.1 shows the lambda 2 design for 9 items and 10 items.

Table 10.1 Balanced Incomplete Block Designs for Triad Tests Involving 9 and 10 Items

 For 9 items, 24 triads are needed, as follows: For 10 items, 30 triads are needed, as follows: Items Items 1, 5, 9 1,2,3 1, 2, 3 6, 8, 9 2,3,8 4, 5, 6 2, 5, 8 7, 10, 3 4, 6, 7 7, 8, 9 3, 7, 4 8, 1, 10 2, 6, 9 1,4,7 4, 1, 6 9, 5, 2 1,3, 4 2, 5, 9 5, 8, 7 10, 6,7 5, 7, 8 3, 6, 8 6, 4, 9 1, 3, 5 3, 7, 9 1,6,9 7,9, 1 2, 7, 6 2, 4, 5 2, 4, 8 8, 10, 2 3, 8, 9 1, 6, 8 3, 5, 7 9, 3, 10 4, 2, 10 4, 8, 9 1, 5,8 10, 6, 5 5, 6, 3 3, 5, 6 2, 6, 8 1, 2, 4 6, 1, 8 1, 2, 7 3, 4, 9 2, 3, 6 7, 9, 2 2, 4, 8 8, 4, 7 4, 9, 5 9, 10, 1 5, 7, 1 10, 5, 4

SOURCE: Reprinted from Social Science Research, Vol. 5, M. L. Burton and S. B. Nerlove, ''Balanced Design forTriad Tests,'' p. 5, © 1976. Reprinted by permission of Academic Press.

For 10 items, a lambda 2 design requires 30 triads; for 13 items, it requires 52 triads; for 15 items, 70 triads; for 19 items, 114 triads; and for 25 items, 200 triads. Unfortunately, there is no easy formula for choosing which triads in a large set to select for a BIB. Fortunately, Burton and Nerlove (1976) worked out various lambda BIB designs for up to 21 items and Borgatti has incorporated BIB designs into ANTHROPAC (1992a). You simply tell ANTHROPAC the list of items you have, select a design, and tell it the number of informants you want to interview. ANTHROPAC then prints out a randomized triad test, one for each informant. (Randomizing the order in which the triads appear to informants eliminates ‘‘order-effects’’—possible biases that come from responding to a list of stimuli in a particular order.)

Boster et al. (1987) used a triad test in their study of the social network of an office. There were 16 employees, so there were 16 ‘‘items’’ in the cultural domain (‘‘the list of all the people who work here’’ is a perfectly good domain). A lambda 2 test with 16 items has 80 distinct triads. Informants were asked to ‘‘judge which of three actors was the most different from the other two.’’

Triad tests are easy to create with ANTHROPAC, easy to administer, and easy to score, but they can only be used when you have relatively few items in a cultural domain. In literate societies, most informants can respond to 200 triads in less than half an hour, but it can be a really boring exercise, and boring your informants is a really bad idea. I find that informants can easily handle lambda 2 triad tests with up to 15 items and 70 triads. But I also find that people generally prefer—even like—to do pile sorts (Further Reading: triad tasks).

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