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ANALYZING TRIAD DATA

Triad tests produce similarity matrices and these can also be analyzed using MDS and clustering. Recall from chapter 10 how triad tests work. Figure 16.14 shows the instructions and first 10 lines of a typical triad test. In this case, the domain is a list of 15 emotions: love, anger, disgust, shame, fear, anguish, envy, anxious, tired, happy, sad, lonely, bored, hate, and excitement. The data come from a class project where we interviewed 40 people and used a lambda-2 design. In a complete design with 15 items, there are n(n — 1)(n —2)/6 = 455 triads, but that’s because every pair ofitems shows up (n — 2) = 13 times. We used a lambda-2, balanced incomplete block design, or BIBD (see chapter 10 for details on BIBDs). In a lambda-2 BIBD, each pair of items shows up twice and this cuts the number of triads down to just 70. Since each pair of items shows up twice, each

FIGURE 16.13.

Redrawing of figure 16.12 showing the results of a cluster analysis for 85 green behaviors. SOURCE: H. R. Bernard, G. Ryan, and S. Borgatti. ''Green Cognition and Behavior: A Cultural Domain Analysis.'' In Networks, Resources and Economic Action. Ethnographic Case Studies in Honor of Hartmut Lang, p. 202. C. Greiner and W. Kokot, eds. Berlin: Dietrich Reimer Verlag.

cell in the item-by-item similarity matrix for each informant can contain just three numbers: 0.00, 0.50, or 1.00.

Figure 16.15 shows the individual similarity matrices from two informants who took the triad test about emotions. Looking across the first row of Matrix #1, we see a 0.00 in the first cell for love-love, and then zeros down the diagonal since the matrix is symmetric. Next, we see that both times the informant saw the pair love-anger, she circled one of them, making the other member of the love-anger pair similar to the third item in that triad. The same thing happened for love-disgust and love-shame. When she saw the pair love-fear, though, she circled one of them once and she circled the third item in the triad once. That is, half the time she kept the pair together (as similar) and half the time she kept them apart (as dissimilar, compared to a third item), so there’s a 0.50 in that cell. She did the same thing for love-hate. She kept the pairs love-happy and love-excitement together both times they showed up in the triad test, and we see 1.00 in those cells.

Compare this to informant #2. He also kept the love-happy and love excitement pairs together both times they show up in his triad test, but he never kept love-fear together; he kept love-envy together once; and he kept love-hate together twice.

To aggregate the 40 individual matrices from this triad test, we stack them on top of each other (software does this for us), sum down each cell and divide by 40 to get an average similarity for each pair of items. Figure 16.16 shows this aggregate similarity matrix.

FIGURE 16.14.

Instructions for a triad test.

FIGURE 16.15.

Two matrices from a triad test.

FIGURE 16.16.

Aggregate proximity matrix for triads: 40 informants, 15 emotions.

Reading across the first line, we see that 82% of the time, these 40 informants put love and happy together but they put love and bored together only 8% of the time. Reading down the second column, we see that informants put hate and anger together 95% of the time but never put anger and tired together.

Figure 16.17 shows the multidimensional scaling, in two dimensions, for the aggregate similarity matrix in figure 16.16.

FIGURE 16.17.

MDS in two dimensions of the data in figure 16.16.

Moore et al. (1999) studied these same emotions, using a triad test, in Japanese speakers, Chinese speakers, and American English speakers. Figure 16.18 shows the shared model for these emotion terms in all three languages. (Moore et al. used correspondence analysis to produce the display in figure 16.18. Correspondence analysis is another method for visualizing relations among sets of items.) Naturally, there is some part of the model that is unique to each language and some part that is unique to each individual. But what stands out to me is the overlap—the sharing of the model in figures 16.17 and 16.18. Using triad tests, pile sorts, and other systematic methods lets you make these kinds of comparisons (Further Reading: triad tests and see Further Reading, chapter 10).

 
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