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Some Examples of a Guttman Scale

Robert Carneiro (1962, 1970) had an idea that cultural evolution is orderly and cumulative. If he is right, then cultures evolve by adding certain traits in an orderly way and should show a Guttman-scale-like pattern. Carneiro coded 100 cultures for 354 traits and looked at the pattern. Table 11.2a shows a sample of 12 societies and 11 traits. When you collect data on cases, you don’t know what (if any) pattern will emerge, so you pretty much grab cases and code them for traits in random order. The 12 societies and traits in table 11.2a are in random order.

The first thing to do is arrange the pluses and minuses in their ‘‘best’’ possible order— the order that conforms most to the perfect Guttman scale—and compute the CR. We look for the trait that occurs most frequently (the one with the most pluses across the row) and place that one at the bottom of the matrix. The most frequently occurring trait is the existence of special religious practitioners. Then we look for the next most frequent trait and put it on the next to the bottom row of the matrix. We keep doing this until we rearrange the data to take advantage of whatever underlying pattern is hiding in the matrix. The best arrangement of the pluses and minuses in table 11.2a is shown in table 11.2b. Now we can count up the ‘‘errors’’ in the matrix and compute Guttman’s coefficient of reproducibility. For these 12 societies and 11 traits, the coefficient is a perfect 1.0 (box 11.1).

DeWalt (1979) used Guttman scaling to test an index of material style of life in a Mexican farming community. He scored 54 informants on whether they possessed eight material items (a radio, a stove, a sewing machine, etc.) and achieved a CR of .95. My hunch is that DeWalt’s material-style-of-life scale has its analog in nearly all societies. The particular list of items that DeWalt used in rural Mexico may not scale in a middle-class

Table 11.2a Carneiro's Matrix Showing the Presence (+ )or Absence (—) of 11 Culture Traits among 12 Societies. The Order of Both the Traits and the Societies Is Random

 Society 1 2 3 4 5 6 7 8 9 10 11 12 Political leader has consider- able authority + + - - + - - + - + - - Sumptuary laws - - - - + - - + - - - - Headman, chief, or king + + - - + + + + - + + + Surplus of food regularly pro- duced + + - - + - - + - + - + Trade between communities + + - + + + + + - + + + Ruler grants audiences - + - - + - - + - + - - Special religious practitioners + + - + + + + + + + + + Paved streets - - - - - - - + - - - - Agriculture provides >75% of subsistence + + - - + - + + - + - + Full-time service specialists - + - - + - - + - - - - Settlements >100 persons + + - - + + + + - + - +

Societies: 1 Iroquois, 2 Marquesans, 3 Tasmanians, 4 Yahgan, 5 Dahomey, 6, Mundurucu, 7 Ao Naga, 8 Inca, 9 Semang, 10Tanala, 11 Vedda, 12 Bontoc

SOURCE: A Handbook ofMethodin CulturalAnthropology by Raoul Narolland Ronald Cohen, eds., copyright © 1970 by Raoul Naroll and Ronald Cohen. Used by permission of Doubleday, a division of Random House, Inc.

neighborhood of Ulan Bator, but some list of material items will scale there. You just have to find them.

The way to do this is to code every household in your study for the presence or absence of a list of material items. The particular list could emerge from participant observation or from informal interviews. Then you’d use ANTHROPAC to sort out the matrix, drop some material items, and build the material index that has a CR of 0.90 or better. Greg Guest (2000) did this in his study of 203 households in an Ecuadorian fishing village. He gave each household a score from 1 to 7, depending how many material items they had. That score correlated significantly with the education level of the head of each household.

Table 11.2b The Data in Table 11.2a Rearranged: The Data Form a Perfect Guttman Scale

 Society 12 3 4 5 6 7 8 9 10 11 12 Paved streets + Sumptuary laws + + Full-time service specialists + + + Ruler grants audiences Political leader has consider- + + + + able authority Surplus of food regularly pro- - - - - - - - + + + + + duced Agriculture provides >75% of - - - - - - + + + + + + subsistence - - - - - + + + + + + + Settlements >100 persons - - - - + + + + + + + + Headman, chief, or king - - - + + + + + + + + + Trade between communities - - + + + + + + + + + + Special religious practitioners - + + + + + + + + + + +

Societies: 1 Tasmanians, 2 Semang, 3 Yahgan, 4 Vedda, 5 Mundurucu, 6 Ao Naga, 7 Bontoc, 8 Iroquis, 9 Tanala, 10 Marquesans, 11 Dahomey, 12 Inca

BOX 11.1

DATA SCALE, VARIABLES DON’T

Given enough items that you think represent a unidimensionl variable, you can usually find a few items that will form a neat Guttman scale. Carneiro coded 100 societies for 354 traits and selected the data that showed the desired pattern. A high coefficient of reproducibility, then, is a necessary but insufficient condition for declaring that (1) a variable is unidimensional, and (2) you've got a scale that measures it. In other words, only data scale, not variables. If the items in a cumulative index form a Guttman scale with 0.90 CR or better, we can say that, for the sample we've tested, the concept measured by the index is unidimensional—that the items are a composite measure of one and only one underlying concept.

By the way, when Carneiro did this work in the 1960s, it was heroic work. Today, ANTHROPAC (Borgatti 1992a) has a routine for looking at big matrices of pluses and minuses, rearranging the entries into the best pattern, calculating the CR, and showing you which units of analysis and traits to drop to find the optimal solution to the problem.

(We’ll get to correlation and statistical significance in chapter 21). Since we expect a correlation between wealth and education, this adds construct validity to Guest’s scale.

Careful, though. Oliver Kortendick tried to develop a Guttman scale of wealth in a village in Papua New Guinea. The idea of property ownership may not have existed in that culture prior to contact with Europeans and Australians in the mid-20th century. It was well understood when Kortendick got there, but some things, like cars, were too expensive for anyone there to possess on their own. So villagers bought and owned those items collectively (Kortendick, personal communication).

Indexes That Don't Scale

Indexes that do not scale can still be useful in comparing populations. Dennis Werner (1985) studied psychosomatic stress among Brazilian farmers who were facing the uncertainty of having their lands flooded by a major dam. He used a 20-item stress index developed by Berry (1976).

Because the index did not constitute a unidimensional scale, Werner could not differentiate among his informants (in terms of the amount of stress they were under) as precisely as DeWalt could differentiate among his informants (in terms of their quality of life). But farmers in Werner’s sample gave a stress response to an average of 9.13 questions on the 20-item test, while Berry had found that Canadian farmers gave stress responses on an average of 1.79 questions. It is very unlikely that a difference of such magnitude between two populations would occur by chance (Further Reading: Guttman scales).

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