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Guttman Scale

Given a data set of a sample of N persons and of a selection of n survey questions (variables) designed for measuring a particular trait—such as people's position on a political issue or their ability in a specific field of human activity—a Guttman Scale is the hypothesis that the data set would have a cumulative structure, in the following sense: For any two persons in the observed sample, one of them would exhibit all the manifestations of the trait that the other person would, and possibly additional ones. That is, there would be no two persons in the sample with the one person higher than the other in one variable but lower than the other in another variable.

To the extent a Guttman Scale hypothesis is supported in a data set, it can be said that all observed persons (and all their observed profiles) are comparable with respect to the selection of observed variables. And—if the data set is sufficiently rich—it can be inferred that members in the population represented by the sample can be meaningfully measured with respect to the trait (represented by the selection of variables) using a single (i.e. one-dimensional) scale.

Example

Consider, for example, public attitudes toward intervention in foreign countries as a trait in question. Presenting an appropriate sample of the adult population with the following questions can serve in measuring this attitude:

In the interest of our national security, do you favor spending money for encouraging a change in the policies of foreign country (C)? 1. No; 2. Yes, but only through nongovernmental organization (tax-deductible) funds; 3. Yes, any money, including nationally budgeted (taxpayers') money.

In the interest of our national security, do you favor sending special civilian advisors in order to encourage a change in the policies of country (C)? 1. No; 2. Yes, but only as part of the normal diplomatic mission; 3. Yes, any size of special civilian mission, as necessary.

In the interest of our national security, do you favor sending military advisers abroad in order to encourage a change in the policies of country (C)? 1. No; 2. Yes. In the interest of national security, do you favor sending our military troops abroad in order to encourage a change in the policies of country (C)? 1. No; 2. Yes.

A respondent who, for the said purpose, favors spending national funds (score 3), sending any size of civilian mission (3) as well as military advisors (2) but objects to sending troops (1), would have the profile 3321, which is comparable to, and represents a more positive intervention attitude than, profile 3221, because the former is equal to or greater than the latter on every variable. But 2111 would be said to be incomparable to 1232, because at least on one variable the former is higher than the latter, and at least on one variable the former is lower than the latter. If, in a particular survey, all profiles are comparable—that is, no incomparable pair of profiles is observed to occur—the result is a Guttman Scale. In the previously mentioned example, if out of the × 3 × 2 × 2 = 36 technically possible profiles, only the 7 profiles shown in the first column of Table 1 are actually observed, the data would constitute a Guttman Scale (or a cumulative scale).

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