Guttman Scale
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Guttman Scale

A Guttman Scale (named after Louis Guttman) is formed by a set of items if they can be ordered in a reproducible hierarchy.[1] For example, in a test of achievement in mathematics, if examinees can successfully answer items at one level of difficulty (e.g., summing two 3-digit numbers), they would be able to answer the earlier questions (e.g., summing two 2-digit numbers).

## Deterministic model

The Guttman scale only applies to tests, such as achievement tests, that have binary outcomes and it is assumed that respondents can only and will always respond in the same way. A perfect Guttman scale consists of a unidimensional set of items that are ranked in order of difficulty from least difficult to most difficult. Therefore, a person scoring a "7" on a ten item Guttman scale, will agree with items 1-7 and disagree with items 8,9,10. This means that a person's entire set of responses to all items can be predicted from their cumulative score because the model is deterministic. The extent to which a scale is reproducible can be estimated from the coefficient of reproducibility [1] and, to ensure that there is a range of responses (not the case if all respondents only endorsed one item) the coefficient of scalability is used.[2] In the creation of Guttman scales items that reduce reproducility of scalabilty are re-written or discarded. In Guttman scaling is found the beginnings of item response theory which, in contrast to classical test theory, acknowledges that items in questionnaires do not all have the same level of difficulty. Non-deterministic (ie stochastic) models have been developed such as the Mokken scale and the Rasch model.

## Example

The Guttman scale useful to design short questionnaires with good discriminating ability and works best for constructs that are hierarchical and highly structured such as social distance, organizational hierarchies, and evolutionary stages. A well-known example of a Guttman scale is the Bogardus Social Distance Scale:

1. Are you willing to permit immigrants to live in your country? (Least difficult)
2. Are you willing to permit immigrants to live in your community?
3. Are you willing to permit immigrants to live in your neighbourhood?
4. Are you willing to permit immigrants to live next door to you?
5. Would you permit your child to marry an immigrant? (Most difficult)

Agreement with item 5 implies agreement with items 1 to 4.

## References

1. ^ a b Stouffer, S.A., Guttman, L., Suchman, E.A., Lazarsfeld, P.F., Star, S.A., Clausen, J.A. (1950) Measurement and Prediction Princeton University Press
2. ^ Menzel, H. (1953) A new coefficient for scalogram analysis in Educational and Public Opinion Quarterly Volume: 15 issue: 2, page(s): 268-280]

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