Guttman scaling (Guttman scalogram analysis)

An approach to ordinal scaling developed by Louis Guttman. The purpose of scalogram analysis is to develop a scale measuring ordered levels of some attitude. Guttman scaling is especially useful in addressing two problems in the measurement of poorly defined or complex attitudes: (1) determining whether or not a series of statements tapping the attitude form a single dimension, and (2) determining whether or not the series of statements can be ordered according to level of the attitude that satisfies the rule of transitivity.
 
The first step in a scalogram analysis is to draft a series of statements which will define the domain of the attitude and assess successive levels of that attitude. In a typical scalogram procedure, statements would be scaled in an agree ? disagree format. Respondents would be asked to agree or disagree with each of the statements. Individual responses would then be analyzed to see if the pattern of agreement or disagreement corresponds to one that would confirm these items as measuring the same dimension and forming an ordinal set of anchors conforming to the rule of transitivity.
 
The exhibit below illustrates an ideal pattern of agreement ? disagreement in scalogram analysis. One would expect, for example, a person who agrees with statement 1 to also agree with statements 4, 2, and 3 in the example of the exhibit with 4 statements. A person who responded in this fashion would agree with each of the statements about the product. If an agreement were scored as a 1 and a disagreement as a 0, the values can be summed and a total score of 4 can be assigned to that respondent, indicating the highest level of attraction or preference. Next, a person might not agree that he would not think of entertaining with the product, but agree that he or she prefers it to all other products. One would logically expect agreement also with statements 2 and 3, yielding a total score for this person of 3.


As a matter of fact, scalogram analysis never yields the perfect pattern illustrated in the exhibit. It employs several criteria for the analysis of patterns like those in the exhibit which allow the researcher to determine whether a set of items constitutes a close enough approximation to a perfect pattern to conclude that they fall in the same dimension. The most important of these criteria is the reproducibility of the responses that is, the proportion of responses of a large number of judges that actually fall into the perfect pattern indicated in the exhibit. As a measure of predicting the entire response structure for an individual respondent from the rank position, Guttman has suggested the coefficient of reproducibility given as
 

Rep (total) =	total number of inconsistent responses
	total number of responses

 
or for the reproducibility of a single item I:
 

Rep (I) =	total number of inconsistent responses item I
	total number of respondents.

 
Many anchors will be discarded in the development of a scalogram. It is advisable to start with at least 12 items in order to end up with 4 anchors for a scale, and do the final scalogram development on at least 100 subjects.
 
Although the technique is useful for determining whether or not a set of already designed items conforms to a single dimension, it offers little help in selecting items that are likely to form a single dimension.
 
Guttman scaling is not really a scaling technique in the classical sense of the term. Rather, it is a procedure for determining whether a set of stimulus objects can be ordered into an internally consistent, unidimensional scale or whether a group of scalers can be ranked along a single, ordered continuum.