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Guttman scaling is also sometimes known as cumulative scaling or scalogram analysis. The purpose of Guttman scaling is to establish a one-dimensional continuum for a concept you wish to measure. What does that mean? Essentially, we would like a set of items or statements so that a respondent who agrees with any specific question in the list will also agree with all previous questions. Put more formally, we would like to be able to predict item responses perfectly knowing only the total score for the respondent. For example, imagine a ten-item cumulative scale. If the respondent scores a four, it should mean that he/she agreed with the first four statements. If the respondent scores an eight, it should mean they agreed with the first eight. The object is to find a set of items that perfectly matches this pattern. In practice, we would seldom expect to find this cumulative pattern perfectly. So, we use scalogram analysis to examine how closely a set of items corresponds with this idea of cumulativeness. Here, I'll explain how we develop a Guttman scale.

Define the Focus. As in all of the scaling methods. we begin by defining the focus for our scale. Let's imagine that you wish to develop a cumulative scale that measures U.S. citizen attitudes towards immigration. You would want to be sure to specify in your definition whether you are talking about any type of immigration (legal and illegal) from anywhere (Europe, Asia, Latin and South America, Africa).

Develop the Items. Next, as in all scaling methods, you would develop a large set of items that reflect the concept. You might do this yourself or you might engage a knowledgeable group to help. Let's say you came up with the following statements:

• I would permit a child of mine to marry an immigrant.
• I believe that this country should allow more immigrants in.
• I would be comfortable if a new immigrant moved next door to me.
• I would be comfortable with new immigrants moving into my community.
• It would be fine with me if new immigrants moved onto my block.
• I would be comfortable if my child dated a new immigrant.

Of course, we would want to come up with many more statements (about 80-100 would be desirable).

Rate the Items. Next, we would want to have a group of judges rate the statements or items in terms of how favorable they are to the concept of immigration. They would give a Yes if the item was favorable toward immigration and a No if it is not. Notice that we are not asking the judges whether they personally agree with the statement. Instead, we're asking them to make a judgment about how the statement is related to the construct of interest.

Develop the Cumulative Scale. The key to Guttman scaling is in the analysis. We construct a matrix or table that shows the responses of all the respondents on all of the items. We then sort this matrix so that respondents who agree with more statements are listed at the top and those agreeing with fewer are at the bottom. For respondents with the same number of agreements, we sort the statements from left to right from those that most agreed to to those that fewest agreed to. We might get a table something like the figure. Notice that the scale is very nearly cumulative when you read from left to right across the columns (items). Specifically if someone agreed with Item 7, they always agreed with Item 2. And, if someone agreed with Item 5, they always agreed with Items 7 and 2. The matrix shows that the cumulativeness of the scale is not perfect, however. While in general, a person agreeing with Item 3 tended to also agree with 5, 7 and 2, there are several exceptions to that rule.

While we can examine the matrix if there are only a few items in it, if there are lots of items, we need to use a data analysis called scalogram analysis to determine the subsets of items from our pool that best approximate the cumulative property. Then, we review these items and select our final scale elements. There are several statistical techniques for examining the table to find a cumulative scale. Because there is seldom a perfectly cumulative scale we usually have to test how good it is. These statistics also estimate a scale score value for each item. This scale score is used in the final calculation of a respondent's score.

Administering the Scale. Once you've selected the final scale items, it's relatively simple to administer the scale. You simply present the items and ask the respondent to check items with which they agree. For our hypothetical immigration scale, the items might be listed in cumulative order as:

• I believe that this country should allow more immigrants in.
• I would be comfortable with new immigrants moving into my community.
• It would be fine with me if new immigrants moved onto my block.
• I would be comfortable if a new immigrant moved next door to me.
• I would be comfortable if my child dated a new immigrant.
• I would permit a child of mine to marry an immigrant.

Of course, when we give the items to the respondent, we would probably want to mix up the order. Our final scale might look like:

 INSTRUCTIONS: Place a check next to each statement you agree with. _____ I would permit a child of mine to marry an immigrant. _____ I believe that this country should allow more immigrants in. _____ I would be comfortable if a new immigrant moved next door to me. _____ I would be comfortable with new immigrants moving into my community. _____ It would be fine with me if new immigrants moved onto my block. _____ I would be comfortable if my child dated a new immigrant.

Each scale item has a scale value associated with it (obtained from the scalogram analysis). To compute a respondent's scale score we simply sum the scale values of every item they agree with. In our example, their final value should be an indication of their attitude towards immigration.

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