Guttman scales

Guttman (Guttman, 1980) scaling is also based on the principle that the composite score indicates how the items making up the scale were answered. The following example will show what we mean. To keep our example simple, we will use only three items for measuring attitudes toward wives working outside the home and use only "agree" or "disagree" as responses. The items are:

1. It is all right for married women without children to work outside the home.
             Agree         Disagree
2. It is all right for a mother with older children to work outside the home.
             Agree         Disagree
3. It is all right for a mother with young children to work outside the home.
             Agree         Disagree

These items were selected because the responses were expected to form a predicted pattern. The greatest amount of agreement was expected for item 1, the least for item 3, with item 2 being in between. Scores of 1 for agreement and 0 for disagreement are assigned to each item. Composite scores, therefore, could vary from 0, when respondents disagree with all three items, to 3, when they agree with all three items. The top half of Table 7.3 shows the responses that would fit the expected pattern.

The first four patterns, which represent the predicted patterns of responses, are known as scale types.   For each scale type a respondent's composite score says exactly which items the respondent agreed with. The bottom half of the table shows patterns of responses that deviate from the predicted patterns. Each of these four mixed types involves a degree of error. No matter how the items are scored, the composite score will not faithfully describe which items the respondent agreed with. For mixed types, we first have to assign a number, called an index score, which comes the closest to describing the response pattern to the items used. Notice that an index score of 1 for mixed types could be obtained under two different response patterns. You can see this for the first and third mixed types.   The same is true for an index score of 2 for the second and fourth   mixed types, but with scale types, the score of 1 and 2 are just as clear as the score of 0 or 3.

Table 7.3. Illustrative scaling response patterns

Scale types	Responses	Score
Agree with all 3 items	1 1 1	3
Agree with items 1 and 2	1 1 0	2
Agree with only item 1	1 0 0	1
Disagree with all 3 items	0 0 0	0

	Responses	Index score	Index score
Mixed types, do not fit the expected pattern	0 1 0	1	2
	1 0 1	2	3
	0 0 1	1	0
	0 1 1	2	3

In developing a composite score, the scores for the scale types are simply added, but scoring the mixed types presents some problems. No matter how they are scored, some error will result. Our objective is to minimize the amount of error that will occur. To achieve this goal, mixed types are first scored by adding the "yes" responses. Scores assigned in this way are shown under the heading "index score" in Table 7.3. The index scores are then converted to scale scores, but in such a way as to minimize the amount of error that is involved. For the mixed type of 0-1-0, a scale score of 1 would imply an actual response pattern of 1-0-0. Giving a score of 1 for the first mixed type would involve 2 errors, 0 to 1 for the first item and 1 and 0 for the second item. But if we assume the 1 response for the second item really meant a 1 response for the first item also, then we could assign a score of 2 to this mixed type.    In making this assumption we are creating an error of 1, but this is lower than the error of 2 that would have occurred if both items had been scored as 1.

Using the same reasoning, we would assign a score of 3 to the mixed type of 1-0-1. From the pattern of the three responses we could assume that the middle response should have been 1 also.    The next mixed type, 0-0-1, is assigned a score of 0. We assume from the pattern that the last 1 response was in error: So, we maintain an error of 1, which is the smallest amount possible. The last mixed type is scored as 3 for the same reason as given for the second type.

After scoring all the mixed types, we determine the percentage of all responses that fit the predicted scale types. The number for all responses is found by multiplying the number of respondents by the number of items used. Assuming that we had a sample of 150 respondents, the number for all responses would be 150(3) or 450 responses. Now we need to find how many of these responses fit the expected pattern by being a scale type. This percentage is called the coefficient of reproducibility and is found by the following formula: