We know the denominator in the fraction, 450, but we need to determine the number of errors that occurred. To get this number, we count how many times each mixed type occurred and then add these frequencies to get the total number of errors that occurred. To complete our calculation, we will use the illustrative frequencies for mixed types shown in Table 7.4, which we created for this illustration of scoring. The frequency of the mixed types of 1-1-0 was 10. Frequencies for other mixed types were 5, 4, and 2.

Table 7.4 Frequencies for mixed types

Mixed Types	Frequency
1 1 0	10
1 0 1	5
0 0 1	4
0 1 1	2
Total	21

A perfect scale is represented by a coefficient of reproducibility of 100%. But such scales seldom occur: almost all sets of items result in some mixed types and coefficients of less than 100%. Researchers accept this fact and have set a standard of 90% as the minimum level of acceptable reproducibility: In other words, about 10% of mixed types is considered acceptable.  

Three final comments are necessary in concluding this discussion of Guttman scaling. First, scale types exist only in terms of a specific set of responses from a specific group of respondents. This means that you have to be careful about using items that formed a scale for some other sample. The same items may or may not form a scale with your sample. You will have to collect the necessary data and test the items to see whether the responses meet the criteria we have just described. Second, Guttman scaling becomes more difficult as the number of items and the number of responses used increases. Both can contribute to a larger number of mixed types which lowers the coefficient of reproducibility. If you plan to try to form Guttman scales, we suggest using a limited number of items and the fewest possible response categories. Third, because of the way Guttman scales are constructed, researchers generally do not report reliability data for them. Sometimes validity data are not reported as well. We recommend, however, that validity data be obtained and reported to strengthen any conclusions you will present. Finally, we probably do not have to tell you that scoring mixed types can be difficult.

For another discussion of Guttman scaling, go to: Guttman Scaling.

Social scientists have developed all kinds of scales. It is not surprising, therefore, that hundreds of Web sites on scaling and scales exist. We refer you to only one of these sites. For an alternative and, in some ways different approach to the development of scales, visit Scaling, a link from this page will take you to General Issues in Scaling.

Looking at these sites should help you grasp the basic idea behind scaling and perhaps give you some ideas for use of scaling in your research.