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The Coefficient of Reproducibility

Unfortunately, we’ve got those other seven people to deal with. For whatever reasons, informants 10-16 do not conform to the pattern produced by the data from informants 1-9. The data for persons 10-16 are ‘‘errors’’ in the sense that their data diminish the extent to which the index of acculturation forms a perfect scale. To test how closely any set of index data reproduces a perfect scale, apply Guttman’s coefficient of reproducibility, or CR. The formula for Guttman’s CR is:

Given the pattern in table 11.1 (and from our hypothesis about the order in which people adopt the three indicators of acculturation), we don’t expect to see those minus signs in column 1 for respondents 10, 11, and 12. If the data scaled according to our hypothesis, then anyone who speaks fluent Spanish and lives in a traditional house should wear Western-style clothes, as is the case with informants 4, 5, and 6. Those informants have a score of 2. It would take three corrections to make cases 10, 11, and 12 conform to the hypothesis (you’d have to replace the minus signs in column one with pluses for respondents 10, 11, and 12), so we count cases 10, 11, and 12 as having one error each.

We don’t expect to see the plus signs in column 3 for informants 13, 14, and 15. If our hypothesis were correct, anyone who has a plus in column 3 should have all pluses and a score of 3 on acculturation. If we give respondents 13, 14, and 15 a scale score of 3 (for living in a Western-style house), then those three cases would be responsible for six errors—you’d have to stick in two pluses for each of the cases to make them come out according to the hypothesis. Yes, you could make it just three, not six errors, by sticking a minus sign in column 3. Some researchers use this scoring method, but I prefer the more conservative method of scoring more errors. It keeps you on your toes.

Finally, we don’t expect that minus sign in column 2 of respondent 16’s data. That case creates just one error (you only need to put in one plus to make it come out right). All together, that makes 3 + 6 + 1 = 10 errors in the attempt to reproduce a perfect scale. For table 11.1, the CR is

which is to say that the data come within 21% of scaling perfectly. By convention, a coefficient of reproducibility of .90 or greater is accepted as a significant approximation of a perfect scale (Guttman 1950). I’m willing to settle for around .85, especially with the conservative method for scoring errors, but .79 just isn’t up to it, so these data fail the Guttman test for unidimensionality.

 
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