Guttman's lower bounds

1. To compute Guttman's lower bounds ¹, recall the Reliability Analysis dialog box.

   

2. Select Guttman as the model.
3. Click OK.

Guttman proposed six measures of reliability that all give lower bounds for the true reliability of the survey. The first is a simple estimate that is the basis for computing some of the other lower bounds. L ₃ is a better estimate than L ₁, in the sense that it is larger, and is equivalent to Cronbach's alpha. L ₂ is better than both L ₁ and L ₃ but is more complex (although, because of today's computers, this is no longer a hindrance to its use). L ₅ is better than L ₂ when there is one item that has a high covariance with the other items, which in turn do not have high covariances with each other. Such a situation may occur on a test that has items that each pertain to one of several different fields of knowledge, plus one question that can be answered with knowledge of any of those fields. L ₆ is better than L ₂ when the inter-item correlations are low compared to the squared multiple correlation of each item when regressed on the remaining items. For example, consider a test that covers many different fields of knowledge and each item covers some small subset of those fields. Most item pairs will not have overlapping fields, but the fields of a single item should be well represented given all the remaining items on the test.

L ₄ is, in fact, the Guttman split-half coefficient. Moreover, it is a lower bound for the true reliability for any split of the test. Therefore, Guttman suggests finding the split that maximizes L ₄, comparing it to the other lower bounds, and choosing the largest.

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