However, the test and retest scores can be thought of as two correlated parallel item scores, and thus their correlation can serve as C α of the single item.
We formulate a statistical model for parallel items to derive power functions as a function of C α under several study designs.
In this paper, to derive closed-from power functions, we formulate a statistical model for parallel items that relates the item scores to a measurement error problem.
To evaluate the impact of FS on construct validity and reliability of progress test scores, a progress test for radiology residents was divided into two tests of 100 parallel items (A and B).
That is, they do not address the issue of what score an individual might obtain on another occasion, or on a set of alternative, parallel items, but simply provide interval estimates for the percentage of the normative population who would score below the score obtained by the individual [ 26].
In this paper, we consider parallel items; for example, items within a same factor could be considered parallel for a unidimensional construct.
It is shown that C α is the same as a test-retest correlation of the scale scores of parallel items, which enables testing significance of C α. Closed-form power functions and samples size determination formulas are derived in terms of C α, for all of the aforementioned comparisons.
Assuming that parallel items were constructed and added to the CHBQ, a total of about only 17 items are required to achieve the same level of reliability as the much longer IMAQ.
This compound symmetry covariance structure, also known as essential τ-equivalence, is the covariance matrix of parallel items each of which targets the underlying true score for a unidimensional construct.
The instrument comprises 72 parallel items organized around eight quality-of-life domains in each of the two forms: a self-report and a report by others.
