Utility Indexes for Composite Scores
نویسندگان
چکیده
iv 1 Components of Reliability and U 1 2 Relative Utility Index Ur for Composite Scores 4 3 Estimating Ur for Raw Scores and Ũr for Scale Scores 5 3.1 Raw Scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Scale Scores . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.2.1 Variance of T ̃ . . . . . . . . . . . . . . . . . . . . . . . . 6 X 3.2.2 Covariance of T Z̃ ̃ and . . . . . . . . . . . . . . . . . . . 7 X 3.3 Estimating σ(Ẽ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.3.1 Linear Transformations . . . . . . . . . . . . . . . . . . . 8 3.3.2 Non-linear Transformations . . . . . . . . . . . . . . . . . 8 4 Examples 8 4.1 SAT⃝c Background . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4.2 Computation of Ũr for H vs. R in the SAT⃝c . . . . . . . . . . . 9 4.3 PSAT⃝c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 5 Concluding Comments 12 5.1 Definitions of Zi, Xi, wi, and vi . . . . . . . . . . . . . . . . . . . 13 5.1.1 The wi Weights . . . . . . . . . . . . . . . . . . . . . . . . 13 5.1.2 The vi Weights . . . . . . . . . . . . . . . . . . . . . . . . 14 5.2 Transformations of Component Parts of Ur . . . . . . . . . . . . 15 5.3 Proportionality Assumption for Scale-score Error Variances . . . 15 5.4 Special Case: Decisions About Subscores . . . . . . . . . . . . . . 17 5.5 Multidimensionality . . . . . . . . . . . . . . . . . . . . . . . . . 17 5.6 Caveats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
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