1_22 - Reliability of a Composite 1. Spearman-Brown formula...

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Reliability of a Composite 1. Spearman-Brown formula • Assume k parallel composite; C = X 1 + X 2 + …. + X k - Reliability is; 2 ' 2 . C T CC C σ ρ= σ - Equal true scores = equal observed score means. - Equal error variance = equal observed score variance. - There are k variance terms and k ( k – 1) covariance terms. • The true score variance of the composite; 12 22 2 2 . Ck i j i j TT T T T T T T ij σ= σ+ σ+ + ρσσ ∑∑ " 2 2 2 (1 ) . Ci i ii i T iT T T kk k k k σ =σ+ −σ =σ+ σ−σ Since 2 1.00 , k T σ =σ = " • The observed variance of the composite; [] 2 2 ' ) 1( 1 ) ) . i j i j j i j i k σ=σ+σ+ +σ+ =σ+ −ρσ  =σ + −ρ =σ + −ρ  "
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• Then, [] 22 2 ' ' 2 2 ' ' ' 1( 1 ) ) . ) Ci i TT CC i i T ii i ii ii k kk k k k k σσ ρ= = + ρ σ +−ρ σ ρ = +−ρ (Spearman-Brown formula) • The Spearman-Brown formula shows that the reliability of a composite is a function of ; - the reliability of a component, and - the number of components. 2. Cronbach’s Coefficient Alpha • It does not have to assume that the components are parallel. • It estimates the lower bound of the reliability of the composite. • Important fact: When the components are “essentially tau-equivalent”, Coefficient Alpha estimates the reliability.
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This note was uploaded on 11/27/2011 for the course EDF 5432 taught by Professor Fenley during the Spring '06 term at FSU.

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1_22 - Reliability of a Composite 1. Spearman-Brown formula...

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