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LECTURE 5

LECTURE 5. TRUE SCORE THEORY. True Score Theory. OBJECTIVES: - know basic model, assumptions - know definition of reliability, relation to TST - be able to compute estimates of reliability for: internal consistency test-retest parallel forms. BASIC EQUATION. x =  + e

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LECTURE 5

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  1. LECTURE 5 TRUE SCORE THEORY

  2. True Score Theory OBJECTIVES: - know basic model, assumptions - know definition of reliability, relation to TST - be able to compute estimates of reliability for: internal consistency test-retest parallel forms

  3. BASIC EQUATION • x =  + e • x = observed score •  = true (latent) score: represents the score that would be obtained over many independent administrations of the same item or test • e = error: difference between y and 

  4. ASSUMPTIONS •  and e are independent (uncorrelated) • The equation can hold for an individual i on item j at one occasion k: • xijk = ijk + eijk (individual) • x*** = *** + e*** (group) • combinations (individual across time)

  5. SOME RESULTS • VAR(X) = VAR() + VAR(e) 2x = 2 + 2e • Correlation of x and  is the index of reliability: x = COV(x, )/ x  =COV(+e, )/ x  = 2 / x  =  / x

  6. PATH DIAGRAM REPRESENTATION x x  e

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