Lecture 5
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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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Lecture 5

LECTURE 5

TRUE SCORE THEORY


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

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 


Assumptions

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)


Some results

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


Lecture 5

PATH DIAGRAM REPRESENTATION

x

x

e


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