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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
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

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