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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.

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Presentation on theme: "LECTURE 5 TRUE SCORE THEORY. True Score Theory OBJECTIVES: - know basic model, assumptions - know definition of reliability, relation to TST - be able."— Presentation transcript:

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: x ijk =  ijk + e ijk (individual) x *** =  *** + e *** (group) combinations (individual across time)

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

6  x xx e PATH DIAGRAM REPRESENTATION


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