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