# LECTURE 5 - PowerPoint PPT Presentation

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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

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

• 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

•  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

• 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

PATH DIAGRAM REPRESENTATION

x

x

e