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LECTURE 5

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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

- 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

- 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)

- 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