True Score Theory
in Measurement
True Score Theory
Holds that the...
Observed
score
True Score Theory
...is a linear additive function of some unseen...
Observed
score
=
True
ability
True Score Theory
...and a random component...
Observed
score
=
True
ability
+
Random
error
True Score Theory
Observed
score
=
True
ability
+
Random
error
T + e
In notational form, the right side of the equation is...
True Score Theory
Observed
score
X
=
True
ability
+
Random
error
T + e
...and the whole model is represented in equation form as...
True Score Theory
Observed
score
=
True
ability
+
Random
error
It follows from this that the variability of the
observed score, X, is the additive combination of
the variability of the true score and the error.
var(X) = var(T) + var(e)
True Score Theory
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Is a simplistic yet powerful model for
measurement
Is not the only model around
Is the foundation of reliability theory
Can be used in computer simulations to
generate “observed” scores with certain
properties