Classical Test Theory

What is Classical Test Theory?

Classical test theory (CTT) is an approach to estimating a latent trait (e.g. math aptitude, attitude toward writing) that uses a measure (test) to estimate a person’s amount of that trait. It’s often contrasted with Item Response Theory.

The idea of CTT is expressed in the very basic equation:

$$X=T+ϵ$$

Or, a person’s score, $X$ on a test is their true score, $T$, plus some error, $ϵ$. The error is assumed to be normally distributed with a mean of 0.