The context for these notes is mostly norm-referenced testing.
Reliability reflects the degree to which true scores and observed scores correspond to each other.
That is, reliability is a measure of the degree to which a test score is free from error. Error is sometimes divided into random and systematic error. In the following discussion we are considering random error. It further assumes that each item has associated with it some variance associated with the variance in the latent trait and that all other variance in each item is error. If we let L be the latent trait and X1, X2, and X3 be three items on a test, we can diagram this situation like this.