If you look at the figure you should see that the only thing that the two observations have in common is their true scores, T . But the true score symbol T is the same for both observations. That the two observed scores, X 1 and X 2 are related only to the degree that the observations share true score. You should remember that the error score is assumed to be random. With this in mind, we can now define reliability more precisely.
Reliability is a ratio or fraction.
So, to get closer to a more formal definition, let's restate the definition above in terms of a set of observations. The easiest way to do this is to speak of the variance of the scores. Remember that the variance is a measure of the spread or distribution of a set of scores. We're getting to the critical part now. But how do we calculate the variance of the true scores.