This question relates to situations where we apply some test to the same people at Time 1 and Time 2, and then calculate the correlation between scores at Time 1 and Time 2.
I am reading the book Principles & Applications of Assessment in Counseling, which states here on p.52 that:
Therefore, if the reliability coefficient using test-retest were .80, using classical test theory we would interpret it by saying that 80% of the variance is true to observed variance and 20% is error to observed variance. In reliability, we don't square the correlation coefficient or use the coefficient of determination. Instead, we simply use the reliability coefficient itself to evaluate the degree of measurement error.
I've seen it suggested in many places that it's a common mistake to square the measurement error in this scenario. However, I do not understand why it is a mistake or precisely what is meant by 'reliable variance'.
Whiston, S. C. (2009). Principles & applications of assessment in counseling. Belmont, CA : Brooks/Cole, Cengage Learning.