Some Implications of Distinguishing Between Unexplained Variance That Is Systematic or Random

Abstract

Because error variance alternatively can be considered to be the sum of systematic variance associated with unknown variables and randomness, a tripartite assumption is proposed that total variance in the dependent variable can be partitioned into three variance components. These are variance in the dependent variable that is explained by the independent variable, variance in the dependent variable that is unexplained but systematic (associated with variance in unknown variables), and random variance. Based on the tripartite assumption, classical measurement theory, and simple mathematics, it is shown that these components can be estimated using observable data. Mathematical and computer simulations illustrate some of the important issues and implications.