Strong tests of developmental ordering hypotheses: integrating evidence from the second moment

Developmental ordering is a fundamental prediction in developmental science. However, tests of ordering hypotheses are not generally available for continuously developing variables. One promising test of developmental ordering, the shape of the relationship between 2 variables, requires that changes in each underlying variable are captured equally well across the developmental span (measures are linearly related to the variables). If either measure is more sensitive to earlier or later developmental changes in the underlying variable, the shape of the relationship changes radically. The article demonstrates that the viable alternative hypotheses for an observed developmental relationship require specific types of nonlinearity in measurement and, therefore, have testable predictions for the residuals (the second moment). Ordering as evidence in developmental science is discussed.