A test for using the sum score to obtain a stochastic ordering of subjects

For many psychological test applications, the simple sum score across the items is used to make inferences about subjects. However, most of the item response theory models for psychological test data do not support such usage of the sum score. A simple test is proposed to assess whether the sum score can be used to obtain a stochastic ordering of subjects. This test is based on general (nonparametric) conditions and requires only the estimation of the unconstrained proportions.