Much research has been devoted to identification of differential item functioning (DIF), which occurs when the item responses for individuals from two groups differ after they are conditioned on the latent trait being measured by the scale. There has been less work examining differential step functioning (DSF), which is present for polytomous…

This overview of the role of error and tolerance for error in measurement asserts that the generic precision associated with a measurement procedure is defined as the root mean square error, or standard error, in some relevant population. This view of precision is explored in several applications of measurement. (SLD)