In many practical applications of item response theory, the parameters of overlapping subsets of test items are estimated from different samples of examinees. A linking procedure is then employed to place the resulting item parameter estimates onto a common scale. It is standard practice to ignore the uncertainty associated with the linking step when drawing inferences that involve items from different subsets, a situation that arises, for example, in the measurement of change. This paper outlines how the uncertainty can be accounted for and exemplifies the ideas with a jackknife approximation for the Stocking-Lord linking procedure. Examples from the National Assessment of Educational Progress suggest that the resulting uncertainty will usually be negligible for inferences about individuals, but can constitute a major source of estimation error in aggregate statistics such as changes in group means. (Contains 2 figures, 9 tables, and 13 references.) (Author)