This research applied a cognitive model to identify item features that lead to irrelevant variance on the Test of Spoken English[TM] (TSE[R]). The TSE is an assessment of English oral proficiency and includes an item that elicits a description of a statistical graph. This item type sometimes appears to tap graph-reading skills--an irrelevant construct; TSE raters report that many examinees perform worse on this item type than they do on the other 11 items in the test. We adapted a cognitive theory of graph comprehension to predict the degree to which TSE graph items tap irrelevant skills such as graph reading. Through analyses of existing TSE data as well as an experiment, we show how the theory provides specific, empirically justified recommendations on the construction of graph items that minimize the influence of extraneous skills. (Contains 7 tables, 9 figures, and 8 notes.)