Detecting unusual similarity in the item responses of a pair of examinees usually conditions on the pair's overall test performance (e.g., raw scores). Doing this, however, often requires assumptions about the invariance of other examinee pair characteristics. In this study, we examined the appropriateness of such assumptions about selected examinee pair characteristics using item response data from the ACT Assessment[R]. We found that the number of identical incorrect responses on multiple choice tests were slightly higher for same high school, female, and twin pairs. Pairs who took the same mathematics courses and received the same grades had slightly higher levels of identical incorrect responses on the ACT Mathematics test. Across the four ACT tests, twin pairs were about twice as likely to have a similarity level described as a one-in-a-thousand event, all other shared characteristics held constant. The results for twin pairs can be used to set an upper bound for the level of similarity in identical incorrect responses that is due to examinee's shared environment and academic experiences. Tables are appended. (Contains 16 tables, 2 figures, and 3 footnotes.)