Many school psychologists use the Cattell-Horn-Carroll (CHC) theory of cognitive abilities to guide their interpretation of scores from intelligence test batteries. Some may frequently assume that composite scores purported to measure the same CHC broad abilities should be relatively similar for individuals no matter what subtests or batteries were administered to obtain these scores. This study examined this assumption using six samples of preschool children, school-age children, or adults who completed two or more intelligence test batteries. From these samples, composites measuring the broad abilities Crystallized Intelligence, Visual Processing, Fluid Reasoning, and Processing Speed were compared to examine their exchangeability. Results indicate that most CHC broad ability composites produced scores that were not as exchangeable for individuals as may have been assumed by some. Discussion focuses on the influence of score reliability and on the interaction between examinee characteristics and the tasks used to measure the broad abilities. (Contains 2 tables and 9 footnotes.)