The nature of percentile ranks scores is explored using concrete heuristic examples. It is explained why arithmetic operations require measurement on equal-interval scales, and that percentile ranks are not measured on equal-interval scales and therefore may not be added or averaged. The consequences of inappropriately adding percentile ranks are explored from the perspectives of various textbook authors. The discussion is couched in the context of the legal requirements for high-stakes testing. The information presented herein is not new or previously unknown, rather, the distinguishing characteristics of the position paper hopefully include clarity and concreteness of presentation. (Five figures and two tables illustrate the discussion, and an appendix provides additional commentary. Contains 31 references.) (Author)