Most researchers and students in psychology learn of S. S. Stevens’ scales or “levels” of measurement (nominal, ordinal, interval, and ratio), and of his rules setting out which statistical analyses are admissible with each measurement level. Many are nevertheless left confused about the basis of these rules, and whether they should be rigidly followed. In this article, I attempt to provide an accessible explanation of the measurement-theoretic concerns that led Stevens to argue that certain types of analyses are inappropriate with data of particular levels of measurement. I explain how these measurement-theoretic concerns are distinct from the statistical assumptions underlying data analyses, which rarely include assumptions about levels of measurement. The level of measurement of observations can nevertheless have important implications for statistical assumptions. I conclude that researchers may find it more useful to critically investigate the plausibility of the statistical assumptions underlying analyses than to limit themselves to the set of analyses that Stevens believed to be admissible with data of a given level of measurement.