Dimensions of Statistics

Summary Physicists have long been accustomed to using conditions of dimensional homogeneity in respect of Mass, Length and Time in order to check the validity of formulae. Experienced statisticians use similar ideas, but do not seem to state them explicitly in books or teaching. A number of examples are presented to illustrate, for univariate and multivariate data, how considerations of dimensionality can rapidly indicate that a proposed formula must be wrong. Arguments based on dimensions are less useful in statistics than in physics for positive inference on the form a result must have, but can be more powerful in detecting errors because of a wider choice of dimensional specifications.