SummaryThe study of multivariate outliers raises many problems of definition, principle and manipulation. Well‐authenticated tests of discordancy exist only for the multivariate normal distribution. Detection of outliers in non‐normal distributions involves the adoption of appropriate criteria to represent ‘extremeness' of observations in a sample; corresponding tests of discordancy usually require tedious, or even intractable, distributional and computational manipulations. A class of transformations of the data is considered with a view of transferring some of the familiar and desirable features of discordancy tests for normal samples to non‐normal sit