Human skeletal muscle consists of contractile elements (fibres) that may be differentiated according to their physiological and biochemical properties. The different types of fibre are distributed throughout each muscle, with the pattern (when viewed as a cross-section) of cell distribution being an important determinant of the functional properties of each muscle. It is well known that the proportions and distributions of muscle fibre types change with advancing age or disease, but few studies have quantitatively investigated these changes. A better knowledge of the nature of changes in muscle fibre distributions is an essential requirement for future development of therapies and interventions directed at maintaining or restoring good muscle function. In this work, we examine several statistical methods designed to gauge the departure of a dichotomously labelled muscle fibre distribution from that of a random fibre-type dispersal. These methods are also applicable to a wide range of biological investigations in which the spatial distribution of cells or specimens underpins an important biological principle. This work includes the proposal of a novel technique, based on weighted kernel-smoothed density ratios, which can account for the variable areas of the individual fibres. We illustrated the methodology by using a number of real-data examples, and we employed a comprehensive set of simulations to assess the empirical power and false-positive rates of these tests. Copyright © 2013 John Wiley & Sons, Ltd.