A multivariate rank test for comparing mass size distributions

Particle size analyses of a raw material are commonplace in the mineral processing industry. Knowledge of particle size distributions is crucial in planning milling operations to enable an optimum degree of liberation of valuable mineral phases, to minimize plant losses due to an excess of oversize or undersize material or to attain a size distribution that fits a contractual specification. The problem addressed in the present paper is how to test the equality of two or more underlying size distributions. A distinguishing feature of these size distributions is that they are not based on counts of individual particles. Rather, they are mass size distributions giving the fractions of the total mass of a sampled material lying in each of a number of size intervals. As such, the data are compositional in nature, using the terminology of Aitchison 1 Aitchison, J. 1986. “The Statistical Analysis of Compositional Data”. London: Chapman and Hall. Crossref] , Google Scholar]] that is, multivariate vectors the components of which add to 100%. In the literature, various versions of Hotelling's T ² have been used to compare matched pairs of such compositional data. In this paper, we propose a robust test procedure based on ranks as a competitor to Hotelling's T ². In contrast to the latter statistic, the power of the rank test is not unduly affected by the presence of outliers or of zeros among the data.