The measurement of poverty involves two problems: identifying the poor and constructing an index to measure the intensity of poverty. The headcount ratio is one of the widely used indices for the measurement of poverty. This article considers some of the other decomposable (i.e. additively separable) poverty measures. The importance of this property (decomposability) and of subgroup consistency for a poverty measure is highlighted. Since most of these poverty measures are estimated on the basis of sample surveys, the statistical significance of the observed differences is tested using the distribution-free approach proposed by Kakwani (1993, Review of Economics and Statistics, 75: 632-40). The Income and Expenditure Survey conducted in 1995 by Statistics South Africa, then called Central Statistical Service, is used in the study.