Several poverty indices have been suggested to measure the intensity of poverty suffered by those below the poverty line. Because the indices are estimated on the basis of sample observations, we need to test whether the observed differences in their values are statistically significant. This paper provides distribution-free asymptotic confidence intervals and statistical inference for additive poverty indices. The methodology developed in the paper is applied to analyse poverty in Cote d'Ivoire from the data of the Living Standards Survey, 1985.