Conventional wisdom says that the middle classes in many developed countries have recently suffered losses, both in terms of the share of the total population belonging to the middle class, and also their share in total income. Here distribution-free methods are developed for inference on these shares, by means of deriving expressions for the asymptotic variances of sample estimates of them, and the covariance of the estimates. Asymptotic inference can be undertaken on the basis of asymptotic normality. Bootstrap inference can be expected to be more reliable, and appropriate bootstrap procedures are proposed. Samples drawn from Canadian census data are used to test various hypotheses about the middle-class shares, and confidence intervals for them are computed. It is found that, for the earlier censuses, sample sizes are large enough for asymptotic and bootstrap inference to be almost identical, but that, in the twenty-first century, the bootstrap fails on account of the growth of heavy right-hand tails in the income distributions of both men and women.