Background This paper examines an aspect of the problem of measuring inequality in health services. The measures that are commonly applied can be misleading because such measures obscure the difficulty in obtaining a complete ranking of distributions. The nature of the social welfare function underlying these measures is important. The overall object is to demonstrate that varying implications for the welfare of society result from inequality measures. Method Various tools for measuring a distribution are applied to some illustrative data on four distributions about mental health services. Although these data refer to this one aspect of health, the exercise is of broader relevance than mental health. The summary measures of dispersion conventionally used in empirical work are applied to the data here, such as the standard deviation, the coefficient of variation, the relative mean deviation and the Gini coefficient. Other, less commonly used measures also are applied, such as Theil's Index of Entropy, Atkinson's Measure (using two differing assumptions about the inequality aversion parameter). Lorenz curves are also drawn for these distributions. Results Distributions are shown to have differing rankings (in terms of which is more equal than another), depending on which measure is applied. Conclusion The scope and content of the literature from the past decade about health inequalities and inequities suggest that the economic literature from the past 100 years about inequality and inequity may have been overlooked, generally speaking, in the health inequalities and inequity literature. An understanding of economic theory and economic method, partly introduced in this article, is helpful in analysing health inequality and inequity.