A point estimate may provide, in logic or in practice, an unsatisfactory answer to some problems, and the additional requirement then arises for estimating limits within which a parameter is thought to lie. An elementary example of such an ‘interval estimate’ occurred in Example 2(c) of § 1, and we may recall the custom of quoting the measurement of a physical constant in such a form as g = 32 ± 2 units—which is an assertion, made according to some convention, that the true value of the quantity g lies between 30 and 34 units. We consider below some of the criteria which have been suggested for interval estimation, some methods of satisfying them, and a few of the results to which they lead.