Confidence intervals and sample sizes

In a recent paper, Beal (1989, Biometrics 45, 969-977) considers the problem of determining the appropriate sample size when inference about a parameter theta is to be made on the basis of a confidence interval (CI). He suggests that the sample size should be chosen so that the probability that the length of the CI is less than a given value, conditional on the interval including the true theta, is greater than a specified level. In this note, in which we concentrate on two-sided intervals, this suggestion is examined, as is the effect of uncertainty in our knowledge of the population variance sigma 2 on estimates of sample size.