The aim of this article is to consider Bayesian and frequentist inference methods for measures of incremental cost effectiveness in data obtained via a clinical trial. The most useful measure is the cost-effectiveness (C/E) acceptability curve. Recent publications on Bayesian estimation have assumed a normal posterior distribution, which ignores uncertainty in estimated variances, and suggest unnecessarily complicated methods of computation. We present a simple Bayesian computation for the C/E acceptability curve and a simple frequentist analogue. Our approach takes account of errors in estimated variances, resulting in calculations that are based on distributions rather than normal distributions. If inference is required about the C/E ratio, we argue that the standard frequentist procedures give unreliable or misleading inferences, and present instead a Bayesian interval.