Confidence Curves: An Omnibus Technique for Estimation and Testing Statistical Hypotheses

Abstract

Abstract A standard practice of physical scientists is to report estimates ("measurements") accompanied by their standard errors (or alternatively "average errors" or "probable errors"). Such reports are interpreted flexibly as appropriate in various contexts of application. With the usual normality assumption, such reports may be read as representing confidence intervals or limits at the various confidence levels, and this omnibus character largely accounts for the convenience and flexibility of such reports and interpretations. For estimators not normally distributed, a formal analogue of such reports is provided by confidence curves, which are estimates of an omnibus form incorporating confidence intervals and limits at various levels. The definition and computation of such estimates, and their graphical representation and interpretation, are discussed and illustrated by an example.