Imaginary Confidence Limits of the Slope of the Major Axis of a Bivariate Normal Distribution: A Sampling Experiment

Abstract

A Monte Carlo study of confidence limits for the slope of the major axis of a bivariate normal distribution confirms that, when imaginary limits are interpreted as corresponding to an infinite interval covering all possible values of the parameter, the confidence interval behaves satisfactorily under repeated sampling. The excess of the actual over the nominal significance level is negligible even if samples are small and correlation is moderate. The probability of detecting a relationship correctly is never smaller for the major axis than for ordinary regression. Imaginary and exclusive confidence limits do not create problems in practice.