A method to reduce the width of confidence intervals by using a normal scores transformation

Abstract

In stating the results of their research, scientists usually want to publish narrow confidence intervals because they give precise estimates of the effects of interest. In many cases, the researcher would want to use the narrowest interval that maintains the desired coverage probability. In this manuscript, we propose a new method of finding confidence intervals that are often narrower than traditional confidence intervals for any individual parameter in a linear model if the errors are from a skewed distribution or from a long-tailed symmetric distribution. If the errors are normally distributed, we show that the width of the proposed normal scores confidence interval will not be much greater than the width of the traditional interval. If the dataset includes predictor variables that are uncorrelated or moderately correlated then the confidence intervals will maintain their coverage probability. However, if the covariates are highly correlated, then the coverage probability of the proposed confidence interval may be slightly lower than the nominal value. The procedure is not computationally intensive and an R program is available to determine the normal scores 95% confidence interval. Whenever the covariates are not highly correlated, the normal scores confidence interval is recommended for the analysis of datasets having 50 or more observations.