Statistical implications of selectively reported inferential results

Researchers sometimes report only the largest estimate, the most significant test statistic and the most shifted confidence interval. The following result quantifies the statistical implications of this behavior, when the choice is restricted to two inferential procedures: the minimum and maximum of two standardized random variables whose distribution is jointly normal is skew-normal. More generally, the distribution of the minimum and maximum of two random variables whose distribution is bivariate normal centered at the origin is a mixture with equal weights of scaled skew-normal distributions. (C) 2002 Elsevier Science B.V. All rights reserved.