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.
Volume (Year): 56 (2002)
Issue (Month): 1 (January)
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- Barry Arnold & Robert Beaver & Richard Groeneveld & William Meeker, 1993. "The nontruncated marginal of a truncated bivariate normal distribution," Psychometrika, Springer;The Psychometric Society, vol. 58(3), pages 471-488, September.
- A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
- Jiang, Jiming, 1997. "Sharp upper and lower bounds for asymptotic levels of some statistical tests," Statistics & Probability Letters, Elsevier, vol. 35(4), pages 395-400, November.
- Aigner, Dennis & Lovell, C. A. Knox & Schmidt, Peter, 1977. "Formulation and estimation of stochastic frontier production function models," Journal of Econometrics, Elsevier, vol. 6(1), pages 21-37, July.
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