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Statistical implications of selectively reported inferential results

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  • Loperfido, Nicola

Abstract

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.

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  • Loperfido, Nicola, 2002. "Statistical implications of selectively reported inferential results," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 13-22, January.
    • Handle: RePEc:eee:stapro:v:56:y:2002:i:1:p:13-22
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    1. Müller K. & Richter W.-D., 2016. "Extreme value distributions for dependent jointly ln,p-symmetrically distributed random variables," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-33, February.
    2. Lui, Kung-Jong & Chang, Kuang-Chao, 2009. "Corrigendum to: "Testing homogeneity of risk difference in stratified randomized trials with noncompliance" [Comput. Statist. Data Anal. 53 (2008) 209-221]," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1529-1529, February.
    3. Young, Phil D. & Kahle, David J. & Young, Dean M., 2017. "On the independence of singular multivariate skew-normal sub-vectors," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 58-62.
    4. Christine Amsler & Alecos Papadopoulos & Peter Schmidt, 2021. "Evaluating the cdf of the Skew Normal distribution," Empirical Economics, Springer, vol. 60(6), pages 3171-3202, June.
    5. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2007. "On the exact distribution of linear combinations of order statistics from dependent random variables," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1876-1894, November.
    6. Fung, Thomas & Seneta, Eugene, 2016. "Tail asymptotics for the bivariate skew normal," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 129-138.
    7. Valentina Mameli & Monica Musio & Erik Sauleau & Annibale Biggeri, 2012. "Large sample confidence intervals for the skewness parameter of the skew-normal distribution based on Fisher's transformation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(8), pages 1693-1702, February.
    8. Fung, Thomas & Seneta, Eugene, 2021. "Tail asymptotics for the bivariate equi-skew generalized hyperbolic distribution and its Variance-Gamma special case," Statistics & Probability Letters, Elsevier, vol. 178(C).
    9. Loperfido, Nicola, 2008. "A note on skew-elliptical distributions and linear functions of order statistics," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3184-3186, December.
    10. Madadi, Mohsen & Khalilpoor, Parisa & Jamalizadeh, Ahad, 2015. "Regression mean residual life of a system with three dependent components with normal lifetimes," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 182-191.
    11. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2008. "On the exact distribution of the maximum of absolutely continuous dependent random variables," Statistics & Probability Letters, Elsevier, vol. 78(1), pages 27-35, January.
    12. Barry Arnold & Robert Beaver & A. Azzalini & N. Balakrishnan & A. Bhaumik & D. Dey & C. Cuadras & J. Sarabia & Barry Arnold & Robert Beaver, 2002. "Skewed multivariate models related to hidden truncation and/or selective reporting," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 11(1), pages 7-54, June.
    13. Roohollah Roozegar & Ahad Jamalizadeh & Mehdi Amiri & Tsung-I Lin, 2018. "On the exact distribution of order statistics arising from a doubly truncated bivariate elliptical distribution," METRON, Springer;Sapienza Università di Roma, vol. 76(1), pages 99-114, April.
    14. Barry C. Arnold & Robert J. Beaver, 2007. "Skewing Around: Relationships Among Classes of Skewed Distributions," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 153-162, June.
    15. Huang, Wen-Jang & Chen, Yan-Hau, 2007. "Generalized skew-Cauchy distribution," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1137-1147, June.

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