Changing Statistical Significance with the Amount of Information: The Adaptive α Significance Level.

We put forward an adaptive alpha which changes with the amount of sample information. This calibration may be interpreted as a Bayes/non-Bayes compromise, and leads to statistical consistency. The calibration can also be used to produce confidence intervals whose size take in consideration the amount of observed information.

[1]  James O. Berger,et al.  The Effective Sample Size , 2014 .

[2]  G. Casella,et al.  Statistical Inference , 2003, Encyclopedia of Social Network Analysis and Mining.

[3]  D. Pauler The Schwarz criterion and related methods for normal linear models , 1998 .

[4]  E. Moreno,et al.  Objective Testing Procedures in Linear Models: Calibration of the p‐values , 2006 .

[5]  L. Pericchi,et al.  Changing the paradigm of fixed significance levels: Testing Hypothesis by Minimizing Sum of Errors Type I and Type II , 2013, 1310.0039.

[6]  I. Good The Bayes/Non-Bayes Compromise: A Brief Review , 1992 .

[7]  M. J. Bayarri,et al.  Calibration of ρ Values for Testing Precise Null Hypotheses , 2001 .

[8]  T. Siegfried Odds are, it's wrong: Science fails to face the shortcomings of statistics , 2010 .

[9]  Gerry Leversha,et al.  Statistical inference (2nd edn), by Paul H. Garthwaite, Ian T. Jolliffe and Byron Jones. Pp.328. £40 (hbk). 2002. ISBN 0 19 857226 3 (Oxford University Press). , 2003, The Mathematical Gazette.

[10]  James O. Berger,et al.  Objective Bayesian Methods for Model Selection: Introduction and Comparison , 2001 .

[11]  J. Brooks Why most published research findings are false: Ioannidis JP, Department of Hygiene and Epidemiology, University of Ioannina School of Medicine, Ioannina, Greece , 2008 .

[12]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[13]  L. Wasserman,et al.  A Reference Bayesian Test for Nested Hypotheses and its Relationship to the Schwarz Criterion , 1995 .

[14]  G. Schwarz Estimating the Dimension of a Model , 1978 .