Generalized p Values and Random p Values When the Alternative to Uniformity Is a Mixture of a Beta(1,2) and Uniform
Combining p values methods and uniformity tests are closely related subjects in meta analysis. In this context it is also known that publication bias can seriously impair an overall decision. The recent concepts of generalized p values and of random p values emphasize that, when faced with a significant number of results that casts some doubt on the null hypothesis, the correct approach to the problem should be to combine evidence under the alternative hypothesis. Following previous research, we investigate generalized p values and random p values for testing uniformity when the alternative is a mixture of a Beta(1,2) and standard uniform random variables.
This research has been supported by National Funds through FCT—Fundação para a Ciência e a Tecnologia, project PEst-OE/MAT/UI0006/2011.
The author would also like to thank Professor Dinis Pestana for the stimulating conversations held about the topics discussed here, and the reviewers for their comments which led to a substantial improvement of the chapter.
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