Median of the p Value Under the Alternative Hypothesis

@article{Bhattacharya2002MedianOT,
  title={Median of the p Value Under the Alternative Hypothesis},
  author={Bhaskar Bhattacharya and Desale Habtzghi},
  journal={The American Statistician},
  year={2002},
  volume={56},
  pages={202 - 206}
}
Due to absence of an universally acceptable magnitude of the Type I error in various fields, p values are used as a well-recognized tool in decision making in all areas of statistical practice. The distribution of p values under the null hypothesis is uniform. However, under the alternative hypothesis the distribution of the p values is skewed. The expected p value (EPV) has been proposed by authors to be used as a measure of the performance of the test. This article proposes the median of the… 
View on Taylor & Francis
lagrange.math.siu.edu
55 Citations
Highly Influential Citations
5
Background Citations
14
Methods Citations
11

55 Citations

Citation Type

Citation Type

P Values are not Error Probabilities
Confusion surrounding the reporting and interpretation of results of classical statistical tests is widespread among applied researchers. The confusion stems from the fact that most of these…
The p value line: a way to choose the tuning constant in tests based on the Huber $${\varvec{M}}$$M-estimator
In this paper, we propose a method to choose a test result from several competing ones. The choice is based on the p value under the alternative, i.e., the probability of obtaining an extreme or a…
PoweR: A Reproducible Research Tool to Ease Monte Carlo Power Simulation Studies for Goodness-of-fit Tests in R
TLDR
An overview of the main design aims and principles of the PoweR package, as well as strategies for adaptation and extension are given, to help new users in getting started.
A Reckless Guide to P-values : Local Evidence, Global Errors.
  • M. Lew
  • Economics
    Handbook of experimental pharmacology
  • 2020
TLDR
This chapter demystifies P-values, hypothesis tests and significance tests and introduces the concepts of local evidence and global error rates, which are useful indices of evidence and deserve their place in the statistical toolbox of basic pharmacologists.
Non-parametric power-law surrogates
Power-law distributions are essential in computational and statistical investigations of extreme events and complex systems. The usual technique to generate power-law distributed data is to first…
To P or not to P: on the evidential nature of P-values and their place in scientific inference
TLDR
It is shown that P-values quantify experimental evidence not by their numerical value, but through the likelihood functions that they index.
Group sequential tests for delayed responses (with discussion)
Summary.  Group sequential methods are used routinely to monitor clinical trials and to provide early stopping when there is evidence of a treatment effect, a lack of an effect or concerns about…
A comparison of normality testing methods by empirical power and distribution of P-values
  • T. Uhm, S. Yi
  • Mathematics
    Communications in Statistics - Simulation and Computation
  • 2021
Normal distribution is commonly assumed distribution in statistical inference. Therefore, goodness-of-fit test for normality is required as a preliminary procedure in the applications. Most relevan...
Statistical inference for molecular shapes
TLDR
This thesis investigates the use of a computationally inexpensive algorithm which is based on the Procrustes tangent space which is specifically designed to accommodate temporal dependence of the configurations within each group and is hence more suitable for the DNA data.
Deep Recurrent Survival Analysis
TLDR
A Deep Recurrent Survival Analysis model is proposed which combines deep learning for conditional probability prediction at fine-grained level of the data, and survival analysis for tackling the censorship, and shows great advantages over the previous works on fitting various sophisticated data distributions.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 15 REFERENCES
P Values as Random Variables—Expected P Values
Abstract p values are extensively reported in practical hypothesis testing situations. Although carefully studied by Dempster and Schatzoff, the stochastic aspect of p values is often neglected. In…
The behavior of the P-value when the alternative hypothesis is true.
TLDR
Potential applications of the P-value distribution under the alternative hypothesis to the design, analysis, and interpretation of results of clinical trials are considered.
Sensitivity Comparisons among Tests of the General Linear Hypothesis
Abstract The expected significance level (ESL) of a test, proposed by Dempster and Schatzoff (4) as a criterion for comparing sensitivities of competing test statistics, is defined as the expected…
P Values: What They are and What They are Not
Abstract P values (or significance probabilities) have been used in place of hypothesis tests as a means of giving more information about the relationship between the data and the hypothesis than…
When is a p-Value a Good Measure of Evidence?
Blyth and Staudte (1993, 1995a) introduced the notion of a level-α weight of evidence for an alternative to a hypothesis; it is an estimator of the ideal power function which gives for each…
Hypothesis Estimates and Acceptability Profiles for 2 × 2 Contingency Tables
Abstract By estimating, rather than testing, hypotheses regarding the degree of dependence between the factors in 2 × 2 tables, the technical difficulties associated with small sample sizes are…
Expected Significance Level as a Sensitivity Index for Test Statistics
Abstract After a brief motivating discussion, of approaches to significance tests in Section 1, the concept of expected significance level (esl) is defined and its basic properties are presented in…
Testing Statistical Hypotheses
The General Decision Problem.- The Probability Background.- Uniformly Most Powerful Tests.- Unbiasedness: Theory and First Applications.- Unbiasedness: Applications to Normal Distributions.-…
1997),“HypothesisEstimation and Acceptability ProŽ les for 2£2 ContingencyTables,
  • Journalof the American Statistical Association,
  • 1997
1997),“The Behaviorof the p Value When the Alternative Hypothesis is True,
  • 1997
...
1
2
...