Hypothesis Significance Testing Research Articles

Bayesian Statistics: Why We All Should Be Bayesians

The purpose of this symposium is to introduce management researchers to the opportunities of Bayesian statistics for empirical research in the management sciences. We will outline the fundamental features of the Bayesian method without delving into the mathematical details. Instead, we will outline the conceptual differences and potential advantages of a Bayesian approach compared to traditional statistical analyses involving null- hypothesis significance tests. We will then introduce several illustrative examples from empirical management research that illustrates opportunities for the useful application of Bayesian data analysis and introduce participants on how to interpret the outcomes of Bayesian analyses for causal inference. Finally, we will discuss why in spite of strong arguments supporting the use of Bayesian statistics, the field of management research has been very reluctant considering Bayesian analysis as an alternative and how management scholars can support related methodological change efforts. The purpose of this symposium is to convince participants of the potential opportunities Bayesian methods can provide and to motivate organizational researchers to consider Bayesian statistics as an alternative in future research.

Simultaneous testing of multiple hypotheses using generalized p-values

In the context of simultaneously testing many hypotheses, Benjamini and Hochberg [1995. Controlling the false discovery rate: a practical and powerful approach to multiple testing. J. Roy. Statist. Soc. Ser. B (Methodological) 57, 289–300] propose a procedure that guarantees that the false discovery rate ( FDR) will be less than or equal to a specified value. Here, the FDR is the expected value of the ratio of the number of incorrectly rejected hypotheses and the total number of rejected hypotheses. To our knowledge, all of the existing research assumes that a usual p-value is available for each hypothesis. However, in circumstances when nuisance parameters are present, the usual p-values may not be free of the nuisance parameters. We develop a simultaneous testing procedure to control the FDR for the problem of simultaneously testing many Behrens–Fisher problems. Our multiple testing procedure, based on generalized p-values [Tsui, K.-W., Weerahandi, S., 1989. Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters. J. Amer. Statist. Assoc. 84(406), 602–607], is then illustrated with an application to data from a microarray experiment.

Distributional properties for the generalized p-value for the Behrens–Fisher problem

The generalized p-value method introduced by Tsui and Weerahandi [1989. Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters. J. Amer. Statist. Assoc. 84 (406), 602–607] has been successfully used to provide small sample solutions for many hypothesis testing problems when nuisance parameters are present. Simulation studies show that generalized p-values have similar distributional properties as ordinary p-values. It is desirable to study theoretical properties of generalized p-values. Given a sample d, let p ( d ) be the generalized p-value for the Behrens–Fisher problem of testing the difference of two independent normal distribution means with possibly unequal distributional variances, as given in Tsui and Weerahandi [1989. Generalized p-values in significance testing of hypotheses in the presence of nuisance parameters. J. Amer. Statist. Assoc. 84 (406), 602–607]. We derive a closed form expression to show that, for small samples, the probability P ( p ( d ) ⩽ r ) is approximately less than or equal to r, for 0 ⩽ r ⩽ 0.5 .

Testing equality of inverse Gaussian means under heterogeneity, based on generalized test variable

The inverse Gaussian (IG) distribution is an ideal candidate for modelling positive, right-skewed data due to the fact that its inference theory and methodology bear a striking resemblance to the normal theory and methods. For testing equality of several IG means under the assumption of equal scale parameters, there exists the ANORE (analysis of reciprocal) F test, which is analogous to the ANOVA F test for the normal distribution. In this article, the concept of generalized P -value, introduced by Tsui and Weerahandi [1989. Generalized P -values in significance testing of hypotheses in the presence of nuisance parameters. J. Amer. Statist. Assoc. 84, 602–607], is applied for testing equality of several IG means for the general cases without the assumption of homogeneity. Simulation results indicate that the proposed test has excellent type I error control under both heterogeneity and homogeneity, whereas the type I error probabilities of the ANORE test can be much larger than the nominal level under heterogeneity. The proposed procedure is illustrated using two examples.

Statistics review 3: hypothesis testing and P values.

The present review introduces the general philosophy behind hypothesis (significance) testing and calculation of P values. Guidelines for the interpretation of P values are also provided in the context of a published example, along with some of the common pitfalls. Examples of specific statistical tests will be covered in future reviews.

On the Behrens-Fisher Problem: A Review

The Behrens-Fisher problem arises when one seeks to make inferences about the means of two normal populations without assuming the variances are equal. This paper presents a review of fundamental concepts and applications used to address the Behrens-Fisher problem under fiducial, Bayesian, and frequentist approaches. Methods of approximations to the Behrens-Fisher distribution and a simple Bayesian framework for hypothesis testing are also discussed. Finally, a discussion is provided for the use of generalized p values in significance testing of hypotheses in the presence of nuisance parameters. It is shown that the generalized p values based on a frequentist probability for the Behrens-Fisher problem are numerically the same as those from the fiducial and Bayesian solutions. A table for tests of significance is also included.

Correction: Generalized p-Values in Significance Testing of Hypotheses in the Presence of Nuisance Parameters

Correction: Generalized p-Values in Significance Testing of Hypotheses in the Presence of Nuisance Parameters

Generalized p-Values in Significance Testing of Hypotheses in the Presence of Nuisance Parameters

Generalized p-Values in Significance Testing of Hypotheses in the Presence of Nuisance Parameters

On Statistical Testing

The statistical testing approaches of Hypothesis Testing (Fisher) and Significance Testing (Neyman-Pearson) are briefly reviewed. Highly related notions of alpha-values, P-values, and magnitude-of-effect are discussed. A statistical testing approach that is a hybrid of Hypothesis Testing and Significance Testing is then advanced. This approach takes into consideration the two decision-error probabilities as well as an alternative hypothesis characterization of interest.