scholarly journals Interval-Based Hypothesis Testing and Its Applications to Economics and Finance

Econometrics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 21
Author(s):  
Jae H. Kim ◽  
Andrew P. Robinson
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Medical Science ◽  
Point Of View ◽  
Economic Time Series ◽  
New Era ◽  
Null Hypothesis Testing ◽  
Point Null Hypothesis ◽  
Economic Time ◽  
Linear Restrictions

This paper presents a brief review of interval-based hypothesis testing, widely used in bio-statistics, medical science, and psychology, namely, tests for minimum-effect, equivalence, and non-inferiority. We present the methods in the contexts of a one-sample t-test and a test for linear restrictions in a regression. We present applications in testing for market efficiency, validity of asset-pricing models, and persistence of economic time series. We argue that, from the point of view of economics and finance, interval-based hypothesis testing provides more sensible inferential outcomes than those based on point-null hypothesis. We propose that interval-based tests be routinely employed in empirical research in business, as an alternative to point null hypothesis testing, especially in the new era of big data.

Bayesian point null hypothesis testing via the posterior likelihood ratio

2005 ◽  
Vol 15 (3) ◽  
pp. 217-230 ◽  
Author(s):  
Murray Aitkin ◽  
Richard J. Boys ◽  
Tom Chadwick
Keyword(s):  
Hypothesis Testing ◽  
Likelihood Ratio ◽  
Null Hypothesis ◽  
Null Hypothesis Testing ◽  
Point Null Hypothesis

scholarly journals Conflicts in Bayesian Statistics Between Inference Based on Credible Intervals and Bayes Factors

2020 ◽  
Vol 18 (1) ◽  
pp. 2-27
Author(s):  
Miodrag M. Lovric
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Bayes Factor ◽  
Credible Interval ◽  
Test Point ◽  
Type I ◽  
Null Hypothesis Testing ◽  
Frequentist Statistics ◽  
Credible Intervals ◽  
Point Null Hypothesis

In frequentist statistics, point-null hypothesis testing based on significance tests and confidence intervals are harmonious procedures and lead to the same conclusion. This is not the case in the domain of the Bayesian framework. An inference made about the point-null hypothesis using Bayes factor may lead to an opposite conclusion if it is based on the Bayesian credible interval. Bayesian suggestions to test point-nulls using credible intervals are misleading and should be dismissed. A null hypothesized value may be outside a credible interval but supported by Bayes factor (a Type I conflict), or contrariwise, the null value may be inside a credible interval but not supported by the Bayes factor (Type II conflict). Two computer programs in R have been developed that confirm the existence of a countable infinite number of cases, for which Bayes credible intervals are not compatible with Bayesian hypothesis testing.

scholarly journals Asymptotic relative submajorization of multiple-state boxes

2021 ◽  
Vol 111 (4) ◽  
Author(s):  
Gergely Bunth ◽  
Péter Vrana
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Alternative Hypothesis ◽  
Standard Form ◽  
Point Of View ◽  
State Discrimination ◽  
Simple Alternative ◽  
Multiple State ◽  
Error Probabilities

AbstractPairs of states, or “boxes” are the basic objects in the resource theory of asymmetric distinguishability (Wang and Wilde in Phys Rev Res 1(3):033170, 2019. 10.1103/PhysRevResearch.1.033170), where free operations are arbitrary quantum channels that are applied to both states. From this point of view, hypothesis testing is seen as a process by which a standard form of distinguishability is distilled. Motivated by the more general problem of quantum state discrimination, we consider boxes of a fixed finite number of states and study an extension of the relative submajorization preorder to such objects. In this relation, a tuple of positive operators is greater than another if there is a completely positive trace nonincreasing map under which the image of the first tuple satisfies certain semidefinite constraints relative to the other one. This preorder characterizes error probabilities in the case of testing a composite null hypothesis against a simple alternative hypothesis, as well as certain error probabilities in state discrimination. We present a sufficient condition for the existence of catalytic transformations between boxes, and a characterization of an associated asymptotic preorder, both expressed in terms of sandwiched Rényi divergences. This characterization of the asymptotic preorder directly shows that the strong converse exponent for a composite null hypothesis is equal to the maximum of the corresponding exponents for the pairwise simple hypothesis testing tasks.

Impact of Biases in the False-Positive Rate on Null Hypothesis Testing

Epilepsy ◽  
2011 ◽  
pp. 241-248
Author(s):  
Ralph Andrzejak ◽  
Daniel Chicharro ◽  
Florian Mormann
Keyword(s):  
Hypothesis Testing ◽  
False Positive ◽  
Null Hypothesis ◽  
False Positive Rate ◽  
Null Hypothesis Testing ◽  
Positive Rate

Null-Hypothesis Testing with Graphs

2016 ◽  
pp. 13-18
Author(s):  
Ton J. Cleophas ◽  
Aeilko H. Zwinderman
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Null Hypothesis Testing

scholarly journals Do psychology students interpret null hypothesis significance testing critically?

2017 ◽  
Author(s):  
Ivan Flis
Keyword(s):  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Statistical Significance ◽  
Psychology Students ◽  
Significance Testing ◽  
Null Hypothesis Significance Testing ◽  
Graduate Studies ◽  
Null Hypothesis Testing ◽  
Level Of Understanding ◽  
Grade Average

The goal of the study was to descriptively analyze the understanding of null hypothesis significance testing among Croatian psychology students considering how it is usually understood in textbooks, which is subject to Bayesian and interpretative criticism. Also, the thesis represents a short overview of the discussions on the meaning of significance testing and how it is taught to students. There were 350 participants from undergraduate and graduate programs at five faculties in Croatia (Zagreb – Centre for Croatian Studies and Faculty of Humanities and Social Sciences, Rijeka, Zadar, Osijek). Another goal was to ascertain if the understanding of null hypothesis testing among psychology students can be predicted by their grades, attitudes and interests. The level of understanding of null hypothesis testing was measured by the Test of statistical significance misinterpretations (NHST test) (Oakes, 1986; Haller and Krauss, 2002). The attitudes toward null hypothesis significance testing were measured by a questionnaire that was constructed for this study. The grades were operationalized as the grade average of courses taken during undergraduate studies, and as a separate grade average of methodological courses taken during undergraduate and graduate studies. The students have shown limited understanding of null hypothesis testing – the percentage of correct answers in the NHST test was not higher than 56% for any of the six items. Croatian students have also shown less understanding on each item when compared to the German students in Haller and Krauss’s (2002) study. None of the variables – general grade average, average in the methodological courses, two variables measuring the attitude toward null hypothesis significance testing, failing at least one methodological course, and the variable of main interest in psychology – were predictive for the odds of answering the items in the NHST test correctly. The conclusion of the study is that education practices in teaching students the meaning and interpretation of null hypothesis significance testing have to be taken under consideration at Croatian psychology departments.

scholarly journals An introductory tutorial on Bayesian inference using a simple pedagogical tool

2017 ◽  
Author(s):  
Guillermo CAMPITELLI
Keyword(s):  
Probability Theory ◽  
Bayesian Inference ◽  
Hypothesis Testing ◽  
Null Hypothesis ◽  
Traditional Approach ◽  
Postgraduate Students ◽  
Data Table ◽  
Null Hypothesis Testing ◽  
Testing Approach ◽  
Hypothesis Testing Approach

This tutorial on Bayesian inference targets psychological researchers who are trained in the null hypothesis testing approach and use of SPSS software. There a number ofexcellent quality tutorials on Bayesian inference, but their problem is that, they assume mathematical knowledge that most psychological researchers do not possess. Thistutorial starts from the idea that Bayesian inference is not more difficult than the traditional approach, but before being introduced to probability theory notation is necessary for the newcomer to understand simple probability principles, which could be explained without mathematical formulas or probability notation. For this purpose in this tutorial I use a simple tool-the parameter-data table-to explain how probability theory can easily be used to make inferences in research. Then I compare the Bayesian and the null hypothesis testing approach using the same tool. Only after having introduced these principles I show the formulas and notations and explain how they relate to the parameter-data table. It is to be expected that this tutorial will increase the use of Bayesian inference by psychological researchers. Moreover, Bayesian researchers may use this tutorial to teach Bayesian inference to undergraduate or postgraduate students.

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