Topic
Statistical hypothesis testing
About: Statistical hypothesis testing is a research topic. Over the lifetime, 19580 publications have been published within this topic receiving 1037815 citations. The topic is also known as: statistical hypothesis testing & confirmatory data analysis.
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Book•
01 Jan 1969
TL;DR: This work describes data -- A Single Variable, a single Variable: Associations between Two Quantitative Variables: Regression and Correlation, and Hypothesis Testing: General Principles and One--sample Tests for Means, Proportions, Counts and Rates.
Abstract: 1. Describing Data -- A Single Variable. 2. Probability, Populations and Samples. 3. Associations: Chance, Confounded or Causal?. 4. Confidence intervals: General principles Proportions, Means, Medians, Counts and Rates. 5. Hypothesis Testing: General Principles and One--sample Tests for Means, Proportions, Counts and Rates. 6. Epidemiological and Clinical Research Methods. 7. Confidence intervals and Hypothesis Tests: Two--group Comparisons. 8. Sample Size Determination. 9. Comparison of More than Two Independent Groups. 10. Associations between Two Quantitative Variables: Regression and Correlation. 11. Multivariate Analysis and the Control of Confounding!. 12. Bias and Measurement Error. Bibliography. Appendix A Computational Shortcuts. Appendix B Statistical Tables. Appendix C A "Cookbook" of Hypothesis Tests and Confidence Intervals. Appendix D World Medical Association Declaration of Helsinki
497 citations
TL;DR: This paper explores one such test applicable to any set of asymptotically normal test statistics and presents two examples and the relative merits of the proposed strategies.
Abstract: Treatment comparisons in randomized clinical trials usually involve several endpoints such that conventional significance testing can seriously inflate the overall Type I error rate. One option is to select a single primary endpoint for formal statistical inference, but this is not always feasible. Another approach is to apply Bonferroni correction (i.e., multiply each P-value by the total number of endpoints). Its conservatism for correlated endpoints is examined for multivariate normal data. A third approach is to derive an appropriate global test statistic and this paper explores one such test applicable to any set of asymptotically normal test statistics. Quantitative, binary, and survival endpoints are all considered within this general framework. Two examples are presented and the relative merits of the proposed strategies are discussed.
495 citations
TL;DR: In this article, the concept of implicit null hypothesis of a test is introduced to show that the effective acceptance region for some tests extends beyond the acceptance region corresponding to the null of interest, and so such tests can be inconsistent against fixed alternatives closely related to the nominal null and alternative.
Abstract: The encompassing principle is used to develop a testing framework which unifies the literature on non-nested testing, allowing analysis of the relationship between alternative tests and in particular enabling asymptotic and finite sample equivalences and identities to be established easily when they exist, as well as embracing nested hypothesis testing. The concept of the implicit null hypothesis of a test is introduced to show that the effective acceptance region for some tests extends beyond the acceptance region corresponding to the null of interest, and so such tests can be inconsistent against fixed alternatives closely related to the nominal null and alternative. The analysis is illustrated by an application to two non-nested linear regression models, and it is shown that the conventional F test, as well as all the one degree of freedom non-nested tests, has an encompassing interpretation, and that the F test is a "complete" parametric encompassing test.
494 citations
Posted Content•
TL;DR: In this paper, spectrum-sensing algorithms are proposed based on the sample covariance matrix calculated from a limited number of received signal samples, which do not need any information about the signal, channel, and noise power a priori.
Abstract: Spectrum sensing, i.e., detecting the presence of primary users in a licensed spectrum, is a fundamental problem in cognitive radio. Since the statistical covariances of received signal and noise are usually different, they can be used to differentiate the case where the primary user's signal is present from the case where there is only noise. In this paper, spectrum sensing algorithms are proposed based on the sample covariance matrix calculated from a limited number of received signal samples. Two test statistics are then extracted from the sample covariance matrix. A decision on the signal presence is made by comparing the two test statistics. Theoretical analysis for the proposed algorithms is given. Detection probability and associated threshold are found based on statistical theory. The methods do not need any information of the signal, the channel and noise power a priori. Also, no synchronization is needed. Simulations based on narrowband signals, captured digital television (DTV) signals and multiple antenna signals are presented to verify the methods.
494 citations