Wilcoxon-Mann-Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules
TLDR
This work collects many of the different perspectives to which a decision rule may be applied collected in one place, since each perspective allows a different interpretation of the associated p-value.Abstract:
In a mathematical approach to hypothesis tests, we start with a clearly defined set of hypotheses and choose the test with the best properties for those hypotheses. In practice, we often start with less precise hypotheses. For example, often a researcher wants to know which of two groups generally has the larger responses, and either a t-test or a Wilcoxon-Mann-Whitney (WMW) test could be acceptable. Although both t-tests and WMW tests are usually associated with quite different hypotheses, the decision rule and p-value from either test could be associated with many different sets of assumptions, which we call perspectives. It is useful to have many of the different perspectives to which a decision rule may be applied collected in one place, since each perspective allows a different interpretation of the associated p-value. Here we collect many such perspectives for the two-sample t-test, the WMW test and other related tests. We discuss validity and consistency under each perspective and discuss recommendations between the tests in light of these many different perspectives. Finally, we briefly discuss a decision rule for testing genetic neutrality where knowledge of the many perspectives is vital to the proper interpretation of the decision rule.read more
Citations
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Statistical method for testing the neutral mutation hypothesis by DNA polymorphism.
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A practical guide for using statistical tests to assess randomized algorithms in software engineering
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A Hitchhiker's guide to statistical tests for assessing randomized algorithms in software engineering
Andrea Arcuri,Lionel C. Briand +1 more
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Using the Student’s t-test with extremely small sample sizes
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References
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Individual Comparisons by Ranking Methods
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Journal Article
Statistical method for testing the neutral mutation hypothesis by DNA polymorphism.
TL;DR: It is suggested that the natural selection against large insertion/deletion is so weak that a large amount of variation is maintained in a population.
Journal ArticleDOI
Statistical method for testing the neutral mutation hypothesis by DNA polymorphism.
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Journal ArticleDOI
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