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Description: Exposition of statistical hypothesis testing using the statistical decision theory of Abraham Wald, with some use of measure-theoretic probability. Importance: Made Wald's ideas accessible. Collected and organized many results of statistical theory that were scattered throughout journal articles, civilizing statistics.
Statistical hypothesis testing is a key technique of both frequentist inference and Bayesian inference, although the two types of inference have notable differences. Statistical hypothesis tests define a procedure that controls (fixes) the probability of incorrectly deciding that a default position (null hypothesis) is incorrect. The procedure ...
Statistical tests are used to test the fit between a hypothesis and the data. [1] [2] Choosing the right statistical test is not a trivial task. [1] The choice of the test depends on many properties of the research question. The vast majority of studies can be addressed by 30 of the 100 or so statistical tests in use. [3] [4] [5]
In statistics, hypotheses suggested by a given dataset, when tested with the same dataset that suggested them, are likely to be accepted even when they are not true.This is because circular reasoning (double dipping) would be involved: something seems true in the limited data set; therefore we hypothesize that it is true in general; therefore we wrongly test it on the same, limited data set ...
In simple terms, the essay states that scientists use hypothesis testing to determine whether scientific discoveries are significant. Statistical significance is formalized in terms of probability, with its p- value measure being reported in the scientific literature as a screening mechanism.
Exploring a forking decision-tree while analyzing data was at one point grouped with the multiple comparisons problem as an example of poor statistical method. However Gelman and Loken demonstrated [2] that this can happen implicitly by researchers aware of best practices who only make a single comparison and only evaluate their data once.
Test statistic is a quantity derived from the sample for statistical hypothesis testing. [1] A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test.
Neyman believed that hypothesis testing represented a generalization and improvement of significance testing. The rationale for their methods can be found in their collaborative papers. [10] Hypothesis testing involves considering multiple hypotheses and selecting one among them, akin to making a multiple-choice decision.