Alternative hypothesis

Résumé

In statistical hypothesis testing, the alternative hypothesis is one of the proposed proposition in the hypothesis test. In general the goal of hypothesis test is to demonstrate that in the given condition, there is sufficient evidence supporting the credibility of alternative hypothesis instead of the exclusive proposition in the test (null hypothesis). It is usually consistent with the research hypothesis because it is constructed from literature review, previous studies, etc. However, the research hypothesis is sometimes consistent with the null hypothesis. In statistics, alternative hypothesis is often denoted as Ha or H1. Hypotheses are formulated to compare in a statistical hypothesis test. In the domain of inferential statistics two rival hypotheses can be compared by explanatory power and predictive power. Basic definition The alternative hypothesis and null hypothesis are types of conjectures used in statistical tests, which are formal methods of reaching con

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https://en.wikipedia.org/wiki/Alternative_hypothesis

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Advantages of Variance Stabilization

Stephan Morgenthaler, Robert Staudte

Variance stabilization is a simple device for normalizing a statistic. Even though its large sample properties are similar to those of studentizing, many simulation studies of confidence interval procedures show that variance stabilization works better for small samples. We investigated this question in the context of testing a null hypothesis involving a single parameter. We provide support for a measure of evidence for an alternative hypothesis that is simple to compute, calibrate and interpret. It has applications in most routine problems in statistics, and leads to more accurate confidence intervals, estimated power and hence sample size calculations than standard asymptotic methods. Such evidence is readily combined when obtained from different studies. Connections to other approaches to statistical evidence are described, with a notable link to Kullback–Leibler symmetrized divergence.

Wiley-Blackwell2012

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Evidence for Alternative Hypotheses

Stephan Morgenthaler, Robert Staudte

Most researchers want evidence for the direction of an effect, not evidence against a point null hypothesis. Such evidence is ideally on a scale that is easily interpretable, with an accompanying standard error. Further, the evidence from identical experiments should be repeatable, and evidence from independent experiments should be easily combined, such as required in meta-analysis. Such a measure of evidence exists and has been shown to be closely related to the Kullback-Leibler symmetrized distance between null and alternative hypotheses for exponential families. Here we provide more examples of the latter phenomenon, for distributions lying outside the class of exponential families, including the non-central chi-squared family with unknown non-centrality parameter.

Springer2012

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Evidence for Alternative Hypotheses

Stephan Morgenthaler, Robert Staudte

Most researchers want evidence for the direction of an effect, not evidence against a point null hypothesis. Such evidence is ideally on a scale that is easily in- terpretable, with an accompanying standard error. Further, the evidence from iden- tical experiments should be repeatable, and evidence from independent experiments should be easily combined, such as required in meta-analysis. Such a measure of evidence exists and has been shown to be closely related to the Kullback-Leibler symmetrized distance between null and alternative hypotheses for exponential fam- ilies. Here we provide more examples of the latter phenomenon, for distributions ly- ing outside the class of exponential families, including the non-central chi-squared family with unknown non-centrality parameter.

Springer2013

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