Question: What is difference between most powerful test and uniformly most powerful test?

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One test may be the most powerful one for a particular value of an unobservable parameter while a different test is the most powerful one for a different value of the parameter. A uniformly more powerful test remains the most powerful one regardless of the value of the parameters.

What does it mean to say that a test is uniformly most powerful?

A Uniformly Most Powerful (UMP) test has the most statistical power from the set of all possible alternate hypotheses of the same size α. It is also the region that gives a UMP test the largest (or equally largest) power function.

What do you mean by most powerful test?

In the theory of statistical hypotheses testing, the best test of all those intended for testing H0 against H1 and offering the same probability of an error of the first kind, or, equivalently, having the same significance level α, is the test that has the highest power. ...

Is the generalized likelihood ratio test uniformly most powerful?

For testing a one-sided hypothesis in a one-parameter family of distributions, it is shown that the generalized likelihood ratio (GLR) test coincides with the uniformly most powerful (UMP) test, assuming certain monotonicity properties for the likelihood function.

What is powerful critical region?

For testing a composite hypothesis, critical regions are deter- mined which are most powerful against a particular alternative at a given level of significance. Here a region is said to have level of significance e if the proba- bility of the region under the hypothesis tested is bounded above by e.

What is the critical value in statistics?

A critical value is the value of the test statistic which defines the upper and lower bounds of a confidence interval, or which defines the threshold of statistical significance in a statistical test.

What package is Lrtest?

Using R for Likelihood Ratio Tests. Before you begin: Download the package “lmtest” and call on that library in order to access the lrtest() function later.

Is Anova a likelihood ratio test?

The analysis of variance test is a likelihood ratio test. Because all of the basic ideas can be seen in the case of two groups, we begin with a development in this case that will lead to the F statistic.

What is a critical value on a graph?

A critical value is a line on a graph that splits the graph into sections. One or two of the sections is the “rejection region“; if your test value falls into that region, then you reject the null hypothesis. A one tailed test with the rejection in one tail.

What is meant by the critical value?

A critical value is the value of the test statistic which defines the upper and lower bounds of a confidence interval, or which defines the threshold of statistical significance in a statistical test.

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