How do you find uniformly most powerful test?

A test in class C, with power function β(θ), is a uniformly most powerful (UMP) class C test if β(θ) ≥ β′(θ) for every θ ∈ Θ0c and every β′(θ) that is a power function of a test in class C.

What is meant by power of a test?

The power of a test is the probability of rejecting the null hypothesis when it is false; in other words, it is the probability of avoiding a type II error. The power may also be thought of as the likelihood that a particular study will detect a deviation from the null hypothesis given that one exists.

What is an unbiased test?

Page 1. STAT 801: Mathematical Statistics Unbiased Tests Definition: A test φ of Θ0 against Θ1 is unbiased level α if it has level α and, for every θ ∈ Θ1 we have π(θ) ≥ α . When testing a point null hypothesis like µ = µ0 this requires that the power function be minimized at.

Which t-test is most powerful?

t-Test for One Sample

The t -test is the most powerful parametric test for calculating the significance of a small sample mean.
The t -test is the most powerful parametric test for calculating the significance of a small sample mean.

What is power in hypothesis testing?

Power is the probability of rejecting the null hypothesis when in fact it is false. Power is the probability of making a correct decision (to reject the null hypothesis) when the null hypothesis is false. Power is the probability that a test of significance will pick up on an effect that is present.

What is a generalized likelihood ratio test?

the generalized likelihood ratio statistic is defined as. Λ = maxθ∈Ω0 lik(θ) maxθ∈Ω lik(θ) . In other words, Λ is the ratio of the values of the likelihood function evaluated at the MLE in the sub-model and at the MLE in the full-model. For large n, under any θ0 ∈ Ω0, −2 log Λ is approximately distributed as χ2.

Why do we use Neyman-Pearson Lemma?

The Neyman-Pearson Lemma is a way to find out if the hypothesis test you are using is the one with the greatest statistical power. The power of a hypothesis test is the probability that test correctly rejects the null hypothesis when the alternate hypothesis is true.