## What does the likelihood ratio test tell us?

The likelihood ratio is a method for assessing evidence regarding two simple statistical hypotheses. Its interpretation is simple – for example, a value of 10 means that the first hypothesis is 10 times as strongly supported by the data as the second.

**What can you conclude from likelihood ratio test?**

In statistics, the likelihood-ratio test assesses the goodness of fit of two competing statistical models based on the ratio of their likelihoods, specifically one found by maximization over the entire parameter space and another found after imposing some constraint.

**What is the formula for likelihood ratio test?**

The idea behind the general likelihood ratio test can be explained as follows: We first find the likelihoods corresponding to the most likely values of θ in S0 and S1 respectively. That is, we find l0=max{L(x1,x2,⋯,xn;θ):θ∈S0},l=max{L(x1,x2,⋯,xn;θ):θ∈S}.

### How do you read the results of the goodness-of-fit test?

In order to interpret a goodness-of-fit test, it’s important for statisticians to establish an alpha level, such as the p-value for the chi-square test. The p-value refers to the probability of getting results close to extremes of the observed results. This assumes that the null hypothesis is correct.

**What is a significant likelihood ratio?**

A relatively high likelihood ratio of 10 or greater will result in a large and significant increase in the probability of a disease, given a positive test. A LR of 5 will moderately increase the probability of a disease, given a positive test.

**What is the null hypothesis of likelihood ratio test?**

The null hypothesis of the test states that the smaller model provides as good a fit for the data as the larger model. If the null hypothesis is rejected, then the alternative, larger model provides a significant improvement over the smaller model.

#### Are likelihood ratio tests always the most powerful tests?

The simplest testing situation is that of testing a simple hypothesis against a simple alternative. Here the Neyman-Pearson Lemma completely vindicates the LR-test, which always provides the most powerful test.

**Which of the following test is based on likelihood ratio?**

The Likelihood-Ratio test (sometimes called the likelihood-ratio chi-squared test) is a hypothesis test that helps you choose the “best” model between two nested models. “Nested models” means that one is a special case of the other.

**Is likelihood ratio the same as chi square test?**

There are other, for example the likelihood-ratio chi-square (“Likelihood ratio” in the output) is an alternative to the Pearson chi-square. It is based on maximum-likelihood theory. For large samples it is identical to Pearson χ2. It is recommended especially for small samples.

## What is a good p-value for a fit?

You should get p-value = 0.5578.)