## What are the four assumptions for the chi-square tests?

The Four Assumptions of a Chi-Square Test

• Assumption 1: Both variables are categorical.
• Assumption 2: All observations are independent.
• Assumption 3: Cells in the contingency table are mutually exclusive.
• Assumption 4: Expected value of cells should be 5 or greater in at least 80% of cells.

## What is likelihood-ratio in chi-square test?

What is a Likelihood-Ratio Test? 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.

What is the difference between chi-square and likelihood-ratio?

Pearson Chi-Square and Likelihood Ratio Chi-Square The Pearson chi-square statistic (χ 2) involves the squared difference between the observed and the expected frequencies. The likelihood-ratio chi-square statistic (G 2) is based on the ratio of the observed to the expected frequencies.

What are the assumptions of chi-square goodness of fit test?

The chi-square goodness-of-fit test requires 2 assumptions2,3: independent observations; for 2 categories, each expected frequency Ei must be at least 5. For 3+ categories, each Ei must be at least 1 and no more than 20% of all Ei may be smaller than 5.

### What are the conditions for validity of chi square test?

For the chi-square approximation to be valid, the expected frequency should be at least 5. This test is not valid for small samples, and if some of the counts are less than five, you may need to combine some bins in the tails.

### How do you interpret the likelihood ratio test?

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 are the conditions for validity of chi-square test?