What is the difference between chi square and f test

Purpose: These two statistical procedures are used for different purposes. Distribution: The chi-square test is non parametric. Types of Tests: Chi square test: - For testing the population variance against a specified value - For testing goodness of fit of some probability distribution - Testing for independence of two attributes Contingency Tables F test - For testing equality of two variances from different populations - For testing equality of several means with technique of ANOVA.

Related Posts. Go to mobile version. In my model, the y j values I observe have the random component u j , Gaussian noise. If it were not for the random component in the y j process, I could estimate b by solving. I cannot make that calculation, because I do not observe u j ; all I know about u j is that it is normally distributed with mean 0.

So, I come up with another estimator of b, in particular. Understand that the true b itself is not random. The true b is just a fixed number such as 3. That turns out to be true for lots of estimators. However, no one really estimates models on asymptotic samples. Your sample has a finite number of observations. In some cases—such as linear regression—we do know the sampling distribution for finite samples and, in those cases, we can calculate a test with better coverage probabilities.

Thus the Wald test is usually discussed as a chi-squared test, because it is usually applied to problems where only the asymptotic sampling distribution is known. But if we do know the sampling distribution for finite samples, we certainly want to use that. More details on how and when the test command report chi-squared or F statistics can be found in the "Methods and formulas" section of [R] test.

The idea of testing hypotheses can be extended to many other situations that involve different parameters and use different test statistics. Whereas the standardized test statistics that appeared in earlier chapters followed either a normal or Student t-distribution, in this chapter the tests will involve two other very common and useful distributions, the chi-square and the F-distributions.

The chi-square distribution arises in tests of hypotheses concerning the independence of two random variables and concerning whether a discrete random variable follows a specified distribution.