Hypothesis Testing:F Test

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F Test:

 F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis. In simpler terms F-Test is basically used to check the equality of two variances. F- Distribution on the other hand is drawn from the population and is used to check whether the two sample populations variance are homogenous or not.

F- test can be:

  1. Two-tailed – The two-tailed version tests against the alternative that the variances are not equal.

F Tset 1

  1. One-tailed- The one-tailed version only tests in one direction that is the variance from the first population is greater than or less than (but not both) the second population variance.

F test 2

f-table

F-test means the different between the samples.

 F test3

F_PDF

Several assumptions one must keep in mind, before using F-test:

  1. The population must ne normally distributed, as N increase the population tends to be normal
  2. Sample must be independent.

 

 

F-Test is also used check the overall significance of the Regression model.

F test4

i.e. there is no significant difference between the intercept only  model and the regression model calculated.

 

F test 5

i.e. at least one of the B’s is significantly different from 0.

If the P value for the F-test test is less than your significance level, you can reject the null-hypothesis and conclude that your model provides a better fit than the intercept-only model.

 

 

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