# F - test to compare two nested models [duplicate]

I want to fully understand how F test is used to compare two nested models. Every information I found about it, is only standard use i.e. to compare model with model containing no variables.

How I perceive it

Let's say I have $$\text{model}_1$$:

$$y = \beta_0+\beta_1x_1 + \beta_2x_2 + \beta_3x_3 + \beta_4x_4$$

And $$\text{model}_2$$:

$$y = \beta_0 + \beta_1x_1 + \beta_2x_2$$

I want to compare those two models using F test. The null hypothesis in this case would be that:

$$H_0: \beta_3 = \beta_4 = 0$$

and alternative

$$H_1: \beta_3 \neq 0 \;\lor \beta_4 \neq 0$$

Now let's say that I fixed significance level at 0.05. It means that when for example $$p-$$value equals $$0.2$$ we have no evidence to say that null hypothesis is not true. In other words we have no evidence to reject $$\text{model}_2$$.

Am I correct with my perceiving of this model?

• Does this answer your question? What are chunk tests? One common example of a chunk test that doesn’t compare to an intercept-only model is ANCOVA.
– Dave
Dec 10, 2021 at 14:12
• I would be very thankful if you could comment my justification, whether it makes sense or not.
– John
Dec 10, 2021 at 14:24
• What you propose is exactly a chunk test.
– Dave
Dec 10, 2021 at 14:46