# how to test interaction with anova?

In a two-ways anova we can decompose the total sum of square in its components.

SST=SSE+SSA+SSB+SSAB


It is a common notation in the field so it should be clear (let me know if it is not).

We then can obtain the related variance dividing each component for its degree of freedom.

We can test the hypothesis $H_0: \alpha_1=\alpha_2=...=\alpha_a=0$ using the F statistics. $F:=\dfrac{\hat\sigma_\alpha^2}{\hat\sigma_e^2}\sim F(a-1,ab(n-1))$.

Suppose now I would like to test the hypothesis:

$H_0^{interaction}$: there are no interaction between $\alpha$ and $\beta$

Can I test this hypothesis using $\hat\sigma_{\alpha\beta}^2=\dfrac{SSAB}{(a-1)(b-1)}$ and the F statistics $F= \dfrac{\hat\sigma_{\alpha\beta}^2}{\sigma_e^2}\sim F((a-1)(b-1),ab(n-1))$ ?

All the books and website report the first example and I did not find anything regarding the second.

• This should be a standard and easy question. Is it possible that no one is answering? Is maybe the question bad written? Mar 24, 2014 at 0:34

SST=SSE+SSA+SSB+SSAB