# is there interaction effect in RCBD with a single observation per cell ?

#### Jesmin

##### New Member
The statistical model for a Randomized Complete Block Design (RCBD) with a single observation per cell is:
$$y_{ij}=\mu+\tau_{i}+\beta_{j}+\epsilon_{ij};\quad i=1,\ldots ,a, \quad j=1,\ldots, b,$$where $$y_{ij}$$ is a random variable that represents the response obtained on the $$i$$th treatment of the $$j$$th block.
If I consider alcohol as treatment and smoke as block, the following contingency table looks like a RCBD with single observation per cell .(1) If this has an interaction effect then why is the interaction effect term not considered in the statistical model for RCBD with single observation per cell?

$$\quad\quad\text{Alcohol}$$
$$\begin{array}{c|lr} \text{Smoke} & \text{Yes} & \text{No} \\ \hline \text{Yes} & 12 & 8 \\ \text{No} & 6 & 4\\ \end{array}$$
(2)What are the interaction effects here? (3)How many interactions are in here?
Additionally, (4)is there Interaction Effect in CRD model?
(5)When does interaction effect occur?
It would be very kind if you do not give the wikipedia source for interaction effect.