# covariance between two observations belonging to the same block

#### mari_08

##### New Member
Hi, does anyone know how to find the
expression for the covariance between two observations belonging to the same
block for a balanced complete block planning?
(block has random effect and treatment has fixed effect).

#### Jake

$$y_{ij}=\mu+\theta_i+u_j+e_{ij}$$
where the $$\theta_i$$ are the treatment effects and the $$u_j$$ are the block effects.
$$\text{cov}(y_{1j}, y_{2j})=\text{cov}(\mu+\theta_1+u_j+e_{1j}, \mu+\theta_2+u_j+e_{2j})$$