= Solution
Put $a=\sigma^2(1-\rho)$ and $c=\sigma^2\rho$. The tree and orchard residual <mean squares in ANOVA> have <expectations> $a$ and $a+30c$. Equating these to the observed values gives the \b[<method-of-moments variance component estimates>]
$$
\boxed{\widehat a=180,\qquad \widehat c=\frac{240-180}{30}=2.}
$$
In particular $\widehat\sigma^2=\widehat a+\widehat c=182$ and the estimated <intraclass correlation coefficient> is $\widehat\rho=2/182=1/91$. These are point estimates from the current experiment, rather than guaranteed variance values for the next season.
Back to article page
