I am currently working through a book/class in quantitative genetics, and in Falconer and Mackay's Introduction to Quantitative Genetics, the following line stumped me: "The between-group component expresses the amount of variation that is common to members of the same group and can equally well be referred to as the covariance of members of the groups."
This is in reference to the calculation of the intra-class correlation coefficient $$t=\frac{\sigma_B^2}{\sigma_B^2+\sigma_W^2}$$ where $\sigma_B^2$ is the between-groups variance and $\sigma_W^2$ is the within-groups variance.
How exactly is the between-groups variance a covariance? I have tried to work through proving that $\sigma_B^2$ can be expressed as a covariance, but I have not been able to do so, and I'm also confused about what Falconer means by "covariance of members of the groups."
Thank you for any help you can give!
