Editing Heritability (section)

=====Intraclass correlations=====
Consider the experiment above. We have two groups of progeny we can compare. The first is comparing the various progeny for an individual sire (called ''within sire group''). The variance will include terms for genetic variance (since they did not all get the same genotype) and environmental variance. This is thought of as an ''error'' term.

The second group of progeny are comparisons of means of half sibs with each other (called ''among sire group''). In addition to the [[Errors and residuals in statistics|error term]] as in the within sire groups, we have an addition term due to the differences among different means of half sibs. The intraclass correlation is
:<math>\mathrm{corr}(z,z') = \mathrm{corr}(\mu + \frac{1}{2}g + e, \mu + \frac{1}{2}g + e') = \frac{1}{4}V_g</math> ,
since environmental effects are independent of each other.