Editing Quantitative genetics (section)

====Applications (siblings)====
The most useful application here for genetical statistics is the ''correlation between half-sibs''. Recall that the correlation coefficient (''r'') is the ratio of the covariance to the variance [see section on "Associated attributes" for example]. Therefore, ''' r<sub>HS</sub> = cov(HS) / s<sup>2</sup><sub>all HS together</sub> ''' = ''' [{{sfrac|1|4}} s<sup>2</sup><sub>A</sub>  + {{sfrac|1|4}} s<sup>2</sup><sub>D</sub> ] / s<sup>2</sup><sub>P</sub> = {{sfrac|1|4}} H<sup>2</sup> '''.<ref>Note that texts that ignore the dominance component of cov(HS) erroneously suggest that r<sub>HS</sub> "approximates" ( {{sfrac|1|4}} h<sup>2</sup> ).</ref> The correlation between full-sibs is of little utility, being ''' r<sub>FS</sub> = cov(FS) / s<sup>2</sup><sub>all FS together</sub> ''' = ''' [{{sfrac|1|2}} s<sup>2</sup><sub>A</sub>  + {{sfrac|1|4}} s<sup>2</sup><sub>D</sub> ] / s<sup>2</sup><sub>P</sub> '''. The suggestion that it "approximates" (''{{sfrac|1|2}} h<sup>2</sup>'') is poor advice.

Of course, the correlations between siblings are of intrinsic interest in their own right, quite apart from any utility they may have for estimating heritabilities or genotypic variances.

It may be worth noting that '''[ cov(FS) − cov(HS)] = {{sfrac|1|4}} s<sup>2</sup><sub>A</sub> '''. Experiments consisting of FS and HS families could utilize this by using intra-class correlation to equate experiment variance components to these covariances [see section on "Coefficient of relationship as an intra-class correlation" for the rationale behind this].

The earlier comments regarding epistasis apply again here [see section on "Applications (Parent-offspring"].