= Mean allele-sharing test for affected siblings
{title2=$Z=(\bar J-1)/\sqrt{1/(2n)}$}
For independent pairs of affected <full siblings> with unrelated, noninbred parents and a fully informative <genetic marker>, the no-linkage null gives shared <identity by descent> count $J\sim\operatorname{Bin}(2,1/2)$. Therefore $EJ=1$ and $\operatorname{Var}J=1/2$. An excess-sharing test uses the displayed approximately <standard normal> statistic and an upper-tail critical value. Pairs sharing family members are dependent, so their variance needs separate treatment. This targeted test differs from an omnibus test of all three sharing probabilities.
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