For pedigrees with a specific mixture of relatives, for example, two sibs and one uncle, the correlation matrix consists of identical sub-blocks: R=(1r1r2000.r11r2000.r2r21000.0001r1r2.000r11r2.000r2r21........) where r1 is the correlation coefficient between two sibs, and r2 is that between a sib and the uncle. It can be shown that the sample size reduction is (7)α=33+2r1+4r2=11+2r¯ where the averaged correlation r̄ = (1/3)r1 + (2/3)r2 is defined in such a way that we can assume all relatives were similar and any two relatives have a correlation coefficient of r̄. The similar derivation can be generalized to any combination of relatives.
