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The information contained in multiple sibling pairs
Author(s) -
Hodge Susan E.,
Rao D. C.
Publication year - 1984
Publication title -
genetic epidemiology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.301
H-Index - 98
eISSN - 1098-2272
pISSN - 0741-0395
DOI - 10.1002/gepi.1370010203
Subject(s) - mathematics , binomial (polynomial) , combinatorics , logarithm , statistics , sibling , measure (data warehouse) , discrete mathematics , computer science , data mining , psychology , mathematical analysis , developmental psychology
In a sibship of size s , s(s − 1)/2 sib pairs can be formed, but these pairs are statistically dependent when s > 2. This study examines how much independent information is obtained when all possible pairs are used to evaluate the sharing of genes identical by descent. A logarithmic measure of information, Σp i log 2 p i [Shannon, 1948], is used. The basic unit of information is the binomial “bit,” or the amount of information in the toss of a fair coin. It is shown that a single independent sib pair contains 1.5 bits. The complete sibship contains a total of 2s−3 + (1/2) s−1 bits, or (2s−3 + (1/2) s−1 )/1.5 pair‐equivalents of information. The information is reduced if all sib genotypes do not occur with equal probability.