Fisher's inequality
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In combinatorial mathematics, Fisher's inequality, named after Ronald Fisher, is a necessary condition for the existence of a balanced incomplete block design satisfying certain prescribed conditions.
Fisher, a population geneticist and statistician, was concerned with the design of experiments studying the differences among several different varieties of plants, under each of a number of different growing conditions, called "blocks".
Let:
- v be the number of varieties of plants;
- b be the number of blocks.
It was required that:
- k different varieties are in each block, k < v; no variety occurs twice in any one block;
- any two varieties occur together in exactly λ blocks;
- each variety occurs in exactly r blocks.
Fisher's inequality states simply that
[edit] References
- R. A. Fisher, "An examination of the different possible solutions of a problem in incomplete blocks", Annals of Eugenics, volume 10, 1940, pages 52–75.
- R. C. Bose, "A Note on Fisher's Inequality for Balanced Incomplete Block Designs", Annals of Mathematical Statistics, 1949, pages 619–620.
