Relation To Mutual Information
For analysis of contingency tables the value of G can also be expressed in terms of mutual information.
Let
- , and
Then G can be expressed in several alternative forms:
where the entropy of a discrete random variable is defined as
and where
is the mutual information between the row vector and the column vector of the contingency table.
It can also be shown that the inverse document frequency weighting commonly used for text retrieval is an approximation of G applicable when the row sum for the query is much smaller than the row sum for the remainder of the corpus. Similarly, the result of Bayesian inference applied to a choice of single multinomial distribution for all rows of the contingency table taken together versus the more general alternative of a separate multinomial per row produces results very similar to the G statistic.
Read more about this topic: G-test
Famous quotes containing the words relation to, relation, mutual and/or information:
“The psychoanalysis of individual human beings, however, teaches us with quite special insistence that the god of each of them is formed in the likeness of his father, that his personal relation to God depends on his relation to his father in the flesh and oscillates and changes along with that relation, and that at bottom God is nothing other than an exalted father.”
—Sigmund Freud (1856–1939)
“The proper study of mankind is man in his relation to his deity.”
—D.H. (David Herbert)
“We call it a Society; and go about professing openly the totalest separation, isolation. Our life is not a mutual helpfulness; but rather, cloaked under due laws-of-war, named “fair competition” and so forth, it is a mutual hostility.”
—Thomas Carlyle (1795–1881)
“Theories of child development and guidelines for parents are not cast in stone. They are constantly changing and adapting to new information and new pressures. There is no “right” way, just as there are no magic incantations that will always painlessly resolve a child’s problems.”
—Lawrence Kutner (20th century)