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:
“You see, I am alive, I am alive
I stand in good relation to the earth
I stand in good relation to the gods
I stand in good relation to all that is beautiful
I stand in good relation to the daughter of Tsen-tainte
You see, I am alive, I am alive”
—N. Scott Momaday (b. 1934)
“Only in a house where one has learnt to be lonely does one have this solicitude for things. One’s relation to them, the daily seeing or touching, begins to become love, and to lay one open to pain.”
—Elizabeth Bowen (1899–1973)
“I describe family values as responsibility towards others, increase of tolerance, compromise, support, flexibility. And essentially the things I call the silent song of life—the continuous process of mutual accommodation without which life is impossible.”
—Salvador Minuchin (20th century)
“Information networks straddle the world. Nothing remains concealed. But the sheer volume of information dissolves the information. We are unable to take it all in.”
—Günther Grass (b. 1927)