A Statistical Test used to determine if there are nonrandom associations between two Categorical
Variables. Let there exist two such variables and , with and observed states,
respectively. Now form an Matrix in which the entries represent the number of observations in
which and . Calculate the row and column sums and , respectively, and the total sum

of the Matrix. Then calculate the conditional Likelihood (

(which is a Hypergeometric Distribution). Now find all possible Matrices of Nonnegative Integers consistent with the row and column sums and . For each one, calculate the associated

The test is most commonly applied to a Matrices, and is computationally unwieldy for large or .

For an example application of the test, let be a journal, say either *Mathematics Magazine* or *Science*, and
let be the number of articles on the topics of mathematics and biology appearing in a given issue of one of these
journals. If *Mathematics Magazine* has five articles on math and one on biology, and *Science* has none on math
and four on biology, then the relevant matrix would be

Computing gives

and the other possible matrices and their s are

which indeed sum to 1, as required. The sum of -values less than or equal to is then 0.0476 which, because it is less than 0.05, is Significant. Therefore, in this case, there would be a statistically significant association between the journal and type of article appearing.

© 1996-9

1999-05-26