An Application of Information Theory to the Analysis of Contingency Tables, With a Table of 2n In n, n=I(I)IO,OOO

In t his p a per we pre~en t a number of useful tests for co nt in gency tables in coniul~ct i on wi th a useful t a bl e to assist in t he necessar y compu tat IOns. A co nsIstent a nd SImple approach based on t he notions of informat~on t heory is used in . dev~loping t ~le vari ous test procedures and t he results are analyzed III t he form of ana lysls-of-lI1formatIOn tables. Beginning wit h tests of h ypotheses for a one-way table, tes ts of h'ypotheses of. ?pecdied probabili t ies independence co ndi tional in dependence, h omogenClty of classlhcat lOns, sy m metr.", ;{nd in teraction ~.]'e developed or indi cated for cont ingency tables of .two, t hree, foul', a nd hi gher-order class ifi ca tions. Extension of t hese procedures to cert a ll1 tests for Markov chains is indi cated . Worked exampl es are g iven t lu'oughou t t he pape!'. A table of 2n In n for n= 1 ( I ) :10.000 is append ed fo r usc in co mp uta tion.

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