A Note on the Subdividsion of χ 2 into Components

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Abstract
In an ( r x s) frequency table with observed frequencies aij and expected frequencies apij, where a =[image]> consider the matrix of [image] standardized variables, Xij -[long dash][plus or minus][long dash][long dash][long dash][long dash][plus or minus][long dash][center dot] The result 3 sppir of premultiplying this matrix by a Helmert matrix constructed from the row marginal values and postmultiplying by the transpose of the Helmert column matrix is an (r x s) matrix with zeroes in the 1st row and in the 1st column, while every other element is the value of X for a particular fourfold table related to the original (r x s) table.
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