Say I have a binary data matrix for which both the rows (observations) and
columns (variables) are computely permutable. (In practice, about 5-20% of
the cells will contain 1's, and the remainder will contain 0's.) Assume
that the expected probability of a cell containing a '1' is identical for
all cells in the matrix. I'd like to be able to test this assumption by
measuring (and testing the significance of) the degree of 'nonrandomness'
of the 1's in the matrix.
If the rows and columns were fixed in sequence, then this would be an easy
problem involving spatial statistics, but the permutability seems to really
complicate things. I think that I can test the rows or columns separately
by comparing the row or column totals against a corresponding binomial
distribution using a goodness-of-fit test, but I can't get a handle on how
to do this for the entire matrix. I'd really appreciate ideas about this.
Thanks in advance.
Rich Strauss
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