On 23 Jul 2001 14:22:58 -0700, [EMAIL PROTECTED] (Rich Strauss)
wrote:
> 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.
I'm not sure that I grasp what you are after, but - an idea.
If they are completely permutable, then "permute":
sort them by decreasing counts for row and for column.
This puts me in mind of certain alternatives to "random."
The set of counts on a margin should be ... Poisson?
The table can be drawn into quadrants or smaller sections,
so that the number of 1s in each can be tabulated, to make
ordinary contingency tables.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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