By The Mathematical Association of America
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Extra info for American Mathematical Monthly, volume 107, number 7, August-September 2000
For tables in three or more dimensions, for example, the hypothesis of interest may not be as simple as independence of the individual dimensions, and the constraints may involve several overlapping two-dimensional arrays of totals to be matched. , in a table with dimensions for gender and for site of cancer. The fact that computer-aided enumeration is not often used for problems of this sort highlights the point that in statistics "computer-intensive" means something more subtle than just very-highspeed plodding.
To mathematics, statistics offers not only the example of an outward looking culture, but also entree to new problems ripe for mathematical study. To statistics, mathematics offers not only the safe harbor of organizational strength, but intellectual anchorage as well: mathematical understanding is an essential part of what distinguishes statistical thinking from most of the rest of information technology. Increased cooperation between mathematical and statistical professional associations can lead the societies, their members, and their disciplines in healthier directions.
12). Diaconis and Sturmfels analyze such a table for 82 descendants of Queen Victoria. Compute row and column sums 0i+ and o+j and the grand total 0++, and use these to find the expected counts under the assumption of independence, e ij = 0i+O+JO++. (Oij - eij )2 /e ij • X2 is a measure of how far the observed values fall from what we would expect if birth and death months were independent. The p-value is the proportion p of tables, among all those with the same row and column sums, for which the value of X2 equals or exceeds the value computed from the data.