A network algorithm for the exact treatment of the 2xk contingency table
Abstract
A common statistical problem encountered in biomedical
research is to test the hypothesis that the parameters of k
binomial populations are all equal. An exact test of significance
of this hypothesis is possible in principle, the appropriate null
distribution being a normalized product of k binomial coefficients.
However, the problem of computing the tail area of this
distribution can be formidable since it requires the enumeration
of all sets of k binomial coefficients whose product is less than
a given constant. Existing algorithms, all of which rely on
explicit enumeration to generate feasible binomial coefficients soon become computationally infeasible. In this paper, we develop
a novel technique which drastically reduces the computational
effort needed to obtain the exact P-value. The problem is transformed
into one of identifying feasible paths through a directed
acyclic network by means of backwards induction and implicit
enumeration. The technique can be generalized for the exact
treatment of the RxC contingency table.
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