A major improvement to the Network Algorithm for Fisher's Exact Test in 2×c contingency tables

  • Authors:

  • F. Requena;N. Martín Ciudad

  • Affiliations:

  • Department of Statistics and O.R., University of Granada, 18071 Granada, Spain;Department of Mathematics, University of Extremadura, 10004 Cáceres, Spain

  • Venue:
  • Computational Statistics & Data Analysis
  • Year:
  • 2006

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Abstract

Based on the Network Algorithm proposed by Mehta and Patel for Fisher's Exact Test on 2xc contingency tables, the relations between maximum subpath lengths are studied. A recurrence relation between maximum subpath lengths is obtained and an ordering of the maximum path lengths is established. Based on these results, some modifications in the Network Algorithm for 2xc tables are proposed. These modifications produce a drastic reduction in computation time which in some cases is higher than 99.5% compared to StatXact-5. Moreover, and with purely practical objectives, a grouping in intervals of subpath lengths of the Network Algorithm is proposed which enable us to obtain the p-value with a limited number of exact figures which is more than sufficient in practice, while with a drastic reduction in the amount of memory required and additional reductions in computational time. The proposed modifications are valid for any 2xc contingency table, and are compatible with other improvements already proposed for the Network Algorithm, and especially with the Hybrid Algorithm of Mehta and Patel.