Abstract
In many experimental situations, subjects are randomly allocated to treatment and control groups. Measurements are then made on the two groups to ascertain if there is in fact a statistically significant treatment effect. Exact calculation of the associated randomization distribution theoretically involves looking at all possible partitions of the original measurements into two appropriately-sized groups. Computing every possible partition is computationally wasteful, so our objective is to systematically enumerate partitions starting from the tail of the randomization distribution. A new enumeration scheme that only examines potentially worthwhile partitions is described, based on an underlying partial order. Numerical results show that the proposed method runs quickly compared to complete enumeration, and its effectiveness can be enhanced by use of certain pruning rules.
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References
A. V. Aho, J. E. Hopcroft and J. D. Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA, 1974.
P. Diaconis and S. Holmes, Gray codes Tor randomization procedures, Statistics and Computing 4 (1994), 287–302.
E. S. Edgington, Randomization Tests, 3rd ed., Marcel Dekker, New York, 1995.
R. A. Fisher, Design of Experiments, Oliver and Boyd, Edinburgh, 1935.
P. Good, Permutation Tests: A Practical Guide to Resampling Methods for Testing Hypotheses, 2nd ed., Springer-Verlag, New York, 2000.
R. P. Grimaldi, Discrete and Combinatorial Mathematics, 5th ed., Addison-Wesley, Reading, MA, 2004.
J. Ludbrook and H. Dudley, Why permutation tests are superior to t and F tests in biomedical research, The American Statistician 52 (1998), 127–132.
B. F. J. Manly, Randomization, Bootstrap and Monte Carlo Methods in Biology, 2nd ed., CRC Press, Boca Raton, FL, 1997.
A. W. Marshall and I. Olkin, Inequalities: Theory of Majorization and Its Applications, Academic Press, New York, 1979.
C. R. Mehta, N. R. Patel and L. J. Wei, Constructing exact significance tests with restricted randomization rules, Biometrika 75 (1988), 295–302
M. Pagano and D. Tritchler, On obtaining permutation distributions in polynomial time, Journal of the American Statistical Association 78 (1983), 435–440.
E. J. G. Pitman, Significance tests which may be applied to samples from any populations, Journal of the Royal Statistical Society, Series B, 4 (1937), 119–130.
StatXact software, Cytel Corp., Cambridge, MA. http: //www.cytel.com/
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Coffin, M.A., Jarvis, J.P., Shier, D.R. (2007). An Efficient Enumeration Algorithm for the Two-Sample Randomization Distribution. In: Baker, E.K., Joseph, A., Mehrotra, A., Trick, M.A. (eds) Extending the Horizons: Advances in Computing, Optimization, and Decision Technologies. Operations Research/Computer Science Interfaces Series, vol 37. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-48793-9_5
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DOI: https://doi.org/10.1007/978-0-387-48793-9_5
Publisher Name: Springer, Boston, MA
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