Exact and Approximate Distributions for the Wilcoxon Statistic with Ties

Kenneth H. Davis; R. E. Folsom; F. Ivy Carroll; Phillip C. Cooley; Lyle M. Retzlaff; Michael F. Weeks; H. Koo; Herbert H. Seltzman; E. Pellizzari; Deborah W. McFadden; Roger D. Austin; Martin B. Lee; Judith T. Lynch; Debra M. Fleischmann; Carol Place; Stephen D. Cooper; Rick L. Williams; Lillie B. Barber; Doris J. Rouse; Ivey A. McDaniel; Charlotte O. Scheper; Paul Kizakevich; Donna M. Jewell; Marion E. Deerhake; Cora B. Parker; Eugene P. Brantly; Phyllis D. Elkins; Patricia A. Cunningham; Robert S. Truesdale; Sara C. Wheeless; Robert M. Bray; Cynthia A. Salmons; Gary B. Howe; Coleen M. Northeim; Susan K. Myers; Gordon M. Cressman; Josephine A. Mauskopf; Tim J. Gabel; Luis Arturo Crouch; Celia D. Keller; Lisa E. Packer; Pamela B. Lamb; Keith White Little; Nathaniel F. Rodman; M. Owen; James P. Hayes; Daniel L. Winfield; Deborah A. Gibbs; Janice E. Kelly-Reid; Wayne G. Winstead; Cindy O. McClintock; Terrence K. Pierson; Johnny R. Albritton; Sherry L. Black; Jeffrey B. Coburn; Joe B. Simpson; Ed E. Rickman; James T. Hanley; R. Suresh; Barbara L. Kroner; K. Heller; James C. Blake; Barri B. Burrus; Anthony C. Clayton; Donna S. Womack; S. Mascarella; Scott A. Guthrie; Sheryl C. Cates; Albert D. Bethke; Suson F. VonLehmden; Kathryn L. Dowd; Daniel J. Pratt; Lisa J. McQuay; Matthew A. Koch; Jonathan T. Ennis; Robert A. Zerbonia; Nick L. Kinsey; Susan H. Kinsey; Christopher P. Carson; J. Newsome; S. Keesling; James A. O'Rourke; Kathryn R. Batts; Craig R. Hollingsworth; Priya Suresh; Joseph Wendell Wilson; Vorapranee Wickelgren; E. Andrew Jessup; Diana S. Goss; Sheri E. Fehnel; Gayle S. Bieler; Donna P. Coleman; R. Crawford; Jeanne Ann Snodgrass; Nellie I. Hansen; Michelle Lang; Deirdre M. Mladsi; Gary A. Zarkin; Rachel A. Caspar; Carol L. Woodell; SY Lehman

Exact and Approximate Distributions for the Wilcoxon Statistic with Ties

Lehman, SY. (1961). Exact and Approximate Distributions for the Wilcoxon Statistic with Ties. Journal of the American Statistical Association, 56(294), 293-298.

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Abstract

The exact distribution of the Wilcoxon statistic was calculated for five specific cases where both samples contained five observations, some of which were tied. The five specific cases were obtained from an actual experiment. The exact distributions for each of these five cases are compared with some approximations at points near 1, 5, and 10 per cent. Critical values and associated probabilities have been calculated for the exact and approximate distributions