Use of Ranks in One-Criterion Variance Analysis

Abstract Given C samples, with n i observations in the ith sample, a test of the hypothesis that the samples are from the same population may be made by ranking the observations from from 1 to Σn i (giving each observation in a group of ties the mean of the ranks tied for), finding the C sums of ranks, and computing a statistic H. Under the stated hypothesis, H is distributed approximately as χ2 (C – 1), unless the samples are too small, in which case special approximations or exact tables are provided. One of the most important applications of the test is in detecting differences among the population means. * * Based in part on research supported by the Office of Naval Research at the Statistical Research Center, University of Chicago. § Department of Horticulture, University of Wisconsin-Madison, Madison, WI, USACommunicated by Ramaswamy H. SarmaThis article was originally published with errors. This version has been corrected. Please see Erratum (http: //dx. doi. org/10. 1080/09599916. 2016. 1214438). DuPont Haskell Laboratory, TRP Toxicology Program, 1090 Elkton Road, Newark, DE, 19714, USA, 302-366-5207 gerald. l. kennedy@usa. dupont. comCollege of Veterinary Medicine, Chonnam National University, Gwangju, 500-757, South KoreaDuPont Haskell Laboratory for Health and Environmental Sciences, P. O. Box 50, 1090 Elkton Road, Newark, DE, 19714-0050, USA michael. p. delorme@usa. dupont. comDuPont de Nemours and Company, Haskell Laboratory for Health and Environmental Sciences, 1090 Elkton Road, Newark, DE, 19714, USAE. I. du Pont de Nemours and Company, Haskell Laboratory for Health and Environmental Sciences, P. O. Box 50, 1090 Elkton Road, Newark, DE 19714, USA david. p. kelly@usa. dupont. com * An invited review of Sidney Siegel, Nonparametric Statistics for the Behavioral Sciences. New York: McGraw-Hill Book Company, 1956. Pp. xvii, 312. 6. 50.