{smcl} {* 9aug2004}{...} {hline} help for {hi:circwwmardia} {hline} {title:Wheeler-Watson-Mardia test for circular data} {p 8 17 2} {cmd:circwwmardia} {it:varlist} [{cmd:if} {it:exp}] [{cmd:in} {it:range}] {cmd:, by(}{it:byvar}{cmd:)} {title:Description} {p 4 4 2} {cmd:circwwmardia} carries out a homogeneity test due to Wheeler and Watson (1964) and Mardia (1972) for circular variables in {it:varlist} with scales between 0 and 360 degrees. The values of each {it:varname} are grouped according to the {it:r} (2 or more) distinct values of {it:byvar}. The hypothesis under test is that the distributions so defined are identical. The test statistic is based on the circular ranks of the data, 2 * pi * rank / {it:n}, where rank varies from 1 to the number of values {it:n}. {p 4 4 2} The W_r statistic can be compared with a chi-square distribution with 2{it:r} - 2 degrees of freedom so long as there are 10 or more values in each group. Randomisation is recommended otherwise to get an estimate of the {it:P}-value. However, {cmd:circwwmardia} carries out the chi-square calculation regardless and the onus is on the user to identify examples with small group sizes and take appropriate action. A tabulation of group frequencies should help here. {p 4 4 2} Note that allowing a {it:varlist} is a convenience to allow many tests from a single command: the tests are separate and users searching for significant results are urged to consider carefully what they are doing. {title:Remarks} {p 4 4 2}This test is called the Mardia-Watson-Wheeler test by Batschelet (1981) and Kanji (1999). {title:Options} {p 4 8 2} {cmd:by()} indicating grouping is a required option. {title:Example} {p 4 4 2}{cmd:. circwwmardia wallasp, by(grade)} {title:Reference} {p 4 8 2}Batschelet, E. 1981. {it:Circular statistics in biology.} London: Academic Press. {p 4 8 2}Fisher, N.I. 1993. {it:Statistical analysis of circular data.} Cambridge: Cambridge University Press. {p 4 8 2}Kanji, G.K. 1999. {it:100 statistical tests.} London: Sage. {p 4 8 2}Mardia, K.V. 1972. A multi-sample uniform scores test on a circle and its parametric competitor. {it:Journal, Royal Statistical Society Series B} 34: 102-113. {p 4 8 2}Wheeler, S. and Watson, G.S. 1964. A distribution-free two-sample test on a circle. {it:Biometrika} 51: 256-257. {title:Author} {p 4 4 2}Nicholas J. Cox, University of Durham, U.K.{break} n.j.cox@durham.ac.uk {title:Acknowledgments} {p 4 4 2}Leora Vegosen found a bug. {title:Also see} {p 4 13 2} On-line: help for {help circtwosample}