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Wheeler-Watson-Mardia test for circular data

circwwmardiavarlist[ifexp] [inrange], by(byvar)

Description

circwwmardiacarries out a homogeneity test due to Wheeler and Watson (1964) and Mardia (1972) for circular variables invarlistwith scales between 0 and 360 degrees. The values of eachvarnameare grouped according to ther(2 or more) distinct values ofbyvar. 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 /n, where rank varies from 1 to the number of valuesn.The W_r statistic can be compared with a chi-square distribution with 2

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 theP-value. However,circwwmardiacarries 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.Note that allowing a

varlistis 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.

RemarksThis test is called the Mardia-Watson-Wheeler test by Batschelet (1981) and Kanji (1999).

Options

by()indicating grouping is a required option.

Example

. circwwmardia wallasp, by(grade)

ReferenceBatschelet, E. 1981.

Circular statistics in biology.London: Academic Press.Fisher, N.I. 1993.

Statistical analysis of circular data.Cambridge: Cambridge University Press.Kanji, G.K. 1999.

100 statistical tests.London: Sage.Mardia, K.V. 1972. A multi-sample uniform scores test on a circle and its parametric competitor.

Journal, Royal Statistical Society Series B34: 102-113.Wheeler, S. and Watson, G.S. 1964. A distribution-free two-sample test on a circle.

Biometrika51: 256-257.

AuthorNicholas J. Cox, University of Durham, U.K. n.j.cox@durham.ac.uk

AcknowledgmentsLeora Vegosen found a bug.

Also see